CA2100359C - Mixed resolution, n-dimensional object space - Google Patents

Abstract

Object spaces which mechanize higher order relationships between attributes which describe a particular problem domain. An abstract object description defined by a set of attributes and their corresponding values is transformed into a mixed-resolution, N-dimensional object space. The mixed-resolution, N-dimensional object space represents a mechanized, logically encoded expression of attribute relationships that can be visualized. The method and apparatus interleave the frame to generate an object descriptor and generate from the frame and the object descriptor, encoded names of spatial locations for each of the N dimensions of the mixed-resolution, N-dimensional, object space, conforming to a primary form of a reflected binary code. A virtual image of the N-dimensional, object space is generated from the dimensional-spatial locations and resolution-spatial locations, and attribute values corresponding to a region of the virtual image may be selected for display.

Description

MIXED-RESOLUTION. N-DIMENSIONAL OBJECT
SPACE METHOD AND APPARATUS
BACKGROUND OF ACHE INVENTION
This invention relates to an apparatus and method for transforming an object description into mixed-resolution, N-dimensional object spaces. This invention also relates to an apparatus acid method for visualizing mixed-resolution, N-dimensional object spaces by projecting a bit-interleaved object descript:or onto a plane. More particularly, this invention relates to an apparatus and method for encoding attribute name: corresponding to spatial locations with a novel k-ary reflected code.
DESCRIPTION OF THE PRIOR ART
In a survey of research directions related to visualization methods, the Microelectronics and Computer Consortium (MCC~) characterized the field of abstract visualization ass a mapping of logical object relations into visual space "...so that inferences drawn from the visual representation can be carried back into the abstract domain." For applications like exploring high-dimensional multivariate data "...visualization of concrete things is not as important as visualization of abstract entities." In such applications "...the problem of what to represent and how to deliver the representation are the key, while photorealism is. not as important."
A significant class of problems related to abstract visualization have solutions which are not arithmetic in nature. Furthermore, the explanation of a particular result is as important. to an appropriate solution as the result itself. Ideally, the method employed for solving such problems should enable abstract visualization of the problem-solving process itself. The simplification of Boolean function expressions is a particularly well-known example of such problems. By constructing truth tables in which all possible values are tabulated for a circuit, the designer is ob7liged to consider all possible inputs, thereby eliminating eri,ors due to certain input conditions being overlooked.
Early approaches to devising a mechanical procedure for improving circuit design included a "chart method" developed by the Harvard University Computation Laboratory, which was further developed by Maurice Karnaugh in "The Map Method of Synthesis of Combinational Logic Circuits," AIEE
Transactions, Fart I, Vol. 72, November 1953, pp. 593-599.
Karnaugh describes a method for mapping abstract representationsc of circuit inputs into visual space. The Karnaugh map, often called a k-map, is a widely known technique for visualizing logical expressions based on a two-valued Boolean algebra. Entries representing circuit inputs correspond to a position in a k-map derived from visualizing ths~ codes as points in a binary n-space. The k-map is a two dimensional representation of this space mapped onto the Carte~;ian plane by labeling each axis with a binary Gray code. Inferences drawn from this visual representation of logic expre~~sions usually result in a reduction of the canonical expression. It has long been known the Karnaugh's graphical method of representing all possible combinations of N switching variables on a plane breaks down for problems with a large number of switching variables.
A well-know aspect common to all Gray codes is that consecutive cod.ewords differ in only one quantum interval, that is, one bit position in the case of binary Gray codes.
A Gray code is said to cycle if its first and last codewords differ in only one quantum interval, otherwise it describes a path. Each consecutive codeword in a binary Gray code can be represented by the bit position that changes. Given an initial codeword and a transition sequence the entire set of codewords can b~e generated. U.S. Pat. No. 2,632,058 issued to Frank Gray distinguishes between a primary form and secondary variants of the reflected binary code:
Because this code in its primary form may be built up from the conventional binary code by sort of a reflection process and because other forms may in turn be built up from the primary form in similar fashion, l:he code in question, which has as yet no recognized name, is designated in this specification and in the claims as the reflected binary code.
Some forms of the reflected binary code offer special advantages oven- others for particular applications.
FIGS. lA-7.E show a prior art method of unfolding a binary 3-cube onto a plane as a k-map, described by Clare in Designing Logic: Svstem Using State Machines, 1973, McGraw-Hill, N1', pp. 14-15.
FIG. 2 is a prior art representation of binary n-cubes as k-maps, showing a 0-cube k-map 200, a 1-cube k-map 201, a 2-cube k-map 202, a 2-cube k-map 203, a 3-cube k-map 204, and a 4-cube k-map 205. The 2-cube k-maps 202, 203 are different representations for a two-variable k-map shown by Karnaugh in they article referenced above. Such alternate spatial representations are inconsistent with each other.
Furthermore, region identifiers A 206, B 207, and C 208 in the 3-cube k-map 204 of FIG. 2 are located in a manner inconsistent with the diagram of the 2-cube k-map 202.
FIG. 3A shows a four-variable Karnaugh map encoded by labeling each axis with a binary Gray code. Map cells 300 of FIG. 3A correspond to the grid cells 301 of FIG. 3B. The labeling method. of FIG. 3B is a simplification of the method of FIG. 3A. Grid cells 301 in FIG. 3B are distinguished by region identifiers 302. Grid cells 301 in FIG. 3B within a particular region 302 have a logical value of one for the bit position in. corresponding map cell 300 names of FIG. 3A.
FIGS. 4A-4B are a prior art method of visualizing the binary 5-cube and the binary 6-cube as k-maps. Clare, in the reference cited above, shows the 5-cube 400 and the 6-cube 402 copied and translated to the right 401 and downward 403, respectively.
FIG. 5 shows a device proposed by Karnaugh, to visualize the synthesis of a network of six variables:
,._ w 21 00359 [ The thrE~e-dimensional cube] ...consists of four 6-inch plE~xiglass sheets supported at 1-1/2-inch intervals by rods.... In using it we employ movable markers.... The extension to seven variables is probably best accomplished by placing two cubes side by side.... Eight variables can be handled with a set of four cubes, and nine variables require eight cubes. In the latter case it is convenient to make them so as to stack easily into two layers of four each. Beyond nine variables, the mental gymnastics required for synthesis will, in general, be formidable.
The application of k-maps for problems of more than four variables has been described in the literature as tedious; therefore, the k-map's utility is generally limited to the introducaion of ideas about logic circuits and their synthesis. An article written by J.P. Roth and entitled, "The Synthesis of Switching Systems I.," Transactions of the American Mathematical Society, Vol. 88, No. 2, July 1958, pp. 301-327, describes an alternate topological representation of Boolean functions called the cubic notation. Although Roth's approach is an improvement over Karnaugh in the: mechanization of Boolean functions, visualization of problems of more that a few variables is not achievable. Gardner states in his book, Loaic Machines and Diaarams, U~niv. of Chicago Press, 1982, p. 135, "There is now a large literature on Karnaugh maps and various geometrical, tabular, or algebraic methods of minimizing logic statements and their corresponding circuitry, but no completely satisfactory systematic procedure has yet been found."
An article by Liu an Fu, "Cellwork, Its Network Duals, and Some Applications -- Three-Dimensional Karnaugh Map and Its Virtual Planar Representation," Information Science, Vol. 24, 1981, pp. 93-109, is representative various attempts to generalize k-map methods to other disciplines.

_ X100350 The "virtual planar representation" of a three-dimensional k-map is used 'to study "cell-work topology" from a network point of view. Other prior art abstract visualization methods include mapping of high-dimensional multivariate functions, preventing a two-dimensional view of a function of many variables. In an article by Patrick et. al., "Mapping Multidimensional Space to One dimension for Computer Outpui~ Display," IEEE Transactions on Computers, Vol. C-17, No. 10, 1968, p. 949, the following problem is presented:
Consider i:he problem of displaying a real-valued function i:(xl, x2 ..., x[n]) of [n) - 1, it is clear how f(x[n]) can be processed for display on a two-dimensional screen; but if [n] > 1, the required ~>rocessing is not as obvious.
Patrick's approach to displaying a two-dimensional view of N-dimensioned funr_tions for n > 1 establishes a one-to-one correspondence between the N-dimensional domain if "f"
is bounded, than is, statically predetermined.
Prior art methods cited above primarily are concerned with the visual. representation of logical objects; however, the prior art also teaches methods for the logical representation of visual objects. Srihari in his article, "Representation of Three-Dimensional Images," Computinct Surveys, Vol. 13, No. 4, December 1981, pp. 401 & 405, describes symmetric recursive indexing as a method of partitioning a volume:
Images that are produced by sensing objects through a form of radiant energy, for example, ...are inherently continuous. Computer representation of 3D images requires a sampling of the volume to extract a discrete set of volumes.... The cubic space is subdivided into eight subcubes (octants) of equal volume. Each of these octants will either be homogeneous (e. g., uniform attenuation) or have some nonuniformity.
The heterogeneous octants are further divided into ~1 0035 9 suboctants. This procedure is repeated as long as necessary until we obtain blocks (possibly single voxels) of uniform properties.
Other prier art methods seek to control the logical representation and visual expression of object relationships. U.S. Patent No. 4,721,952 entitled, "Apparatus and Process for Graphically Representing Three-Dimensional Objects in Two Dimensions", issued to Huber describes a process for the perspective representation of objects on the screen of a numerically controlled machine tool. The objE~ct is resolved into a series of sections (slices) which are represented successively to produce a visual image oi° the object. Huber's invention claims an improvement of ...a process for controlling a display device to represent a three-dimensional object such as a workpiece, wherein the representation is based upon data commands stored in a computing device such as a computer.
As machines and process operations become more specialized, controllers that are capable of adapting to changes due to unforeseen application requirements or further specialization become necessary. Federico and Webster in U.S. Patent No. 4,475,156, entitled "Virtual Machine Control.," teach that "...a totally hardware controller to ~~rovide these features is often prohibitive, inflexible, and. costly." Problems with prior art controls include a lack of appropriate modularity and a lack of sufficient mechanisms to support appropriate modularity in the firmware. Other prior art controls require a detailed knowledge of the operation of the control kernel for usage.
Further problems with prior art controllers include a general lack of appropriate mechanisms for accomplishing the specialized objectives.
Heath in an article "The Hypercube: A Tutorial Overview," Hypercube Multiprocessors 1986, SIAM, Philadelphia, 1986, pp. 7-l0, teaches:

...in a hypercube (also variously called the binary N-cube, cosmic cube, homogeneous ensemble machine, etc.), 2N processors are consecutively numbered (or tagged) by binary integers (e.g., bit strings of length N) from 0 through 2n-1. Each processor is connected to all of the other processors whose binary tags differ from its own by exactly one bit. Topologically, this arrangement places processors at the vertices (corners) of an N-dimensional cube. In practice, the actua:L layout of the processors is a linear arrangement in a card cage or a planar arrangement on a prini~ed circuit board; the cube connections are made by wires, conducting layers, or a backplane"
FIGS. 6A-EiD are diagrams of a binary 6-cube encoded in accordance with prior art n-cube replication methods. Seitz in the article, "The Cosmic Cube," Communications of the ACM, Vo. 28, No. 1, January 1985, p. 22, describes 64 computers "...c:onnected by a network of communication channels in they plan of a binary 6-cube." The interconnection pattern of FIG. 6A is similar to that used by Seitz. Each node of FIG. 6B is linked by arcs to six other nodes.
FIGS. 10A-~lOB show a diagram of a four-dimensional hypercube, called a binary 4-cube. Each element of FIG. 10A
is referred to as a node 1000. The dimensions of FIG. 10A
are represented as a link 1001 connecting nodes 1000. The binary 4-cube is shown partitioned 1004 in FIG. lOB as two subspaces: subspace OCBA 1002 and subspace 1CBA 1003.
Hypercubes of arbitrary dimension can be made using a linear arrangement with connecting wires (FIG. 2). The cube of each dimension is obtained by replicating the one of next lower dimension, then connecting corresponding nodes.
The node names resulting from such hypercube interconnection schemes correspond to prior art two-dimensional recursive indexing methods, similar to the method described by Srihari _g_ in his article referenced above. Recursive indexing has been independently discovered by practitioners in diverse fields. Recursive indexing is not extendable to generalized N-dimensional resolution, where the resolution of each dimension is permitted to differ. A hypercube, when projected onto a plane using the method of recursive indexing is routinely referred to in prior art literature as a binary n-curve. This binary space partitioning procedure, however, actually describes an k-ary 2-cube, that is, a two-dimensional splice with k=2 bits of resolution for each dimension, who;~e elements are interconnected as a binary n-cube. Such topological ambiguity frustrates the mechanized visualization of higher-order, N-dimensional spaces.
Marihugh <~nd Anderson in their article, "The H Diagram:
A Graphical Approach to Logic Design", IEEE Transactions on Computers, Vol~. C-20, No. 20, October 1971, pp. 1192-1196, describe a geometric model which is intended to visually aid the analysis oi: binary functions. Their method is based on geometrically transforming the coordinates of a hypercube onto a plane. The H diagram method of visualizing the coordinates of a binary hypercube by transforming its coordinates onto a plane is not extendable to generalized N-dimensional space, where the resolution of each dimension is permitted to differ. Sivilotti in a paper, "A Dunamically Configurable Architecture For Prototyping Analog Circuits,"
in Advanced Research in VLSI, Proceedings of the Fifth MIT
Conference, 1988, MIT, p. 248, describes a binary H-tree hierarchical interconnect structure used to physically place leaf cells and crossbar interconnect switches on a grid with parallel decoders around the chip perimeter as a simpler alternative to a hierarchical decoder. Sivilotti also refers to indirect element name (switch address) transformation as the "...mapping between hierarchical interconnect matrix coordinates and flat Cartesian coordinates performed by the embedding compiler."
Colorimetry is a perceptual science which studies and attempts to quantify how the human visual system perceives _. ,..,:

_g_ color. This study of perception has resulted in various systems of colder representation, each intending to reduce problems associated with subjective color selection and reproduction. Six color systems often used in association with computer-:related information display include: the Munsell color ;system, HSV hexcone, HSL double hexcone, HSL
double cone, H;SL cylinder, and the RGB color cube.
The Munse:ll color system is described in an article by Meyer and Greenburg entitled, "Perceptual Color Spaces for l0 Computer Graph:ics," Computer Graphics, Vol. 14, No. 3, 1980, pp. 254-261, in relation to reproduction of color on a television monitor:
Deciding which Munsell renovation colors are reproducible on the monitor is difficult because the monitor and Munsell color gamuts (regions of realizablca color) have irregular shapes and their intersection is not well defined.
A.R. Simth in "Color Gamut Transformation Pairs," ACM
Computer Graphics (SIGGRAPH 78), VOL. 12, No. 3, pp. 12-19, describes the HSV (hue, saturation, and value) hexcone, which used a neutral axis from black to white. At the white point is a hexagon with vertices representing the colors at the vertices oi: the color cube.
D.F. Rogers in his book, Procedural Elements for Comt~uter Graphics, McGraw-Hill, NY, 1985, pp. 403-404, describes the HSL (hue, saturation, and lightness) double hexcone. This color system is similar to the NSV hexone with the exception that the full colors are represented with a value of 0.5 instead of being equal to white.
Joblove and Greenburg in their paper, "Color Spaces for Computer Graphi.cs," ACM Computer Graphics (SIGGRAPH 78), Vol. 12, No. 3, pp. 20-25, describe a variant of the HSL
double hexcone called the HSL double cone, whose cross-section is circular rather than hexagonal. In the same paper Jobleove and Greenburg describe the HSL cylinder, which expands the base and top of the double cone into black and white circles.
y -lU-Each of tile color representation systems mentioned above use some variant of a radial coordinate system to compute the location of a particular color sensation in their respective color spaces. Meyer and Greenburg in their article referenced above make the following observation:
...A problem inherent with any color organization such as The Munsell Book of Color that uses cylindric<~1 coordinate system is that the spacing between colors changes as two radial lines are followed outwards from the center of the cylinder.
...The idea is to define a color system in which an equal perceptual distance separates all of the colors. For example, the grayscale of the system should provide a smooth transition betwEaen black white... such an ideal systeam has yet to be found....
The RGB color cube represents the red, green, and blue monitor primaries as orthogonal axes. The colors that are displayable on the monitor are within the cube from (0, 0, O) to (~_, 1, 1). The neutral axis is a (diagonal) line from the black point (0, 0, 0) to the white point (1, 1, 1). Then color cube has been referred to in the literature as ~~ "natural" coordinate system in the sense that the three color components are mapped into a orthogonal coordinate system in the same fashion as three-dimensional geometry.
Color representations used in computer graphics are closely linked to both the color reproduction device and to a method of color selection. Uniform color spaces can be used to decide at what level of resolution the color information should be encoded. Two-dimensional data plots, for example, require uniform color spaces to select color scales. In the: prior art color systems referred to above the pigment gamut used to derive color spaces is generally smaller than th.e gamut of a color monitor and the pigment gamut is irregular. Accordingly to Meyer and Greenburg, . ..:

referenced above (p. 260), "...this makes it difficult to find color scales that incorporate the most brilliant monitor colors."
Richard P~srez, in his book Electronic Display Devices, TAB Professional and Reference Books, Blue Ridge Summit, PA, 1988, pp. 69-1;Z9, presents a detailed description of CRT
electronic display device technology. The number of colors that can be produced on a CRT display, for example, depends on the number of steps of gray level obtainable for each phosphor (compounds that emit light when bombarded by electrons). IiE the electron gun can be stepped over four levels (2 bits;l, the resulting palette has sixty-four colors. Some ;systems currently available are capable of 1024 steps of dray from each gun (10 bits). Systems capable of 256 steps oi: gray from each gun (8 bits) are more common, however. Such systems can produce a palette of over 16 million unique combinations. The eye is not capable of discriminating many of the small changes in color so that the viewable palette has many fewer colors. In a chapter entitled, "Color Displays and Color Science," Color and the Computer, Academic Press, Boston, 1987, p. 13, the section entitled, "Visual Display Descriptive Systems," Gerald Murch makes the following observation:
...Under optimal conditions, a total of about three million discriminable colors can be produced in a visual display; that is, colors that are recognizax~ly different when placed adjacent to one another. The palette shrinks to about 7000 when colors located at different screen areas must be immediately recognized as different from one another. ...The obtainable level of saturation for additively-mixed colors can be extended by increasing the number of primaries.... The color television industry experimented with four or five primaries but concluded that the improvement in color did not offset the increase in the expenses of production of such receivers. Visual displays followed 'the lead.
In U.S. Portent No. 4,887,878 entitled, "Optical Modulation Dev:ice," Robinson and Sanford teach: "To convey information on an optical wave, some property of that wave has to be modu:Lated or changed in accordance with the information and adopted coding system." Well known in the art are device:a which rely on various electro-optical, thermo-optical,, or acousto-optical properties of materials for modulating electromagnetic carrier waves in the optical region of the spectrum.
Separation requires couplers, like the one shown in FIG. 7, that are sensitive to wavelength, so light 700 can be directed along different paths 702-706. A diffraction grating 701 is used to spread out a spectrum of light from the input fiber- 700 and focus specific wavelengths in that spectrum onto i-.'ibers in a linear array 702-706. Conversely, if the outputs were reversed, the grating 701 would combine the five wavelengths 702-706 into a single output at the top fiber 700.
In the article "Integrated Optics," in Optics Source Book, S. Parker, ed., McGraw-Hill, NY, 1988, pp. 287-291, Streifer describes light transmission in planar waveguides based on "...di.electric structures that confine the propagating light to a region with one or two very small dimensions, on the order of the optical wavelength." FIG. 8 shows prior art. prism input coupling 800 and grating output coupling 803 of an external light beam 801 into a thin-film waveguide 802. By reversing the incident 801 and output 804 beam directions the roles of the prism 800 and grating 803 couplers are interchanged. Streifer further describes optical integrated circuit (oIC) switching and modulation applications:
Both lithium niobate and gallium arsenide belong to the family of electro-optically active crystals. When an electric field is applied to these materials, their refractive indices are modified. ...If the waveguides are suitably designed, the applications of specific small voltages to the electrodes will cause the transfer of optical power from one waveguide to its neighbor wraith high efficiency and little residual power in 'the initial guide.
FIG. 9 shows a prior art "4 by 4" directional coupled switching netw~~rk in which each of four input optical signals 900 may be switched to any one of four outputs ports 904. Conducting electrodes 901 deposited on the surface of a crystalline substrate 902 parallel to two closely-spaced waveguides 903. Such an optical integrated circuit serves to interconneci~ four computers through optical fibers.
Switches are in effect modulators. Prior art modulation is a process in which information is encoded onto an optical wave. According to Streifer, referenced above, "...pulse modulation results simply by interrupting or connecting a light wave in <i manner intelligible to a receiver. By transferring light into or out of a waveguide in response to an electric signal at a switching electrode, the output optical wave becomes modulated; that is the switch acts as a modulator."
A long felt need exists for a systematic method which distinguishes between the essentials of a problem and the formulation of a solution. The separation of problem space formulation and formulation of solution strategies which navigate problem space relationships requires a mechanized method which can be visualized. The invention disclosed herein permits a problem characterized by attributes comprising an object description to be transformed into a mixed-resolution, N-dimensional object space of encoded attribute relationships which can be visualized.
Accordingly, the foregoing discussion of the prior art is representative of the problem of representing mixed-resolution, N-dimensional objects and spaces.

OBJECTS OF THE INVENTION
An object of an aspect of the invention is to mechanize the generation of mixed-resolution, N-dimensional object spaces related to complex problems with a large number of variables, where the number of variables is not limited by the method.
An additional object of an aspect of the invention is to mechanize the visualization of mixed-resolution, N-dimensional object spaces related to complex problems with a large number of variables, where the number of variables is not limited by the method.
Another object of an aspect of the invention is to represent logical objects visually such as logical color specifications and visual color sensations.
A further object of an aspect of the invention is concurrent control of a plurality of views of one or more object spaces.
A still further object of an aspect of the invention is an apparatus described herein as the kernel of a modular object description system.
An object of an aspect of the invention is to dynamically control the logical representation and the visual expression of object descriptions in an object space.
Another object of an aspect of the invention is concurrent control of a plurality of transition paths in an object space.
SU1~ARY OF THE INVENTION
Object spaces representing very simple object descriptions can be formed manually and, in a few instances, mentally; however, description spaces of actual systems quickly exceed the feasible limits of mental visualization and manual procedures.
The present invention, therefore, mechanizes higher order relationships between attributes which describe a particular problem domain. The novel method and apparatus disclosed herein transforms an abstract object description defined by a set of attributes and their corresponding values into a mixed-resolution, N-dimensional object space. The mixed-resolution, N-dimensional object space represents a mechanized, logically encoded expression of attribute relationships that can be visualized.
Therefore, an illustrative embodiment of the present invention is an apparatus that is part virtual machine, providing an appropriate level of application independence and device transparency.
According to one aspect of the present invention there is provided a process for generating and visualizing mixed-resolution, N-dimensional object spaces using a computing device such as a computer is provided. The computing device may be of the type comprising means for inputting, storing and processing frames, data, and commands; means for generating a logical representation of the N-dimensional object space in response to the stored frames, data, and commands; display logic for generating a virtual image representing the N-dimensional object space in response to the stored frames, data, and commands; and display means for displaying a visible representation of logical regions selected from the virtual image.
In the case of user-specified attributes the process starts with the user inputting to the computing device the attributes and the computing device generating from the attributes a frame for the N-dimensional object space.
The bits of the frame are then interleaved to generate and object descriptor. From the frame and the object descriptor, the computing device generates dimensional-spatial location in the N-dimensional object space. The computing device also generates object selectors which correspond to interleaved frame data fox each dimensional-spatial location in the N-dimensional object space. The computing device generates a virtual image of the N-dimensional object space from the dimensional-spatial locations and the object selectors. A user or an application procedure selects a logical region of the virtual image. The process may further include the step of displaying the selected logical region of the virtual image of the N-dimensional object space on the display means.
The process further includes having the computing device generate, from the frame and the object descriptor, resolution-spatial locations for resolution levels of each of the N-dimensions for a mixed-resolution, N-dimensional object space. Subsequently an object selector is generated from the frame data for each spatial location in the mixed-resolution, N-dimensional object space. A
virtual image of the N-dimensional object space is generated from the resolution-spatial locations and the dimensional-spatial locations. A user or an application procedure selects a logical region of the virtual image.
The process may include using the computing device for displaying the selected logical region of the virtual image of the mixed-resolution, N-dimensional object space on the display means.
According to another aspect of the present invention there is provided a process for dynamically configuring a logical architecture for using a digital-computing device and for controlling fundamental operations to transform said digital-computing device from a fixed-radix mode of operation imposed by physical architecture of said digital-computing device to a mixed-radix mode of operation, comprising the steps, using said digital computing device, of:
a. encoding with said digital-computing device a logical name for each attribute describing a problem space to form an object frame for organizing a contiguous sequence of coded attribute names, each object frame having a logical one bit representing a dimension of an N-dimensional object space and having a logical zero bit representing a degree of resolution for a range of possible values for a particular attribute for a dimension of an N-dimensional object space;
b. interleaving bits of said object frame to generate an object descriptor, said object descriptor representing a name format for referencing storage locations of said digital-computing device and for controlling an order of the storage locations, the storage locations configured as spatial locations of said N-dimensional, object space;
c. configuring, from said object frame and said object descriptor, the spatial locations as dimensional-spatial locations of said N-dimensional, object space;
d. configuring, from said object frame and said object descriptor, the spatial locations as resolution-spatial locations for a mixed-resolution, N-dimensional, object space; and whereby, said mixed-radix mode of operating said computing device mechanizes methods of selecting mixed-radix expressions for elements, paths and relations of said mixed-resolution, N-dimensional object spaces.
According to yet another aspect of the present invention there is provided an apparatus for generation and visualization of mixed-resolution, N-dimensional object spaces. In the case of user object description, a -17a-user specifies a particular set of attributes defining dimensions and resolution levels. In the case of an application-driven object description, an application procedure specifies a particular set of attributes defining dimensions and resolution levels. In the case of sensed physical phenomena, such as electromagnetic signals, the apparatus transforms analog signal into a digital form which specifies a particular set of attributes defining dimensions and resolution levels.
The apparatus includes means for generating a frame from the specified attributes for the N-dimensional object space. Means for interleaving bits generates an object descriptor which corresponds to interleaved frame data.
Using the frame and the object descriptor the present invention uses means for generating dimensional-spatial locations of the N-dimensional object space. The frame data is used to generate an object selector for each dimensional-spatial location in the N-dimensional object space. The dimensional-spatial locations and the object selectors are used to generate a virtual image of the N-dimensional object space. A logical region or relation of the virtual image is selected. Display means may display the selected logical region of the virtual image of the N-dimensional object space.
The apparatus of the present invention additionally may include means for generating resolution-spatial locations for resolution levels of each of the N
dimensions for a mixed-resolution, N-dimensional object space using the frame and the object descriptor. The frame and object descriptor are used to generate an object selector for each resolution-spatial location in the mixed-resolution, N-dimensional object space. Using the frame, frame data, the resolution-spatial locations, and the dimensional-spatial locations, a virtual image of the -17b-N-dimensional object space is generated, and means is provided for selecting a logical region of the virtual image. Frame data for a particular object are used to generate a single object selector to reference a particular location in the mixed-resolution, N-dimensional object space.
According to still yet another aspect of the present invention there is provided an object description system for controlling the logical manipulation of data storage locations of a memory of a digital-computing device configured as at least one mixed-resolution, N-dimensional object space, wherein the object description system is described as a special purpose computing device having a mixed-radix logical architecture, said digital computing device, including a processor for accessing said data storage locations; signal communication means, operatively coupled to said processor means, for communicating control signals, address signals, and data signals to and from said processor means; an input coupled to said processor means by said signal communication means for receiving an object description; and, a memory coupled to said processor by said signal communication means for storing data, said object description system comprising:
object means, operatively coupled to said processor means by said signal communication means, including, frame means operatively coupled to said processor means by said signal communication means for generating said N-dimensional, object space, said frame means including, means for interleaving the bits of coded attribute names of an object frame to generate an object descriptor and for interleaving the bits of a particular instance of frame data to generate an object selector; and at least one register for storing said object frame for controlling the order of the interleaving of bits of -17c-said object frame by said interleaving means and for controlling the order of the interleaving of bits of said frame data by said interleaving means;
whereby, said data storage locations of said apparatus, when configured as mixed-resolution, N-dimensional object spaces, are logically addressed and manipulated by fundamental data storage operations.
An illustrative example of the present invention relates to color perception, color specification, and color spaces; and, in particular, to the production and visualization of uniform color spaces. A color naming method for controlling RGB values by indirectly specifying RGB signal voltages and visualizing the resulting distribution of perceivable colors in the RGB color space is presented in accordance with the method disclosed herein.
The color naming method described below in accordance with the present invention, is the process by which the name of a particular color experience is encoded for both the purpose of uniform color selection and the purpose of reproduction on an electronic display. The system of color representation used to form a uniform color space is to name colors in terms. of the additive relations of red, green and blue. The resultant RGB system specifies a trio of values ranging from 0% to 100 for each of the three primaries.
The color relationships that result form a cube. The RGB
system is a simple and direct approach to the problem of color description that incorporates the principles of additive color mixture; that is, the user specifies color directly in terms of the electrical activity that the specification will induce. In the reference by Murch, cited in the Description of the Prior Art, the difficulty of specifying additive color relationships is discussed:
...For individuals understanding the nuances of additive color mixture, the RGB System is comfortable, ... Even for those individuals with a clear understanding of additive color, the location and proper specification of colors within the interior of the cube, when some real value for all three primaries is required, proves difficult.
Imagine selection of a medium brown, for example.
The greatest difficulty is encountered when a color of ~~roper hue and brightness has been located and a shift in saturation is desired.
Such a shift would require a disproportionate change in all three values.
The novel method for generating, controlling and visualizing they distribution of perceivable colors in a RGB
color space, is described below. A primary aspect of the method disclosed herein is that the encoded pattern of bits which specifie:c (physical) RGB signal voltages also (logically) names a particular location in a displayable, uniform color space. Another aspect of the method disclosed herein is that the logical naming method of the invention illustrated by the color space example may be generalized to include a novel. method for optical modulation.
Additional. objects and advantages of the invention are set forth in pert in the description which follows, and in part are obvious from the description, or may be learned by :, _19_ 2100359 practice of ths~ invention. The objects and advantages of the invention also may be realized and attained by means of the instrumenta~lities and combinations particularly pointed out in the appended claims.
BRIEF DESCRIPTION OF THE DRAWINGS
The accomxranying drawings, which are incorporated in and constitute a part of the specification, illustrate preferred embodiments of the invention, and together with the description, serve to explain the principles of the to invention.
FIGS. 1A-7.E are diagrams of the binary 3-cube "unfolded" in e~ccordance with prior art methods;
FIG. 2 is a prior art representation of n-cubes as k-maps;
FIGS. 3A-?~B are a prior art representations of a four-variable P;arnaugh map;
FIGS. 4A-4~B are a prior art representation of a binary 5-cube and a binary 6-cube;
FIG. 5 shows a prior art device for extending the binary 6-cube t:o visualize higher order spaces;
FIGS. 6A-END are diagrams of a binary 6-cube encoded in accordance with prior art two-dimensional recursive indexing methods;
FIG. 7 shows prior art distribution of multiple wavelengths to separate fibers;
FIG. 8 shows prior art prism input coupling and grating output coupling of an external light beam into a thin-film waveguide;
FIG. 9 shows a prior art "4 by 4" directional coupler switch;
FIGS. l0A-~lOB are prior art diagrams of a four-dimensional hypercube;
FIG. 11 stows an intuitive procedure for generating spaces, spatial. element linkage, and a binary 4-cube projected onto a plane;
:: .

FIG. 12 is: a flow chart for the case of user-specified attributes which shows the process of the invention;
FIG. 13 shows expressions of a zero-cube;
FIG. 14 stows expressions of a one-dimensional object space;
FIG. 15 snows expressions of a two-dimensional, object space;
FIG. 16 snows expressions of a three-dimensional, object space;
FIG. 17 snows expressions of a four-dimensional, object space;
FIG. 18 stows expressions of a five-dimensional, object space;
FIG. 19 snows expressions of a six-dimensional, object space;
FIGS. 20A--20C are diagrams of a k-ary one-dimensional, object space;
FIG. 21A-21B are diagrams of 4-dimensional object spaces;
FIGS. 22A--228 are diagrams of a mixed-resolution, 4-dimensional object space derived from a binary, 4-dimensional object space;
FIG. 23 is a functional diagram of the object description process;
FIGS. 24A--248 show block diagrams of physical modules in an object description system;
FIG. 25 snows a functional module of an object description system;
FIGS. 26A--26H show the object space configurations formed by the 46-bit frame logic module;
FIGS. 27A--27C are diagrams of an eight-element RGB
color space;
FIGS. 28A-~28C are diagrams of a sixty-four-element RGB
color space;
FIG. 29A-29C show relationships between three-dimensional splices with different resolutions;
,~.A

- .".".
,..., FIG. 30 shows a graph of matching curves for 445 nm, 535 nm, and 630 nm control sources; and FIGS. 31A--31C show how percentages of spectral intensities over a range of values for each primary are determined in ~~ sixty-four element RGB color space.

Reference will now be made in detail to the present preferred embodiments of the invention, examples of which are illustrated in the accompanying drawings, wherein like reference numerals indicate like elements throughout the several views.
Given the intellectual process of system description, the present invention mechanizes a novel representation of that system's description. Object descriptions have meaning, that :Ls, they refer to or describe some system with certain physical or conceptual properties.
For color graphics, the objects may be particular color sensations described in terms of attributes such as: red;
green; blue; which define a color space. For optical communications,, the objects may be a particular coherent light source dsascribed in terms of its lightwave components, which define a signal space. The significant aspect of system descripi~ion is that the actual description is one selected from ~~ set possible descriptions. The invention is a general apparatus and method, designed to operate for each possible problEam selection, not just the one which will actually be chosen since this is unknown at the time of design.
The process of the present invention enables representing sE~nsed physical phenomena logically and logical objects visual:Ly. Most of the prior art methods referred to in Description of the Prior Art sought to visualize some aspect of a problem-solving process by mapping logical object descripi:ions onto visual space.
Most prior art methods assume visual space to be Euclidean or Cartesian metric spaces, in that, logical objects are mapped onto the real line, the plane, or cubic space. An objE~ct~s location in visual space, accordingly, is metrically determined relative to one or more coordinate axes. Herein lies the principal departure of the present invention from these prior art methods: the method and apparatus of the present invention define a novel form of object name space, such that, component relationships in this object space are logically named, rather than metrically labsaled. Other prior art methods referred to in Description of the Prior Art sought to visualize some aspect of the problem--solving process by recursive indexing on some variant thereoi'. Such prior art methods, however, determine locations by decomposing a domain.
The proce:~s which transforms an object description into an object name space is directed by object descriptions in accordance with the method of the present invention.
Object expressions are represented by a unique binary-coded name which direactly correspond to a position in the object space of the present invention. The present invention is first described as the method of reflecting binary N-dimensional object spaces. Then the present invention is described as the generalized method of reflecting mixed-resolution, N-dimensional object spaces. The process of the present invention results in an interleaving of the N-dimensions. Bit interleaving is often employed in structuring data, as well as part of the data representation itself. Samet ~:n his book, The Design and Analysis of Spatial Data Structures, 1989, Addison Wesley, NY, p. 109, states:
...bit interleaving makes it possible to balance a data base of multidimensional point data dynamically. It leads to logarithmic insertion, deletion and search algorithms. It does have drawbacks, however. First, and most serious, is that bit interleaving is not performed efficiently on genera7_ computers. Its complexity depends on ,.. , the total number of bits in the keys.
Because efficient interleaving of binary-coded data is essential to the visualization process described herein, an embodiment of t:he invention is described as an apparatus with a virtual component. Before describing an embodiment of the invention in detail the following terminology is defined 1. Object: a structural and/or behavioral expression of some real-world or imaginary phenomenon.
2. Object descriptor: a collection of interleaved, logically encoded attributes which describes a schema for a particular kind of object expression describing named attribute relat:ionships in an object space.
3. Object selector: a collection of interleaved, logically encocled attribute values associated with the descriptor of a specific object expression, defining the name of a locat:ion in the object space which names a specific attribute.
4. Object: space: an expression of bit-interleaved names for the set of possible relationships between a plurality of ataributes which describe some real-world or imaginary phenomenon.
5. Object name: a logically encoded representation of an object selecaor in an object space.
6. Visual space: a graphical expression for a logical space of object: names projected onto a plane.

7. Dimension: each attribute of an object descriptor which corresponds to a dimension in both object space and visual space.

8. Dimensional resolution: the range of values associated with each attribute of an object descriptor.

9. Quanti~:ation: assigning a logical name to a range of values.

10. Object: Frame: describes the format of an object descriptor, where each attribute (dimension) is denoted by a "1" followed b5r "Os" representing the additional bits of .",,:_ .

resolution.

11. Frame Data: a collection of concatenated attribute values corresponding to their respective bit positions in an object frame.
The present invention provides a process for visualizing N-dimensional object space using a computing device such as a computer. The computing device may be of the type comprising means for inputting, storing and processing data. and commands; means for generating a logical representation of the N-dimensional object space in response to the stored frames, data, and commands; frame logic for generating a virtual image representing the N-dimensional, object space in response to the stored data and commands, and display mea~.ns for displaying a visible representation of logical regions. selected from the virtual image. The process uses the computing device.
FIGS. 11A-~11C show an intuitive procedure for reflecting a mixed-resolution, 4-dimensional object space onto a plane. F;eferring to FIG. 12, a flow chart showing the case of user-s~>ecified attributes, the process starts with the step of inputting the attributes 1201 to the computing device. The ataributes describe the problem. A color display, for e~;ample, may have the attributes of three or more primary colors: red; green; and blue. Each attribute corresponds to a dimension of the problem. For the color display, each of the three primary colors may be considered a dimension, giving a dimension of three (N = 3). The computer generates 1202, from the user specified attributes, a frame for the' N-dimensional object space. The frame is a coded representation of attribute descriptions for a particular problem domain. In a color space each attribute corresponding t:o a primary hue is described by a bitfield in the frame. Thsa first bit of each bitfield is always a logical one. Subsequent bits in a given bitfield are logical zeros. Each logical zero represents an additional bit of resolution.
As a first: example, a three-dimensional object space, ,.,",.

with two bits resolution for each dimension would have a frame (0, 1, 0, 1, 0, 1). A 1-bit represents each dimension and a first level of resolution. A 0-bit placed before the corresponding 1-bit represents a second bit of resolution.
For the color display, two bits of resolution on each of three dimensions might correspond to four intensity values for each of the: primary colors.
As a second example, a three-dimensional object space with three bits'. of resolution on the first dimension, one bit of resolution on the second dimension, and two bits of resolution on t:he third dimension, would have the frame:
(0, 1, 1, 0, 0, 1). For color space: the right three bits might represent: eight levels of resolution for the red attribute; the second 1-bit from the right might represent two levels resolution for the green attribute; and the left two bits might represent four levels of resolution for the blue attribute.
As a third example, for a three dimensional, object space with one bit resolution on each dimension would have a frame (1, 1, 1). Each bit, from right to left, might represent the red attribute, the green attribute and the blue attribute, respectively. The frame is a positional notation system which denotes the number of attributes and the resolution of each attribute. The frame data are the values or senses of each bit position in a given frame.
Referring to FIG. 12, the bits of the frame are interleaved 1203 to generate an object descriptor. For the first example, the object descriptor is (0, 0, 0, 1, 1, 1) for the frame I;O, 1, 0, 1, 0, 1). For the second example, the object descriptor is (0, 0, 0, 1, 1, 1) for the frame (0, 1, 1, 0, 0,, 1). For the third example, the object descriptor is (1, 1, 1) for the frame (1, 1, 1). The computing device generates 1204 from the frame and the object descripl:or, dimensional-spatial locations of the N-dimensional object space. For each 1-bit from the object description, the computing device generates a dimension of dimensional-sp<itial locations, which correspond to the x,uo.: r.
...~r... ~.

21 00359 y attributes of the problem.
FIGS. 13 through 19 illustrate n-cube projection in accordance with. methods of the invention now further described as a process to mechanize and visualize reflected N-dimensional object spaces for any N, where N is a positive integer. It should be noted that each of the FIGS. 13 through 19 show three expressions of N-dimensional element configurations.
The n-cubes of FIG. 13 is referred to herein as a 0-dimensional object space. FIG. 13 show that an object space with a dimension of zero (n = 0) has only one element; that is, one dimensional-spatial location.
The binary 1-cube of FIG. 14 is referred to herein as a 1-dimensional object space with one bit of resolution. FIG.
14 shows that am object space with a dimension of one (n = 1) has two elements; that is, two dimensional-spatial locations. They 1-d, 1-bit object space of FIG. 14 can be visualized as a linear region comprising two elements "named" logical. zero and logical one, respectively. The linear region of FIG. 14 is generated by reflecting a first 0-dimensional object space named "0" to the right. Thereby, a second 0-dimensional object space named "1" is produced.
The name of a dimensional-spatial location is called an object selector-.
FIGS. 15 through 19 show the progressive projection of reflected binary n-cubes, where N varies from two to six.
In FIGS. 15-19, each dimensional-spatial location is represented as a cell, which is drawn as a square. N-dimensional object spaces are reflected as regions in an orthogonal direction determined by control signals from an apparatus described below. Referring to FIGS. 15 through 19, it should be noted that the values of the n-1 rightmost object selector bits in a second (reflected) region are the same as the n-~_ rightmost object selector bits of the corresponding object selectors which comprise a first region (i.e., where N is the number of bits in an object selector).
It should be further noted that the value of the leftmost ._ ~ 2100359 object selector bit of a first region is always a logical zero, and the leftmost selector bit of a second region is always a logical one.
The binary 2-cube of FIG. 15 is referred to herein as a 2-dimensional object space with one bit of resolution. FIG.
shows that a.n object space with a dimension of two (n =
2) has four elements; that is, dimensional-spatial locations. The: 2-dimensional, 1-bit object space of FIG. 15 can be visualized as two linear regions comprising four 10 elements "namedl" in accordance with a reflected binary Gray code (e.g., 00, O1, 11, 10). The object space of FIG. 15 is generated by reflecting a first linear region upward.
Thereby, producing a second (reflected) linear region. The resulting objects space can be visualized as a square region.
15 It should be noted that the corresponding object selectors in each linear region have the same value in the rightmost bit position; however, the values differ in the leftmost bit position. The leftmost bit of the first linear region's object selectors is a logical zero. The leftmost bit of the second (reflect:ed) linear region's object selectors is a logical one.
The binar~~ 3-cube of FIG. 16 is referred to herein as a 3-dimensional object space with one bit of resolution. FIG.
16 shows that an object space with a dimension of three (n = 3) has eight elements; that is, dimensional-spatial locations. The' 3-dimensional, 1-bit object space of FIG. 16 can be visuali~:ed as two square regions, each comprising four elements. These eight elements are named in accordance with a reflects~d binary Gray code (e. g., 000, 001, 011, 010, 110, 111, 101, 100). The object space of FIG. 16 is generated by reaflecting a first square region comprising for elements to they left. Thereby, a second square (reflected) region is produced. It should be noted that the values of the two rightmost object selector bits in the second (reflected) square region are the same as the two rightmost bits of the corresponding object selectors, which comprise the first square region. The value of the leftmost object selector bit of the first square region is a logical zero.
The value of th.e leftmost object selector bit of the second square region is a logical one.
The binary 4-cube of FIG. 17 is referred to therein as a 4-dimensional. object space with one bit of resolution.
FIG. 17 shows that an object space with a dimension of four (n = 4) has sixaeen elements; that is, dimensional-spatial locations. They 4-dimensional, 1-bit object space of FIG. 17 can be visualized as two rectangular regions, each comprising eight elements. These sixteen elements are named in accordance with a reflected binary Gray code. The object space of FIG. 1.7 is generated by ref lecting a first rectangular regions comprising eight elements downward.
Thereby, a second rectangular (reflected) region is produced.
The binary 5-cube of FIG. 18 is referred to therein as a 5-dimensional. object space with one bit of resolution.
FIG. 18 shows that an object space with a dimension of five (n = 5) has thirty-two elements; that is, dimensional-spatial locations. The 5-dimensional, 1-bit object space of FIG. 18 can be visualized as two square regions, each comprising sixteen elements. These thirty-two elements are named in accordance with a reflected binary Gray code. The object space of FIG. 18 is generated by reflecting a first square regions comprising sixteen elements to the right.
Thereby, a second square (reflected) region is produced.
The binar~~ 6-cube of FIG. 19 is referred to therein as a 6-dimensional. object space with one bit of resolution.
FIG. 19 shows that an object space with a dimension of six (n = 6) has sisay-four elements; that is, dimensional-spatial locations. The 6-dimensional, 1-bit object space of FIG. 19 can be visualized as two rectangular regions, each comprising thirty-two elements. These sixty-four elements are named in accordance with a reflected binary Gray code.
The object space of FIG. 19 is generated by reflecting a first rectangu7_ar region comprising thirty-two elements ,~, upward. Thereby, a second rectangular (reflected) region is produced.
The process of naming spatial elements for any N-dimensional space is intuitively understood as a "function" of reflecting its subspaces. The space generation method illustrated by FIGS. 13 through 19, when projected onto a plane, results in a two-dimensional visual representation of reflected N-dimensional spaces. The novel method of the present invention can be used for visualizing progressive space generation for any N-dimensional object space.
The dimensional-spatial locations can be produced by reflecting cells right, up, left, down, right, up, left, down, etc., in what is considered a counter-clockwise direction.
Alternatively, the dimensional-spatial locations can be produced by reflecting cells to the left, up, right, down, left, up, right, down, etc., in what is considered a clockwise direction.
The dimensional-spatial locations may be reflected in a clockwise or counter-clockwise direction. Further, the dimensional-spatial locations can be produced by reflecting cells in a single direction or selected direction. For illustrative purposes the counter-clockwise embodiment for producing dimensional-spatial locations is used throughout this disclosure, with the understanding that the alternative embodiments produce semantically equivalent dimensional-spatial locations.
Referring to FIG. 12, when all the dimensional-spatial locations are generated 1205 representing all the dimensions of the problem, then the computing device gets 1206 the first attribute bitfield in the frame. From this bitfield, the computing device determines 1207 whether resolution-spatial locations need to be generated from this bitfield. If no resolution-spatial locations are to be generated, then the computing device determines 1209 whether this is the last bitfield of the frame. If yes, then the computing device checks 1211 if there are any additional resolution-spatial locations to be generated for any bitfield. If no~ resolution levels are required, then the computing device generates 1212 an object selector which corresponds to interleaved frame data for each dimensional-spatial location in the N-dimensional object space. The object selectors are generated by interleaving bitfields of frame data. The object selectors define unique cell locations representing dimensional-spatial locations.
If all object ;electors have been generated 1213 for all the dimensional-spatial locations for the N-dimensional object space, then they computing device generates 1214 a virtual image of the N-dimensional object space from the dimensional-spatial locations and the object selectors. A
user or application procedure may select 1215 a logical region of the virtual image for machine control, display, or other application-driven function. The process further may include using t:he computing device for displaying the selected logical region of the virtual image of the N-dimensional object space on the display means. The process additionally may use the computing device for generating 1208, from the frame and the object descriptor, resolution-spatial locations for resolution levels of each of the N dimen:~ions for a mixed-resolution,.N-dimensional object space.
FIGS. 20-~!2 illustratively show the generation of resolution-spatial locations. Referring to FIG. 20, the number of elements in a k-ary 1-dimensional object space is determined by t:he number of bits of resolution as a power of two. For example, a 4-ary 1-dimensional object space with two bits of resolution has four elements and an 8-ary 1-dimensional object space with three bits of resolution has eight elements,. When elements of k-ary 1-dimensional object spaces are ref7lected linearly as shown in FIGS. 20A-20C, the element transit:ion sequences correspond to the primary form of the reflectE~d binary code, but may be interpreted as a reflected, mixEad-resolution k-ary code.
FIG. 20A :shows a binary 1-cube referred to herein as a 1-dimensional object space with one bit of resolution. The 1-dimensional, 1-bit object space of FIG. 20A comprises two object selectors named "0" and "1" respectively. The object selectors of a 1-dimensional, 1-bit object space represent dimensional-spatial locations.
FIG. 20B illustrates a 1-dimensional object space with two bits of resolution. In this case, the original dimensional-spatial locations of FIG. 20A have been reflected to the right to increase the resolution in the direction of the first dimension. Note that the reflection for increased resolution is in the same direction as the reflection which generated the dimension. The object selectors of the original dimensional-spatial locations have a 0-bit placed in front of them, and the newly generated resolution-spatial locations have the original object selectors reflected therein with a 1-bit placed in front of them.
FIG. 20C :shows a 1-dimensional object space with three bits of resolui:.ion, which has been generated from the 1-dimensional, 2-bit object space of FIG. 20B. In this case object selectors from the 1-dimensional, 2-bit object space (2-ary 1-dimensional object space), have a 0-bit placed in front of them, and the object selectors generated by reflection haven a 1-bit placed in front of them.
FIGS. 21A--21B are diagrams of 4-dimensional object spaces. FIG. 2:LA shows a 4-dimensional object space with one bit of resolution. FIG. 21B shows a 4-dimensional object space with two bits of resolution, in each dimension. In this case, aftEar generating all of the dimensional-spatial locations for i~he four dimensions, the resolution-spatial locations are <generated. Accordingly, the sixteen dimensional-spatial locations for the four dimensions are reflected initially to the right to generate two levels of resolution for the first dimension. At this stage, there are thirty-two dimensional-spatial locations and resolution-spatial locations. To generate two levels of resolution in i~he second dimension, thirty-two resolution-spai~ial locations are generated by reflecting in an upward direction the combination of thirty-two dimensional-spatial locations and resolution-spatial locations. Now there are a total of sixty-four spatial locations. They two level resolution-spatial locations for the third dimension are generated by reflecting sixty-four resolution-spatial locations to the left of the previously generated sixty-four spatial locations. The two level resolution-spatial locations may be generated for the fourth dimension by reflecting 128 resolution-spatial locations in a downward direction from the mixture of 128 mixed-resolution spatial locations from the first, second, and third dimensions. Accordingly, a total of 256 spatial locations are generated for the 4d, 2-bit object space.
Object selectors are generated in a similar fashion as previously described for each mixed-resolution spatial location.
FIGS. 22A--22B are diagrams of a mixed-resolution, 4-dimensional object space derived from a binary, 4-dimensional object space. FIG. 22A again shows the 4-dimensional object space with one bit of resolution.
FIG. 22B :shows a mixed-resolution, 4-dimensional object space. In a mixed-resolution object space the number of bits of resolution for each dimension is permitted to differ. Prior art methods for naming elements of an object space can be characterized as container-oriented in that the number of addrEassable element locations are a function of the container':a extent. Alternatively, the method disclosed herein is characterized as self-referencing, in that, the extent and configuration of an object space is a function of its content de:~cription. In the object space of FIG. 22B the first and third dimensions each have two bits of resolution and the second and fourth dimensions have only one bit of resolution. Therefore, the object selectors for the object space of FIG. :>.2B have a total of six bits. Recall that the number of bits in an object selector, when viewed as a power of two, describes the number of elements in a given object space. Therefore, the object space of FIG. 22B comprises ~w~

sixty-four elements. It should be noted that prior art representations. of higher-dimensional spaces typically fix the resolution for each dimension relative to the greatest number of bits required for any dimension. Thereby, an inefficient spatial representation is created. The method of the present invention generates logical object spaces by a process which relies on a novel object description rather than a process of spatial decomposition. In the case of FIG. 22B, the dlimensional-spatial locations for one bit of resolution in each of the four dimensions are generated.
Then, the resolution-spatial locations for the first and the third dimensions are generated. Sixteen dimensional-spatial locations comprise a first square region. A first square region of sixteen elements is reflected to the right;
thereby, producing a second (reflected) square region. The direction (right) of reflection is determined by the additional bit of resolution in the first dimension. This step results in a rectangular region comprising thirty-two elements. The :second dimension has no additional bits of resolution and the next orthogonal direction (upward) is bypassed. The third dimension, however, has an additional bit of resolution. Therefore, the rectangular region comprising thirty-two elements is reflected in the next orthogonal direction (left). Thereby a second (reflected) rectangular region is produced. The resulting first and second (reflect:ed) regions account for the sixty-four elements shown in the object space of FIG. 22B.
Given an object space description where one or more dimensions have' two or more bits of resolution (e.g., a k-ary object space), the object selectors describe a novel form of reflected Gray code called the k-ary reflected Gray code. An object: selector is generated 1212, as illustrated in FIG. 12, for each resolution-spatial location in the mixed-resolution, N-dimensional object space. When all object selectors are generated 1213, from the resolution-spatial locations, the dimensional-spatial locations and i:he object selectors, a virtual image is generated 1214 of the N-dimensional object space. A user or machine may select 1215 a logical region of the virtual image for use e~r display. The computing device may display the selected logical region of the virtual image of the mixed-resolution, N-dimensional object space on the display means.
FIG. 23 shows a functional diagram of the object description process. Four procedures comprise the object description process: expression 2301; quantization 2304;
transformation 2307; and execution 2310. In the case of user-specified attributes a user inputs a domain 2300 of an object which is expressed 2301 as an object description 2302. The object description is encoded as a set of attributes. Each attribute selected corresponds to one dimension of an N-dimensional object space. The order in which the attributes are specified determines a sequence in which an object: space is generated.
The range 2303 of possible values of each attribute is encoded by a quantization 2304 procedure which assigns a logical name to range 2303 of values. The resolution is the degree of ranges 2303 of values. The degree of range compression (e.g., scaling of values) is part of the attribute specification. Coded attribute values correspond to the transition sequence of a reflected binary code.
Intuitively, the most straightforward way of naming or coding an ordered set of objects, where each codeword is a unique sequences of binary digits, is to count in binary, but consecutive codewords usually differ by more than one bit position. Some forms of the reflected binary code, referenced above in the Description of the Prior Art, offer special advantages over others for particular applications.
The maximum number of bits required to represent a coded attribute values defines its dimensional resolution.
The range 2303 of values associated with each dimension of the object description 2302 is quantized 2304 to form a coded object description 2305, called a frame 2306. The format of a frame 2306 is a bit pattern read from the right ,;

-- ~ 2100359 that represents a contiguous sequence of coded attributes or bitfields. The rightmost bit of each attribute's bitfield is a logical one denoting a spatial dimension. Additional bits of resolution for a given attribute, if any, are assigned a logical zero; e.g., (0, 1, 0, 1) is a frame 2300 for coded objecit description representing two four-valued attributes.
The bits o:E the object frame 2306 are then transformed 2307 to form an interleaved object frame 2308 called a descriptor 2309. The object descriptor represents the name format for specific object expressions. A collection of coded attribute values associated with the interleaved frame 2308 of a named object expression is called an object selector. The abject descriptor 2309 controls the execution process 2310 fo:r forming a visual space 2311. The bitwise control sequence can be understood by considering the interleaved object frame 2306 in an expanded form. The number of dimensions N describing a unit object space is defined in the first interval of the expanded frame. Each subsequent interval extends the dimensional resolution of the object space 2311. A blank interval position in the expanded object descriptor 2309 may be thought of as the termination of 'the spatial control sequence for that particular dimension.
The object spaces shown in FIGS. 14-19 are simple enough to be formed manually and, in a few instances, mentally; however, description spaces of actual systems quickly exceed the feasible limits of mental visualization and manual procedures. Therefore, an embodiment of the present invention is described as an electronic controller.
It should be understood that the control of various types of machines and application processes are contemplated within the scope of this invention. A frame controller is the syntactic expression of a visual space. A region controller is part virtual machine which determines semantic expression of an object space as a name space.

Given a us~ar-specified set of attributes defining dimensions and resolution levels in a particular object space, an illusitrative embodiment of an object description system comprise:~ a plurality of physical modules which may be operatively ~~oupled in various logical configurations to efficiently mechanize the method of the present invention.
There are two kinds of physical modules in an illustrative embodiment of an object description system: modules of a host computing device and object modules operatively coupled to modules of a host computing device.
Referring to FIG. 24A, a computing device 2400 is shown including an inlput device 2401, a processor 2402, memory 2403, and a dislplay device 2404. The input device 2401, by way of example, may be a key board, computer port, or an application witlhin a computer. The processor 2402 is coupled between the input device 2401, memory 2403 and display device .2404.
FIG. 24B chows abject module 2405 having object frame module 2406, object region module 2407, and object selector module 2408 operatively coupled to the computing device 2400. Each object module 2405 comprises at least one register device having at least one storage cell;
combinational logic devices which relate to the registers;
data signal paths which link devices within a module and which link devices in different modules; and control signal paths which link devices within a module and which link devices in different modules. The region module 2407 is operatively coupled to the input logic of the computing device 2400 and the object frame module 2406. The object region logic 2407 is used for selecting relations of the object space.
As with the process of the present invention, a user may specify semantic expressions for a particular set of attributes defining dimensions and resolution levels in the object space. A user, using the input device 2401, inputs an object description for the particular set of attributes of a problem for the mixed-resolution, N-dimensional object space. The input logic of the computing device of the processor 2402 is operatively coupled to the input device 2401 and interfaces the input device 2401 with the memory 2403.
The frame logic of the object frame module 2406 interleaves the frame to generate an object descriptor.
The frame logic of the object frame module 2406 also generates, from the frame and the object descriptor, dimensional-spatial locations for N dimensions. From the frame and the object descriptor, the frame logic of the object frame module 2406 generates resolution-spatial locations for resolution levels of each of the N dimensions of the mixed-resolution, N-dimensional object space. The object selector module 2408 uses frame data to generate, for a particular spatial location, an object selector. The object selector, as previously described conforms to a primary form of a reflected binary code. Using the dimension-spatial locations and the object selectors, the frame logic of the object frame module 2406 generates a virtual image of the N-dimensional objection space. The computing device, using region logic of the object region module 2407, manipulates the virtual image with bit selectors.
The apparatus of the present invention may be used for visualising a mixed-resolution, N-dimensional object space. The user specifies an object space described by a set of attributes defining dimensions and resolutions levels in the abject space. The user may, using the input device 2401, input attribute values.
The object frame module 2406 receives from the computing device coded representations of the attributes called an object frame. These coded representations of the attributes stand for actual values. Instances of such coded attributes stand for actual values. Instances of such coded attribute values are concatenated by the object frame module 2406 to generate frame data. The frame data represents the actual values behind the coded representations of the attributes.
The object frame module 2406 interleaves the object frame to generate an object descriptor and, using the object frame and object descriptor, the object frame module 2406 generates dimensional-spatial locations for N-dimensions. The object frame module 2406 also generates, from the frame and the object descriptor, resolution-spatial locations for resolution levels of each of the N-dimensions for a mixed-resolution, N-dimensional object space.
The object selector module 2408 generates an object selector for each dimensional-spatial location and for each resolution-spatial location. An object selector is formed by interleaving the frame data. The object selector identifies the name of a specific location in the object space. The location names a specific attribute. Thus, the object selectors define unique cell locations representing dimensional-spatial location s and resolution-spatial locations.

The obj ect frame module 2406 generates a virtual image of the N-dimensional space using the frame, the frame data, the dimensional-spatial locations and the resolution-spatial locations.
The object region module 2407 is used for selecting one or more elements of the virtual image. The object region module 2407 stores the selected region of the virtual image and the display device 2404 displays the virtual image of the N-dimensional object space.
Various logical configurations of physical modules implement the procedural behaviour of an object description systems. An object description system can be regarded as an implementation of procedures that transforms mixed-resolution, N-dimension object description into a mechanical from which can be logically manipulated. An object description system also can be regarded as an implementation of procedures that transforms mixed-resolution, N-dimensional object descriptions into a perceptible form which can be presented as an image on a graphics display device.
Referring to FIG. 25, these transformation procedures can be organised and abstracted into a functional model 2500 of an object description system. The functional model of an object description system comprises a plurality of logical processors, which perform the correlative functions corresponding to the reference numerals of FIG. 12:

application input processor 2501 (1201) frame processor 2502 (1202) descriptor processor 2503 (1203/1204) dimension-location processor 2504 (1204/1205) resolution-location processor 2505 (1206-1211) selector processor 2506 (1212/1213) virtual image processor 2507 (1214/1215) A logical processor in the functional model corresponds to one or more physical modules, and two logical processors in the functional model may share a physical module.
Similarly, representations of object spaces may exist in one or more different memories. Alternatively, a plurality of such object description systems may be operatively coupled in various logical configurations dictated by the conceptual problem domain, enabling concurrent manipulation of a plurality of o~~ject space descriptions or concurrent manipulation of a plurality of views of a particular object space description.
FIG. 26A-26H shows the object space configurations formed by the 9-bit frame logic module. Each object space 2602 shown in FIGS. 26A through 26H is associated with a diagram of its object frame selector 2600 and the logical names of their frame and interleaved frame 2603. The logical names of the frame and interleave frame 2601 shown in FIGS. 26E through 26H are the same, resulting in the practical observation that the object frames for these spaces are in their interleaved form.
DESCRIPTION OF AN ILLUSTRATIVE EXAMPLE
An exampls~ of a uniform color space generated in accordance with the method of the present invention is now described to better understand how to practice the invention. Then discussion of prior art color models referred to in Description of the Prior Art established a long felt need for a method of representing a uniform color space, such that, specific color sensations could be algorithmicall~~ specified. In particular, this example demonstrates how a range of color sensations described by an RGB color cube can be uniformly projected onto a plane.
This example teaches: how to describe the attributes of an RGB color cube; how the perceptual attributes of a color specification correspond directly to the problem description process of the invention; and this example also teaches the correspondence between the problem description process of the invention and the electronic production of color sensations.
Visible light, called the physical color space, is a small segment of the continuum of electromagnetic radiation, which includes, for example, radio waves, radar, microwaves, infrared and ultraviolet light, x-rays, and gamma rays. A
color representation system determines the location of a particular color sensation in a visual space, called the logical color space. The system is a color representation system; the input is white light; and response is a color space generated in accordance with the method of the present invention.
A color representation system determines the location of a particular' color sensation in a visual space, called the logical color space. The system is a color representation system; the input is white light; and the response is a color space generated in accordance with the method of the present invention. A color representation system determines the location of a particular color sensation in a visual space called the color space. Color space expressions indirectly produce physical device control signals for a color display. The RGB color cube represents red, green, and blue primaries as orthogonal axes. The displayable colors are within the cube from (0, 0, 0) to (1, 1, 1). The neutral axis is a (diagonal) line from the black point (0, 0, 0) to the white point (1, 1, 1). The color cube has been referred to in the literature as a "natural"
coordinate system in the sense that the three color components are mapped into an orthogonal coordinate system in the same fa:~hion as three-dimensional geometry. In a chapter entitlE~d, "Color Displays and Color Science," Color and the Computer, Academic Press, Boston, 1987, p. 23, the section entitlsad, "Visual Display Descriptive Systems,"
Murch makes the' following observation: "...the location and proper specification of colors within the interior of the cube, when some real value for all three primaries is required, provEas difficult."
.;

Color specification means interactive visualization and control of the perceptual color gamuts (range of producible colors) of color display devices. An ideal color model should accomplish intuitive addressability; uniformity;
independent control of lightness and chromatic contrast;
display device characterization in perceptual terms; and a basis is for naming color specifications.
Intuitive addressability is the specification of color representations in perceptual terms. Perceptual specifications may include, by way of example, hue, saturation and intensity. Hue is the basic component of color and is primarily responsible for a specific color sensation (e. g., red, green, blue, etc.). Saturation is most closely related to the number of wavelengths contributing to a color sensation. Saturation depends on the relative dominance of a pure hue in a color specification. Intensity is an increased. level of illumination permitting a broader range of hues t.o be visible. Uniformity is the regular representation of gradations in perceived color, due to the perceptual relationship of color expressions. Independent control of lightness and chromatic contrast is the opportunity to expand chromatic contrast independently of intensity or vice versa. Display device characterization in perceptual terms chooses appropriate display representations and controls their production. A basis for naming color specifications is the opportunity to use a consistent method of color referencing to construct multidimensional models of process exprese;ions in terms of spectral descriptors.
The illustrative example of the invention applied to the problem of color space description teaches a method for representing visual color sensations logically and reproducing logical color spaces visually. Color specification and color space organization conventionally involve levels of computational indirection between the specification of color in terms of its perceptual attributes (e. g., hue, saturation and intensity) and subsequent production of ealectronic color signals. The process enables the description of a logical color space expressed in terms of perceptual color attributes to be directly realized in terms of a given display device's physical color space. The approach to the problem is a descriptive specification of color space component relationships.
The domain description of a color representation system is the human visual system's response to a limited portion of the electromagnetic spectrum called visible light. Light generally refers to electromagnetic radiation from 38onm to 770nm. The observed color of light results from a mixture of intensities at different wavelengths. The rate of change in intensity for a given control source is a function of wavelengths. In R. Hall, Illumination and Color in Computer Generated Imacte~~, Springer-Verlag, NY, 1988, pp. 47-52, the graph of intensity as a function of wavelength is the spectral curve for a given test color. This graph represents a schematic for determining control light intensities for a given test color spectral curve. Each control source spectral curve corresponds to a dimensional component of the color space domain. Colors mixed in a fashion in which bands of wavelengths are added to one another is called an additive color mixture.
The illustrative RGB color space is dimensionally described in terms of three color primaries (e.g., hue =
domain dimension): high wavelength (R) red primary; medium wavelength (G) green primary; and low wavelength (B) blue primary. In an N-dimensional color space where each dimension corrE~sponds to a color primary, the resolution of color space is determined by defining the number of values for each primary (e.g., saturation = range resolution). The range of dimen::ional resolution is determined by one or more bits for each dimension. The number of bits specified for each dimension may differ. Two bits of resolution (e. g., four values) are specified for each primary in the RGB color space generated below.
Value quantization can be described as spectral sampling. In t:he prior art spectral sampling means reducing a spectral curve to a set of sample values for subsequent color computations. Spectral sampling herein means reducing a spectral curve to a set of intensity values associated with logical names in a color space generated by the method of the present invention (e. g., intensity = value).
Generation of a logical color space (e. g., a space of color names) is performed as follows. The frame is a coded representation of user-specified attribute descriptions for a problem domain. In a color space each attribute corresponding t.o a primary hue is described by a bitfield in the frame. The: first bit of each bitfield is always a logical one. Subsequent bits in a given bitfield are logical zeros. Each logical zero represents an additional bit of resolution.
In an illustrative color space a frame "010101"
comprises three: two-bit bitfields where: the rightmost pair of bits represents the red attribute; the center pair of bits represent; the green attribute; and the leftmost pair of bits represents the blue attribute. The primary function of a frame is ais an interpreter which distinguishes between the possible meaning of an object descriptor or an object selector.
In an illustrative color space the object descriptor is the result of a transformation of a frame where the bits of each frame bitfield are interleaved. When, for example, the frame "010101" is interleaved the result is the object descriptor "000111." The primary function of an object descriptor is its role in generating N-dimensional object spaces. Using the frame to distinguish dimensional bits from resolution bits, the object descriptor determines the orthogonal generation of N-dimensional object spaces.
There are two notions of cycles associated with the orthogonal generation of N-dimensional object spaces. The first cycle is the order of interpretation of the object descriptor. Object descriptor bits are logically grouped into dimensional intervals, e.g., "000 111". Each e~w ' -44- 2100359 system is the human visual system's response to a limited portion of the electromagnetic spectrum called visible light. Light generally refers to electromagnetic radiation from 38u nm to 770 nm. The observed color of light results from a mixture of intensities at different wavelengths.
The rate of change in intensity for a given control source is a function of wavelengths. In R. Hall, Illumination and Color in Computer Generated Imaqery, Springer-Verlag, NY, 1988, pp. 47-52, the graph of intensity as afunction of wavelength is the spectral curve for a given test color.
This graph represents a schematic for determining control light intensities for a given test color spectral curve.
Each control source spectral curve corresponds to a dimensional comvponent of the color space domain. Colors mixed in a fashion in which bands of wavelengths are added to one another is called an additive color mixture.
The illustrative RGB color space is dimensionally described in teams of three color primaries (e.g., hue =
domain dimension): high wavelength (R) red primary; medium wavelength (G) green primary; and low wavelength (B) blue primary. In an N-dimensional color space where each dimension corresponds to a color primary, the resolution of color space is determined by defining the number of values for each primary (e. g., saturation = range resolution).
The range of dimensional resolution is determined by one or more bits for e~ich dimension. The number of bits specified for each dimension may differ. Two bits of resolution (e.g., four valves) are specified for each primary in the RGB color space generated below.
Value quant=ization can be described as spectral sampling. In the prior art spectral sampling means reducing a spectral curve to a set of sample values for subsequent color- computations. Spectral sampling herein means reducing a spectral curve to a set of intensity values associated with logical names in a color space ,.,.

._ shows how the elements, name space labels, of a binary RGB
color space are labeled. The vertical regions labeled"R"
2704 contain elements whose rightmost bit position is set.
The horizontal region labeled "G" 2705 contains elements whose middle bit position is set. The left half labeled "B"
2706 contain elements whose leftmost bit position is set.
FIGS. 28A-28C show the elements of a sixty-four element RGB color space. FIG. 28B shows how the elements of a sixty-four element RGB color space are labeled. FIG. 28C
shows the object selectors of a sixty-four element RGB color space which correspond to the logical names of each color sensation.
FIGS. 29A-29C show the relationships between three-dimensional spaces with different resolutions. R. Hall in, Illumination and Color in Computer Generated Imagery, Springer-Verlag, NY, 1988, p. 48, plots the intensities of the control lights required to match any wavelength as a function of wavelength.
FIG. 30 shows a graph of the resulting matching curves for 445nm, 535nm, and 630nm control sources. FIGS. 31A-31C
show how percentages of spectral intensities over a range of values for each. primary are determined in a sixty-four element RGB color space, using the graph of matching curves of FIG. 30.
Manipulation of a logical color space is accomplishEd by methods associated with a particular logical view, such as: elements; relations; paths; regions; and subspaces.
Referencing a particular color sensation as an element of a logical color ~~pace may be accomplished in two ways:
reference by value or reference by location.
Reference by value means a user or an application process provides a description of a particular color sensation in terms of its component hues and their respective intensities, typically as frame data. Recall that the frame is a positional notation which denotes the number of attributes and the resolution of each attribute.
Therefore, frame data correspond to the value or sense of each bit position in a given frame. For example, given the frame "010101" .and frame data "000010" the rightmost bitfield of frame data "10" represents a value for a particular intensity of the red attribute in a color specification.
Reference by location means a user or an application process selects a particular color sensation in terms of its location; either indirectly by index (e. g., palette entry) or directly by its selector. Recall that the object selector is a transformation of frame data where the bits of each frame data bitfield are interleaved. For example, given the frame "010101" and frame data "000010" where the frame data is interleaved the result is the object selector "001000." The name of each location in an N-dimensional space corresponds to an object selector.
Referencing a set of harmonious color sensations as relations of a logical color space may be accomplished by generating combinations of n-things taken k at a time, where n is the number of elements in a logical color space and k is the number of selector bits. The elements of a set are said to be neighbors or logically adjacent because one can be obtained from the other by switching a "0" and a "1" in a particular selector bit position. The number of elements in each logical relation corresponds to the number of selector bits. Referencing various sets in a logical color space may be accomplished selectively masking one or more selector bits.
Generating a harmonious sequence of color sensations as paths in a logical color space may be accomplished because the collection of element names describe a Gray sequence, where the Hamming distance between successive elements is one. The sequence of color sensations is said to cycle if its first and 7Last element codewords differ in only one quantum interval. Otherwise, the sequence of color sensations is ~;nown as a path. Given an initial element codeword and a transition sequence the entire set of element codewords in a logical color space can be generated.
q1 a a ...

Referencin~~ various relations of a logical color space may be accomplished selectively by masking or changing the sense of one or more selector bits.
The process by which a logical color frame is interpreted to electronically produce color sensations is referred to herein as reflected Gray code (RGC) demodulation. 'The inverse of RGC demodulation is the conversion of analog information to a digital form (e. g., quantization, spectral decomposition, etc.) by the process of RGC modulation. The method of the present invention represents a novel logical coding system. Object descriptions have meaning, that is, they refer to or describe some system with certain physical or conceptual properties. For color graphics, the objects may be particular color sensations described in terms of attributes such as: red; green; blue; which define a color space. For optical communications, the objects may be a particular coherent light source described in terms of its lightwave components, which define a signal space.
The significant aspect of system description is that the actual description is one selected from a set possible descriptions. The invention is a general apparatus and method, designed to operate for each possible problem selection, not just the one which will actually be chosen since this is unknown at the time of design.
It will beg apparent to those skilled in the art that various modifications can be made to the apparatus and method for visualizing mixed-resolution, N-dimensional object space of the instant invention without departing from the scope or spirit of the invention, and it is intended that the present invention cover modifications and variations of t:he apparatus and method for visualizing mixed-resolution, N-dimensional object space provided they come within then scope of the appended claims and their equivalents.

Claims (14)

WHAT IS CLAIMED IS:

1. A process for dynamically configuring a logical architecture for using a digital-computing device and for controlling fundamental operations to transform said digital-computing device from a fixed-radix mode of operation imposed by physical architecture of said digital-computing device to a mixed-radix mode of operation, comprising the steps, using said digital computing device, of:
a. encoding with said digital-computing device a logical name for each attribute describing a problem space to form an object frame for organizing a contiguous sequence of coded attribute names, each object frame having a logical one bit representing a dimension of an N-dimensional object space and having a logical zero bit representing a degree of resolution for a range of possible values for a particular attribute for a dimension of an N-dimensional object space;
b. interleaving bits of said object frame to generate an object descriptor, said object descriptor representing a name format for referencing storage locations of said digital-computing device and for controlling an order of the storage locations, the storage locations configured as spatial locations of said N-dimensional, object space;
c. configuring, from said object frame and said object descriptor, the spatial locations as dimensional-spatial locations of said N-dimensional, object space;
d. configuring, from said object frame and said object descriptor, the spatial locations as resolution-spatial locations for a mixed-resolution, N-dimensional, object space; and whereby, said mixed-radix mode of operating said computing device mechanizes methods of selecting mixed-radix expressions for elements, paths and relations of said mixed-resolution, N-dimensional object spaces.

2. The process as set forth in claim 1 further including the step of repeating steps a through d in response to input to said computing device which changes the description of said problem space, wherein said steps configure a new logical architecture for a mixed-radix mode of operating said computing device.

3. The process as set forth in claim 1 or 2 wherein a machine process dynamically determines a problem space described by at least one attribute defining at least one dimension having at least one level of resolution for configuring storage locations of a digital computing device as spatial locations for a mixed-resolution, N-dimensional object space.

4. The process as set forth in claim 1 or 2 wherein a user interactively determines a problem space described by at least one attribute defining at least one dimension having at least one level of resolution for configuring storage locations of a digital computing device having a display device for visualizing said problem space description as spatial locations for a mixed-resolution, N-dimensional object space.

5. The process as set forth in claim 1 or 2 wherein an object selector for referencing a spatial location in a memory configured as a named spatial location of said mixed-resolution, N-dimensional object space is logically generated by interleaving bits of a particular instance of frame data for a mixed-radix mode of operating said computing device.

6. The process as set forth in claim 1 or 2 wherein a relation between spatial locations in a memory configured as named spatial locations of said mixed-resolution, N-dimensional object space is logically generated by changing the sense of particular object selector bits for a mixed-radix mode of operating said computing device.

7. The process as set forth in claim 1 or 2 wherein a path comprising a plurality of spatial locations in a memory configured as named spatial locations of said mixed-resolution, N-dimensional object space is logically generated by changing the sense of particular object selector bits in a particular sequence for a mixed-radix mode of operating said computing device.

8. The process as set forth in claim 1 or 2 wherein a region comprising a plurality of spatial locations in a memory configured as named spatial locations of said mixed-resolution, N-dimensional object space is logically generated by suppressing particular object selector bits for a mixed-radix mode of operating said computing device.

9. The process as set forth in claim 1 or 2 wherein multiple paths for concurrently selected paths comprising a plurality of spatial locations in a memory configured as named spatial locations of said mixed-resolution, N-dimensional object space are logically generated by changing the sense of a plurality of object selector bits in a particular sequence for a mixed-radix mode of operating said computing device.

10. An object description system for controlling the logical manipulation of data storage locations of a memory of a digital-computing device configured as at least one mixed-resolution, N-dimensional object space, wherein the object description system is described as a special purpose computing device having a mixed-radix logical architecture, said digital computing device, including a processor for accessing said data storage locations; signal communication means, operatively coupled to said processor means, for communicating control signals, address signals, and data signals to and from said processor means; an input coupled to said processor means by said signal communication means for receiving an object description; and, a memory coupled to said processor by said signal communication means for storing data, said object description system comprising:
object means, operatively coupled to said processor means by said signal communication means, including, frame means operatively coupled to said processor means by said signal communication means for generating said N-dimensional, object space, said frame means including, means for interleaving the bits of coded attribute names of an object frame to generate an object descriptor and for interleaving the bits of a particular instance of frame data to generate an object selector; and at least one register for storing said object frame for controlling the order of the interleaving of bits of said object frame by said interleaving means and for controlling the order of the interleaving of bits of said frame data by said interleaving means;
whereby, said data storage locations of said apparatus, when configured as mixed-resolution, N-dimensional object spaces, are logically addressed and manipulated by fundamental data storage operations.

11. The apparatus as set forth in claim 10 further including:
selector means coupled to said frame means and coupled to said processor means by said signal communication means for selecting elements and paths of said memory configured as said mixed-resolution, N-dimensional object space, wherein said selector means includes at least one register for storing an object selector; and means for changing the sense of particular object selector bits forming attribute relations between particular elements of said memory configured as said mixed-resolution, N-dimensional object space; and region means coupled to said frame means and coupled to said processor means by said signal communication means for manipulating regions comprising a plurality of related elements of said memory configured as said mixed-resolution, N-dimensional object space, wherein said region means includes at least one register for storing an object selector; and means for suppressing particular object selector bits forming a region comprising a plurality of related elements of said memory configured as said mixed-resolution, N-dimensional object space.

12. The apparatus as set forth in claim 10 or 11 wherein said computing device includes display means for visualizing problem space descriptions as spatial locations for a mixed-resolution, N-dimensional object space, said display means operatively coupled to said processor means and said inputting means by said signal communication means, whereby a user interactively controls the internal operation of said computing device.

13. The apparatus as set forth in claim 10 or 11 for controlling the logical manipulation of data storage locations of at least one memory of a plurality of computing devices configured as at least one mixed-resolution, N-dimensional object space, wherein the apparatus is described as a special purpose multiprocessor having a mixed-radix logical architecture, wherein representations of said object spaces may exist in one or more different memories.

14. The apparatus as set forth in claim 10 or 11 wherein a plurality of object description systems are operatively coupled in various logical configurations dictated by the conceptual problem domain, enabling at least one of concurrent manipulation of a plurality of object space descriptions and concurrent manipulation of a plurality of views of a particular object space description.