Method and system for display of an additional dimension

• US 6,271,860 B1
• Filed: 07/22/1998
• Issued: 08/07/2001
• Est. Priority Date: 07/30/1997
• Status: Expired due to Fees

• Current Assignee: David Grosso
• Original Assignee: David Grosso
• Inventors: Gross, David
• Primary Examiner(s): Luu, Matthew
• Assistant Examiner(s): CUNNINGHAM, GREGORY F
• Application Number:
  US09/120,764
• Time in Patent Office: 1,112 Days
• Field of Search: 345/259, 345/427, 345/431, 345/440, 345/419, 345/442, 345/443, 395/118, 395/140
• US Class Current: 715/700
• CPC Class Codes: G06T 11/40 Filling a planar surface by adding surface attributes, e.g. colour or texture
• CPC Class Codes: G06T 17/00 Three dimensional [3D] modelling, e.g. data description of 3D objects

Abstract

A method AND A SYSTEM for displaying in an N-dimensional display means the N+1^st dimension of an equation of N+1 variables, comprising converting the equation into the form inwhich the N+1^st dimension is a variable that is a function of the other first N variables, computing, by means of the function, the scalar value of each pixel, whose N coordinates represent the specific values of the first N variables, and coloring or shading the pixel according to a predetermined color pattern bywhich the scalar value conforms to a predetermined color or shading. The N dimensional display may comprise 2 or 3 dimensions and may include a computer screen, a TV monitor, a print on a printable substrate a hologram, a holographic screen, a stereoscopic TV or video display, or another two or three dimensional display means. The predetermined color pattern may be the pattern defined by the manufacturer of the computer or of the display means.

Claims

1. A method for displaying in an N-dimensional display means including two or three dimensions of the N+1^st dimension of a function of N+1 variables, comprising the following steps:

A. converting the function into a form in which the N+1^st dimension is a variable that is a function of the other first N variables and starts from a lower function and goes upwardly;

B. computing directly, by means of said function, the scalar value of each pixel, whose N-coordinates represent the specific values of said first N variables, producing a function for each said pixel; and

C. coloring or shading said pixel according to a predetermined color pattern by which said scalar value conforms to a predetermined color or shading.

2. A method as in claim 1, wherein said display means include a computer screen, a TV monitor, a print on a printable substrate or another two dimensional display means.

3. A method as in claim 1, wherein said display means include a hologram, a holographic screen, a stereoscopic TV or video display, a stereoscopic print on a printable substrate or another three dimensional display means.

4. A method as in claim 1, wherein said function is a function of N Cartesian variables, whereby each variable of said N variables represents the coordinate of the specific value computed for the N+1^st variable.

5. A method as in claim 1, wherein said predetermined color pattern is the pattern defined by the manufacturer of the display means.

6. A method as in claim 1, wherein said predetermined color pattern is defined by the coloring corresponding to discrete values.

7. A method as in claim 6, wherein the coloring of values between said discrete values is defined by color corresponding to the closest discrete value.

8. A method as in claim 6, wherein the pixels having values between said discrete values are uncolored.

16. A method as claimed in claim 1, wherein the function is convertible into the form in which the N +1^st dimension is a variable that is a function of the other first N variables.

17. A method as claimed in claim 1, wherein the N display of the function is a two dimensional display.

18. A method as claimed in claim 1, wherein the N display of the function is a three-dimensional display.

19. A method as claimed in claim 1, wherein the function is a mathematical function.

9. A method for displaying the N+1^st dimension in an N-dimensional display means including two or three dimensions of a first function of N+1 variables, comprising the following steps:

A. converting said first function into the form by which the N+1^st variable is a second function of the first N variables;

B. computing, by said second function, the scalar value of each pixel, whose N-coordinates represent the specific values of said first N variables; and

C. coloring or shading said pixel according to a predetermined color pattern by which each scalar value conforms to a predetermined color or shading.

10. A method for displaying in an N-dimensional display means including two or three dimensions the N+2^nd dimension of an equation of N+2 variables, comprising the following steps:

A. converting said equation into the form in which the N+2^nd dimension is a variable that is a function of the other first N+1 variables;

B. computing, by means of said function, the scalar value of each pixel, whose N+1 coordinates represent the specific values of said first N+1 variables;

C. computing, by means of a predetermined isometric function, the deviation of each pixel from its first N coordinates to altered first N coordinates and eliminating each pixel that is determined by said isometric function as hidden behind a frontal pixel; and

D. coloring or shading said pixel, if said pixel is not eliminated in step C, according to a predetermined color pattern by which said scalar value conforms to a predetermined color or shading.

11. A method including two or three dimensions for displaying in an N-dimensional display means the N+1^st dimension that is a function of the other first N variables in an equation of N+1 variables, comprising the following steps:

A. computing, by means of said function, the scalar value of each pixel, whose N-coordinates represent the specific values of said first N variables; and

B. coloring or shading said pixel according to a predetermined color pattern by which said scalar value conforms to a predetermined color or shading.

12. A system including two or three dimensions for displaying the N+1^st dimension of an equation of N+1 variables in an N-dimensional display means, comprising:

(a) interface means for receiving input concerning said equation;

(b) conversion means for converting said equation into the form in which the N+1^st dimension is a variable that is a function of the other first N variables;

(c) computing means for computing, by means of said function, the scalar value of each pixel, whose N-coordinates represent the specific values of said first N variables;

(d) coloring means for coloring or shading said pixel according to a predetermined color pattern by which said scalar value conforms to a predetermined color or shading; and

(e) an N-dimensional display means comprising a display interface, or storage or transmittal means adapted to instruct such display interface, wherein, the color or shade of each pixel in said display means is determined by said coloring means.

13. A system including two or three dimensions for displaying the N+1^st dimension of a first function of N+1 variables in an N-dimensional display means, comprising:

(a) interface means for receiving input concerning said equation;

(b) conversion means for converting said first function into the form by which the N+1^st variable is a second function of the first N variables;

(c) computing means for computing, by means of said second function, the scalar value of each pixel, whose N-coordinates represent the specific values of said first N variables;

(d) coloring means for coloring or shading said pixel according to a predetermined color pattern by which said scalar value conforms to a predetermined color or shading; and

(e) an N-dimensional display means comprising a display interface, or storage or transmittal means adapted to instruct such display interface, wherein, the color or shade of each pixel in said display means is determined by said coloring means.

14. A system including two or three dimensions for displaying the N+2^nd dimension of an equation of N+2 variables in an N-dimensional display means, comprising:

(a) interface means for receiving input concerning said equation;

(b) conversion means for converting said equation into the form in which the N+2^nd dimension is a variable that is a function of the other first N+1 variables;

(c) first computing means for computing, by means of said function, the scalar value of each pixel, whose N+1 coordinates represent the specific values of said first N+1 variables;

(d) second computing means for computing, by means of a predetermined isometric function, the deviation of each pixel from its first N coordinates to altered first N coordinates and eliminating each pixel that is determined by said isometric function as hidden behind a frontal pixel;

(e) coloring means for coloring or shading said pixel according to a predetermined color pattern by which said scalar value conforms to a predetermined color or shading; and

(f) an N-dimensional display means comprising a display interface, or storage or transmittal means adapted to instruct such display interface, wherein, the color or shade of each pixel, if said pixel is not eliminated by said second computing means, in said display means, is determined by said coloring means.

15. A system including two or three dimensions for displaying the N+1^st dimension that is a function of the other first N variables in an equation of N+1 variables in an N-dimensional display means, comprising:

(a) Interface means for receiving input concerning said equation;

(b) computing means for computing, by means of said function, the scalar value of each pixel, whose N-coordinates represent the specific values of said first N variables;

(c) coloring means for coloring or shading said pixel according to a predetermined color pattern by which said scalar value conforms to a predetermined color or shading; and

(d) an N-dimensional display means comprising a display interface, or storage or transmittal means adapted to instruct such display interface, wherein, the color or shade of each pixel in said display means is determined by said coloring means.