Computer graphics processing and selective visual display system – Computer graphics processing – Graph generating
Reexamination Certificate
1998-07-22
2001-08-07
Luu, Matthew (Department: 2779)
Computer graphics processing and selective visual display system
Computer graphics processing
Graph generating
C345S427000
Reexamination Certificate
active
06271860
ABSTRACT:
FIELD OF THE INVENTION
This invention relates to a method and a system for display of functions in general, and to display of a third or fourth dimension in a two dimensional computer interface display in particular.
BACKGROUND OF THE INVENTION
The digital display of three dimensional objects in a conventional two dimensional screen or printable substrate is possible in several ways. The most instructive display is usually made possible by an isometric-perspective representation. However, such a presentation, when required to be computed by a suitable software involves complicated computations that consume precious computing time, memory, hardware, complicated software and other scarce computer resources. In addition, in a perspective view the “rear” parts or surfaces of the object are always hidden behind the frontal parts. Moreover, for many purposes, the display may be reduced to a simplified top, bottom or side view, inwhich two Cartesian dimensions are represented by the X-Y raster display of the screen or the substrate, and “depths” and “heights” of the third Z dimension or coordinate are represented by altitude lines or coloring. Such a display is relatively economical in the consumption of scarce computer resources and since only one “surface” is shown, it seldom leaves hidden parts or surfaces when presented from an appropriate angle.
The conventional way by which a surface view is computed, is by computing the values of the third dimension of each pixel, and drawing equivalence lines, whereby each equivalence line represents equivalent “height” or “depth”. For enhancing the view, it is common to provide coloring or shadowing characteristics to the lines or the areas between them. Shadowing or coloring which are relative to the abruptness of steep slopes or density of equivalence lines is another possible representation, once such equivalence lines are computed and defined. Nevertheless, the computing of such equivalence line still requires substantial computing resources as well as the determination of the coloring or the shadowing.
It is therefore an object of the invention present to provide a novel method and device for displaying a third dimension of an object or a surface.
It is another object of the present invention to provide a method and device for use in conjunction of conventional computer monitor, TV screen, digital print on a printable substrate, or other two or three dimensional display means.
It is a further object of the invention, to provide a method and a device for displaying a fourth or a fifth dimension of an object, in a two or three dimensional display means, correspondingly.
Yet, a further object of the present invention is to provide a method and a device for defining by a single step the coloring or shading of each pixel for a given function representing an “object”, without computing equivalence lines of the object.
It is yet another object of the present invention to provide a method and a device for displaying on an N-dimensional displaying means, a further “N+1” dimension or further “N+2” dimensions.
Still, another object of the invention is to provide a method and a device that will involve, minimal computing steps, and will use minimal computer resources.
It is still a further object of the invention to provide a method and a device that will adapt for use with the conventional hardware or software bywhich each numerical value has a pre-defined coloring or shading.
These and other objectives are provided by the invention described below.
SUMMARY OF THE INVENTION
There is thus provided according to the present invention a method 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 by which the scalar value conforms to a predetermined color or shading. The N dimensional display may comprise 2 or 3 dimensions and 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.
Preferably, the function is a function of N Cartesian variables, whereby each variable of the N variables represents the coordinate of the specific value computed for the N+1
st
variable. Further preferably, the predetermined color pattern is the pattern defined by the manufacturer of the computer or of the display means, and may define the coloring corresponding to discrete values, wherein the coloring of values between the discrete values may be either defined by color corresponding to the closest discrete value or uncolored.
For a given first function of N+1 variables, the method for displaying the N+1
st
dimension in an N-dimensional display means may comprise converting the first function into the form bywhich the N+1
st
variable is a second function of the first N variables, computing, by the second 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 each scalar value conforms to a predetermined color or shading.
According to another feature of the invention, the method for displaying in an N-dimensional display means the N+2
nd
dimension of an equation of N+2 variables, comprises converting the equation into the form inwhich the N+2
nd
dimension is a variable that is a function of the other first N+1 variables, computing, by means of the function, the scalar value of each pixel, whose N+1 coordinates represent the specific values of the first N+1 variables, 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 the isometric function as hidden behind a frontal pixel, and coloring or shading the pixel, if the pixel is not eliminated in step C, according to a predetermined color pattern bywhich the scalar value conforms to a predetermined color or shading.
According to another aspect of the invention there is provided a system for displaying the N+1
st
dimension of an equation of N+1 variables in an N-dimensional display means, comprising interface means for receiving input concerning the equation, conversion means for 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 means for computing, by means of the function, the scalar value of each pixel, whose N-coordinates represent the specific values of the first N variables, coloring means for coloring or shading the pixel according to a predetermined color pattern bywhich the scalar value conforms to a predetermined color or shading, and 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 the display means is determined by the coloring means.
For a given first function of N+1 variables, the system comprises interface means for receiving input concerning the equation, conversion means for converting the first function into the form bywhich the N+1
st
variable is a second function of the first N variables, computing means for computing, by means of the second function, the scalar value of each pixel, whose N-coordinates represent the specific values of the first N variables, coloring means for coloring or shading the pixel according to a predetermined color pattern bywhich the scalar value conforms to a predetermined color or shading, and an N dimensional display mean
Cunningham G. F.
Luu Matthew
Reed Smith LLP
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