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Effecting Fast Correction of Surface Normals in Computer Generated Three Dimensional Depictions

IP.com Disclosure Number: IPCOM000081719D
Original Publication Date: 1974-Jul-01
Included in the Prior Art Database: 2005-Feb-28
Document File: 4 page(s) / 51K

Publishing Venue

IBM

Related People

Appel, A: AUTHOR [+2]

Abstract

In the generation of three-dimensional depictions utilizing the techniques of computer graphics, many problems such as hidden-line elimination, development of polyhedra, and the numerical controlling of tools, etc., it is necessary to know which side of a surface is substance and which side is space. Thus, in the above set forth problems, the following needs for such knowledge obtain, respectively: a) Hidden-line Elimination - There is not required the attempt to draw surfaces or surface patches which are viewed from the substance side. In addition, if a line is the intersection of two surfaces, one of which is viewed from the substance side, then that line is a contour line.

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Effecting Fast Correction of Surface Normals in Computer Generated Three Dimensional Depictions

In the generation of three-dimensional depictions utilizing the techniques of computer graphics, many problems such as hidden-line elimination, development of polyhedra, and the numerical controlling of tools, etc., it is necessary to know which side of a surface is substance and which side is space. Thus, in the above set forth problems, the following needs for such knowledge obtain, respectively:
a) Hidden-line Elimination - There is not required the attempt

to draw surfaces or surface patches which are viewed from

the substance side. In addition, if a line is the

intersection of two surfaces, one of which is viewed from the

substance side, then that line is a contour line. Detection

of contour lines is an important step in fast hidden-line

elimination, since the visibility of lines changes when

crossing contour lines.
b) Development of Polyhedra - The true shape of polygonal

surfaces are generally drawn as if they were perpendicular

to the surface, but outside of the enclosed volume.
c) Numerically Controlled Tools - The tool path has to be

outside of the volume.

Substantially all programs in computer graphics for rendering three-dimensional depictions require that the listing of points that describe the outline of a surface or surface patch be in an order, such that the loop so described is consistent, i.e., all loops are described either consistently in the counterclockwise or clockwise direction. Thus, for example, the polyhedron shown in Fig. 1 can have its surface list set forth in either of the arrangements shown immediately hereinbelow: Surface List Surface List

I 1, 2, 3, 4 I 4, 3, 2, 1

II 3, 6, 5, 4 or II 5, 6, 3, 4

III 4, 5, 7, 1 III 5, 4, 1, 7

etc. etc.

However, such listing of points which describe a loop either consistently in the clockwise or counterclockwise direction may be very difficult to achieve in many instances, for the following reasons:
1) The three-dimensional object to be depicted may be of a very

complex configuration.
2) The listing of points may be semiautomatic, depending upon

the program which is utilized.
3) A listing of points may be fully automatic, such as

encountered in pattern or scene analysis arrangements.
4) Object volumes may be converted to holes or voids as is

effected in combinatorial techniques.

1

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In known programs for producing three-dimensional depictions of complex polyhedra, there has to be detected the substance side by relatively complex techniques such as, for example:
1. The determination of the surface normal from an acute corner

of the surface.

Referring to Fig. 2, there is known the acute corner of the surface I of the polyhedron depicted therein Ax + By + Cz + D = 0

The surface normal is either

At + Xo = x )

)

Bt + Yo = y ) 1

)

Ct + Zo = z )

or

-At + Xo = x )

)

-Bt + Yo = y ) 2

-Ct + Zo = z )
2. The testing of the possibilities 1 and 2 to see which is

valid, or whic...