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IP.com Disclosure Number: IPCOM000034237D
Original Publication Date: 1989-Jan-01
Included in the Prior Art Database: 2005-Jan-27
Document File: 4 page(s) / 73K

IBM

## Related People

Lindgren, T: AUTHOR

## Abstract

Identifying a minimal reduced boundary for scan line interpolation, a process which is useful for shading a convex polygon, such as a triangle, is carried out during the processing of the edges of the polygon. Standard shading algorithms calculate the intensities for the vertices, linearly interpolate between the vertices, and then perform scan line interpolation to fill the triangle with shading. The following correctly identifies a minimal reduced boundary for the scan line interpolation as the edges of the polygon are being processed. (Image Omitted) Assumptions: Orientation of the convex polygon is known. Let Fig. 1 be any convex polygon A=[Ei] i=1 (the edge set). Let y max, y min be the greatest and least y values of the polygon projected to two dimensions.

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Identifying a minimal reduced boundary for scan line interpolation, a process which is useful for shading a convex polygon, such as a triangle, is carried out during the processing of the edges of the polygon. Standard shading algorithms calculate the intensities for the vertices, linearly interpolate between the vertices, and then perform scan line interpolation to fill the triangle with shading. The following correctly identifies a minimal reduced boundary for the scan line interpolation as the edges of the polygon are being processed.

(Image Omitted)

Assumptions:

Orientation of the convex polygon is known. Let Fig. 1

be any convex polygon A=[Ei] i=1 (the edge set).

Let y max, y min be the greatest and least y values of

the polygon projected to two dimensions.

L = [Ej Ej is to the left of the line connecting y

max and y min].

R = [Ej Ej is to the right of the line connecting y

max and y min]. Let w : [Ei] n --> {0, 1} be defined by w(i) = 0 if Ei eR i=1 1 if Ei eL It is desired now to correctly select the most interior subset of pixels satisfying: 1. For each scan line intersecting the polygon there are at most two pixels present in the subset and there is

one only at an "extreme" point of the polygon (y min or

y max). 2. For each scan line there is at most one pixel from a

given line; select in Fig. 2 the pixels shown by the

boxed-X.

(Image Omitted)

Note in Fig. 2 that the pixels in the top and bottom rows adjacent to the circled-X pixels are not

needed, since there is no need to process y m...