Introduction to Polygons. Different types of Polygons Simple Convex Simple Concave Non-simple : self-intersecting With holes. Convex. Concave. Self-intersecting. Introduction to Polygons. Convex
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Convex
Concave
Self-intersecting
A region S is convex iff for any x1 and x2 in S, the straight line segment connecting x1 and x2 is also contained in S. The convex hull of an object S is the smallest H such that S
Xk+1,yk+1
Scan Line yk +1
Scan Line yk
Xk , yk
Interior-defined region
Interior-defined region
Push the seed pixel onto the stack
While the stack is not empty
Pop a pixel from the stack
Set the pixel to the required value
For each of the 4 connected pixels
Adjacent to the current pixel, check if it is a boundary pixel or if it has already been set to the required value.
In either case ignore it. Otherwise push it onto the stack
10 14 18 24
Interior pixels along a scan line passing through a polygon area
(a)
(b)
Adjusting endpoint values for a polygon, as we process edges in order around the polygon perimeter. The edge currently being processed is indicated as a solid like. In (a), the y coordinate of the upper endpoint of the current edge id decreased by 1. In (b), the y coordinate of the upper end point of the next edge is decreased by 1
Figure 3-36
Intersection points along the scan lines that intersect polygon vertices. Scan line y generates an odd number of intersections, but scan line y generates an even number of intersections that can be paired to identify correctly the interior pixel spans.