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Extra info for Computer Graphics for Java Programmers
5. The corresponding alternative method insideTriangle (listed in Appendix F), is slightly faster than the one above if a single triangle ABC is to be used for several points P. It is also more general in that it does not rely on ABC being counter-clockwise. We will not discuss this alternative method here because it is easier to understand after the discussion of matrix multiplication and inverse matrices in Chapter 3. 5 might be slightly faster. 9 POINT-IN-POLYGON TEST The notion of orientation is also useful when we need to determine whether a given point P lies within a polygon.
11 shows how to compute the distance between a point and a line. We perform this computation three times to determine which of the three triangle sides AB, BC and CA (or rather the infinite lines through these sides) lies closest to point P. 12 to compute the projection P′ of P on the triangle side in question (or on an extension of it). We draw both the triangle and the line segment PP′. If the projection point P′ lies on an extension of a side, we also connect this point to the side (AB, BC or CA), to indicate clearly which of the three lines has been used.
We will discuss a comparatively simple algorithm. 5), containing the polygon vertices in counter-clockwise order. The triangulate method that we will discuss takes such an array as an argument. java: Class to store a triangle; // vertices in logical coordinates. 5). c = c; } } If the given polygon has n vertices, this triangle array should have length n − 2. The algorithm works as follows. Traversing the vertices of the polygon in counter-clockwise order, for every three successive vertices P, Q and R of which Q is a convex vertex (with an angle less than 180°), we cut the triangle PQR off the polygon if this triangle does not contain any of the other polygon vertices.