Real-Time Rendering, Third Edition, 3rd Edition

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798 17. Collision Detection

positive half-space of the plane, i.e., where n · x + d ≥ 0, we would have

to subtract the radius r from d. Note then that the negative half-space is

considered “solid,” i.e., something that the character cannot step through.

A sphere does not approximate a character in a game very well.

1

The

convex hull of the vertices of a character or a cylinder surrounding the

character does a better job. In order to use these other bounding volumes,

d in the plane equation has to be adjusted differently. To test a moving

convex hull of a set of vertices, S, against a BSP tree, the scalar value in

Equation 17.2 below is added to ...