Collision Detection between Spheres and B-spline Surfaces using Distance Functions from Curves

Collision detection is one of the most important aspects of Computer Graphics, CAD, games, or particle simulations. This paper presents collision detection between spheres and B-spline surfaces. The representative surfaces, Bézier, B-spline surfaces and NURBS, are defined by control points and they are often rendered by polygonal approximation. This paper introduces accurate and effective collision detection between spheres (circles) and surfaces (curves) without polygonal approximation. The distance between curves and points is represented by a Bézier function. The calculation of the shortest distance using the convex hull obtained from the control points of this function enables a more efficient collision detection. This proposed method is installed to the commercial software to confirm this is a software to confirm this is a practical and effective algorithm.