“Interval methods for multi-point collisions between time-dependent curved surfaces” by Snyder, Woodbury, Fleischer, Currin and Barr

  • ©John M. Snyder, Adam R. Woodbury, Kurt Fleischer, Bena Currin, and Alan H. Barr




    Interval methods for multi-point collisions between time-dependent curved surfaces



    We present an efficient and robust algorithm for finding points of
    collision between time-dependent parametric and implicit surfaces.
    The algorithm detects simultaneous collisions at multiple points of
    contact. When the regions of contact form curves or surfaces, it
    returns a finite set of points uniformly distributed over each contact
    Collisions can be computed for a very general class of surfaces:
    those for which inclusion functions can be constructed. Included
    in this set are the familiar kinds of surfaces and time behaviors
    encountered in computer graphics.
    We use a new interval approach for constrained minimization to
    detect collisions, and a tangency condition to reduce the dimensionality of the search space. These approaches make interval methods
    practical for multi-point collisions between complex surfaces. An
    interval Newton method based on the solution of the interval linear equation is used to speed convergence to the collision time and
    location. This method is more efficient than the Krawczyk–Moore
    iteration used previously in computer graphics.


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