Ronald Umble

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Let I be a 3D digital image, and let Q(I) be the associated cubical complex. In this paper we show how to simplify the combina-torial structure of Q(I) and obtain a homeomorphic cellular complex P (I) with fewer cells. We introduce formulas for a diagonal approximation on a general polygon and use it to compute cup products on the cohomology H * (P (I)).(More)
1. INTRODUCTION. The trajectory of a billiard ball in motion on a frictionless billiards table is completely determined by its initial position, direction, and speed. When the ball strikes a bumper, we assume that the angle of incidence equals the angle of reflection. Once released, the ball continues indefinitely along its trajectory with constant speed(More)
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