New Solutions of Connection Problems of Free-form Curves and Surfaces

概要

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Two Classes of surface patches are treated: those generated from the tensor product of Two Curve expressions and those that Cannot be produced by the tensor product method. For the former, the basic curve is constructed by Bezier curve segments connected in C^(n-1) or in G^(2). For the latter, methods of satisfying given boundary condition on all sides are described. At first a "connection defining polygon" is introduced together with a scale ratio: the former determines the continuity condition of two Bezier curves, and the latter is the ratio of the magnitudes of the constituent curve segment. A spline polygon is then defined as a polygon for controlling and array of connection-defining polygons. Formulas for locating Bezier control polygons connected in C^(n-1)or G^(2) are given. By the tensor product method, Bezier control nets are derived from a given spline net. Next, a compensating patch that modifies derivative vectors along the boundaries of a patch is defined. It has null position vectors and arbitrary higher-degree derivative vectors on its patch boundaries. These vectors are used to determine the surface expressions of a region surrounded by given patches with given continuity conditions.
一般社団法人情報処理学会の論文
1992-03-15