三辺形パッチの接続とその応用

概要

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This paper presents a general method of free-form surface synthesis using only triangular patches with control points and also a method of embedding a triangular patch in a usual spline surface net. Degree of surface patches is two and their connection is in C^l, though their degree may be higher. In the first part, a geometric condition for connection of triangular patches is established : control quadrilaterals which derived from the control points of the constituent patches are a basis for their C^l connection. Since they are tightly constrained to adjacent ones, local control of shapes are not so easy as spline nets of four-sided patches. To give more freedom in shape control in using triangular patches, an idea of corrective across-boundary tangent vector is introduced in the second part. For practical use and explanation of this method, smooth embedding a triangular patch in a usual spline net is treated. This is an important technique to produce special shapes which appear in rounding parts of vertices of box type shape. Uses of these two methods are shown by several application examples which are not produced from usual spline nets of surface. And also their evaluation of connection of quality is examined by contour line patterns.
社団法人精密工学会の論文
1989-10-05