Quadratic blending surfaces for complex corners
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The potential method for blending implicitly defined surfaces is extended in several ways. First, the method of blending an arbitrary number of surfaces to form a convex corner is shown. Second, blending surfaces are constructed for all cases where three surfaces meet transversely. In all cases only quadratic blendings are needed. These two extensions constitute the first part of the paper.
In the second part a construction is given for a very general class of corners, which contains the corners studied in the first part. The general method is not a straight-forward extension of the constructions in the first part. In particular, the blendings produced by the special-purpose methods of the first part are more symmetric.
All constructions rely on some simple properties of quadratic hypersurfaces and can easily be automated. The resulting blendings enjoy some highly desirable properties: they are easily computed, have simple descriptions and are well suited for the subsequent computations which may need to be done — for instance, for rendering purposes.
Detailed numerical examples are included in both parts of the paper.
Key wordsBlending surfaces Computeraided geometric design Graphics Quadratic surfaces Solid modeling Surface modeling
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