Quadratic blending surfaces for complex corners
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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- 1.Barr AH (1981) Superquadrics and angle-preserving transformations. IEEE Comput Graph Appl 1(1):11–23Google Scholar
- 2.Hoffmann C, Hopcroft J (1985) Automatic surface generation in computer-aided design. The Visual Computer 1(3):92–100Google Scholar
- 3.Hoffmann C, Hopcroft J (1985) The potential method for biending surfaces and corners. Tech Rep no. 85-699, Dep Comput Sci, Cornell UnivGoogle Scholar
- 4.Middleditch A, Sears K (1985) Blend surfaces for set theoretic volume modelling systems. Comput Graph 19(3):161–170Google Scholar
- 5.Rossignac JR, Requicha AG (1984) Constant radius blending in solid modeling. Computers Mech Eng 3:65–73Google Scholar
- 6.Sederberg TW, Anderson DC (1985) Steiner surface patches. IEEE Comput Graph Appl 5(3):23–36Google Scholar
- 7.Warren J (1987) Blending quadric surfaces with quadric and cubic surfaces. Proc Third Annual Symposium on Computational Geometry, Waterloo, Ontario, June 8–10, pp 341–347Google Scholar
- 8.Hoffmann C, Hopcroft J (1985) Automatic surface generation in computer aided design. The Visual Computer 1(3):92–100Google Scholar
- 9.Hoffmann C, Hopcroft J (1985) The potential method for blending surfaces and corners. Tech Rep no. 85-699, Dep Comput Sci, Cornell UnivGoogle Scholar
- 10.Kosters, MT (1989) Quadratic blending surfaces for complex corners. Tech Rep no. CS 8804, Dep Math Comput Sci, Groningen Univ, The Visual Computer 5:134–146Google Scholar
- 11.Middleditch A, Sears K (1985) Blend surfaces for set theoretic volume modelling systems. Comput Graph 19(3):161–170Google Scholar