In this paper a general method is given for combining CSG modeling with soft blending using implicit surfaces. A class of various blending functions sharing some desirable properties like differentiability and intuitive blend control are given. The functions defining the CSG objects satisfy the Lipschitz condition that gives the possibility of fast root finding but can also prove useful in the field of collision detection and adaptive triangulation.
Bloomenthal J (1988) Techniques for implicit modeling. Xerox PARC technical report P89-00106, November 1988Google Scholar
Bohm W et al (1984) A survey of curve and surface methods in CAGD. Comput Aided Geom Des 1(1):1–60CrossRefGoogle Scholar
Hart J (1996) Sphere tracing: a geometric method for the antialiased ray tracing of implicit surfaces. Vis Comput 12(10):527–545 An earlier version appeared in the SIGGRAPH ’93 course notes as WSU Technical Report EECS-93-015CrossRefGoogle Scholar
Pasko A, Adzhiev V, Sourin A, Savchenko V (1995) Function representation in geometricmodeling: concepts, implementation and applications. Vis Comput 11(8):429–446CrossRefGoogle Scholar