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An algorithm for the polygonization of implicit surfaces is described and an implementation in C is provided. The discussion reviews implicit surface polygonization, and compares various methods. Introduction Some shapes are more readily defined by implicit, rather than parametric, techniques. For example, consider a sphere centered at C with radius r. It(More)
Three-dimensional space curves can represent the path of an object or the boundary of a surface patch. They can also participate in various free-form geometric constructions. For example, the generalized cylinder (a cylinder with arbitrary cross-sections along a central, space curve axis) is used in Computer Graphics to good effect. Establishing reference(More)
A method is presented for representing botanical trees, given three-dimensional points and connections. Limbs are modeled as generalized cylinders whose axes are space curves that interpolate the points. A free-form surface connects branching limbs. "Blobby" techniques are used to model the tree trunk as a series of non-circular cross sections. Bark is(More)
In recent years, numerous techniques have been developed for the polygonization of implicit surfaces. This article reviews the principal algorithms and provides a framework for identifying their conceptual similarities as well as their practical differences. Particular attention is devoted to the much discussed problem of topological ambiguity, with(More)
The relationship between surface bulges and several implicit blend techniques, particularly those based on convolution of a skeleton, is discussed. An examination of branching skeletons reveals that for two and three-dimensional skeletons, the surface will be bulge-free if elements are sufficiently large with respect to the convolution kernel.