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This paper discusses a numerical technique that approximates an implicit surface with a polygonal representation. The implicit function is adaptively sampled as it is surrounded by a spatial partitioning. The partitioning is represented by an octree, which may either converge to the surface or track it. A piecewise polygonal representation is derived from… (More)

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)

The authors review the principal algorithms for the polygonization of implicit surfaces and provide a framework for identifying their conceptual similarities and practical differences. The algorithms' merits are evaluated according to topological disambiguation, implementation complexity, and triangle count. Special attention is devoted to the ambiguity… (More)

Vertex deformation is a popular technique to animate an erstwhile static object. It is difficult, however, to deform those vertices near multiple limbs of the controlling stick-figure skeleton while maintaining a natural-appearing surface.By applying convolution to the medial axis/surface of the object, the weights associated with vertex deformation can be… (More)

Recent research has demonstrated the usefulness of implicit surfaces for modeling geometric objects. The interactive design of such surfaces has not, however, received the same attention as has the design of parametric surfaces. Principally this is due to the difficulty of controlling the shape of implicit surfaces while displaying the changes quickly… (More)

Smoothly blended articulated models are often difficult to construct using current techniques. Our solution in this paper is to extend the surfaces introduced by Blinn [Blinn 1982] by using three-dimensional convolution with skeletons composed of polygons or curves. The resulting convolution surfaces permit fluid topology changes, seamless part joins, and… (More)