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)
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)
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)
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.
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)