The geometric skeleton is derived from a static object using an implicit 'directions' method; an IK skeleton is derived from and used to manipulate the geometric skeleton. The model may be reconstructed from the modified skeleton using implicit distance and convolution methods.

The relationship between surface bulge 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 skeletal elements are sufficiently large with respect to the convolution kernel.

A method is presented to broaden implicit surface modeling. The implicit surfaces usually employed in computer graphics are two dimensional manifolds because they are defined by real-valued functions that impose a binary regionalization of space (i.e., an inside and an outside). When tiled, these surfaces yield edges of degree two. The new method allows the definition of implicit surfaces with boundaries (i.e., edges of degree one) and intersections (i.e., edges of degree three or more). These non-manifold implicit surfaces are defined by a multiple regionalization of space. The definition includes a list of those pairs of regions whose separating surface is of interest. Also presented is an implementation that converts a nonmanifold implicit surface definition into a collection of polygons. Although following conventional implicit surface polygonization, there are significant differences that are described in detail. Several example surfaces are defined and polygonized. CR Categories and Subject Descriptors: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling - Curve, Surface, Solid, and Object Representations. Additional Keywords and Phrases: Implicit Surface, NonManifold, Polygonization. 1

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 efficient implementation.

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 enough for use within an interactive design environment. This paper describes progress towards interactive control of implicit surfaces and introduces new techniques useful to the designer.

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 simulated with a bump map digitized from real world bark; leaves are textures mapped onto simple surfaces.

An edge, when point-sampled for display by a raster device and not aligned with a display axis, appears as a stair-case.This common aliasing artifact often occurs in computer images generated by two- and three-dimensional algorithms. The precise edge information often is no longer available but, from the set of vertical and horizontal segments which form the staircase, an approximation to the original edge with a precision beyond that of the raster may be inferred. This constitutes a smoothing of the staircase edge.