We present a new particle-based approach to sampling and controlling implicit surfaces. A simple constraint locks a set of particles onto a surface while the particles and the surface move. We use the constraint to make surfaces follow particles, and to make particles follow surfaces. We implement control points for direct manipulation by specifying particle motions, then solving for surface motion that maintains the constraint. For sampling and rendering, we run the constraint in the other direction, creating floater particles that roam freely over the surface. Local repulsion is used to make floaters spread evenly across the surface. By varying the radius of repulsion adaptively, and fissioning or killing particles based on the local density, we can achieve good sampling distributions very rapidly, and maintain them even in the face of rapid and extreme deformations and changes in surface topology. CR Categories: I.3.5 [Computer Graphics]: Computational Geometry and Object Modeling:...

This paper describes a simple and efficient polygonization algorithm that gives a practical way to construct adapted piecewise linear representations of implicit surfaces. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In that way, the inherent complexity of the problem is tamed by separating structuring from sampling and reducing part of the full three dimensional search to two dimensions.

A comprehensive analysis of various convolution kernels is presented. Computational complexity and compatibility between the kernels and a number of modeling primitives are examined. A number of practical suggestions are given how to choose the proper kernel function, with a special attention to polynomial kernels. Mathematical formulations for convolved line segments are given. Key words: Geometric modeling -- Isosurfaces -- Polynomial line segments -- Implicit modeling primitives 1 Introduction A convolution surface is the set of points (x; y; z) that satisfy f(x; y; z) = T (1) where T is some scalar value and the field function f(x; y; z) is obtained via a 3D convolution of a kernel function h(p) and a skeleton function g(p): f(p) = Z S g(r)h(p \Gamma r) dr; (2) integrating for all points r that belong to the skeleton S. Skeleton elements may be points, line segments, curves, polygons, and other geometrical modeling primitives. Kernels may be represented by a number of funct...

How can Implicit Surfaces be used in the context of high-end Computer Animation ? This paper compares two different representations of field functions -- the constructive approach and the field image approach. Their respective advantages and limitations for the definition of animation and morphing algorithms, and for the visualization of an animation are discussed. We show that efficient solutions to the animation of textured objects can be provided by hybrid methods that combine these representations together and/or with parametric surfaces. This point is illustrated by two case studies: the animation of deformable characters and the simulation of textured lava-flows.

Implicit surfaces are well suited to modelling organic forms that consist of an internal skeleton and deformable flesh smoothly blended around it. An implicit surface can represent such an object's geometric "skin" that deforms according to the motion of the skeleton. We propose a new, simple and e#cient method for calculating local deformations to be applied to implicit surfaces during collisions with other objects or between di#erent parts of one object. We discuss applications of this method to deformable object simulation, character animation and interactive sculpture. 1 Introduction Of growing popularity in computer graphics, implicit surfaces [16] are particularly well suited to modelling organic forms [11, 2, 14] since they generate a smooth surface around skeletons of arbitrary geometry and topology. Animation of such forms is well established [1, 6, 8] and is normally performed in a layered model, in which the internal skeleton is used to specify the global behaviour of an ob...

. This paper describes a simple algorithm for the adaptive polygonization of implicit surfaces. It gives a practical way to construct optimal piecewise linear representations. The method starts with a coarse uniform polygonal approximation of the surface and subdivides each polygon recursively according to local curvature. In that way, the inherent complexity of the problem is tamed by reducing part of the full three dimensional search to two dimensions. 1 Introduction Implicit models constitute a powerful mathematical description of the geometry of three dimensional objects [10]. Under this framework, a surface is defined as the set of points which satisfy the equation f(x; y; z) = 0. Simple primitive implicit shapes can be specified by algebraic functions, such as quadrics, [5]. More complex implicit shapes can be specified by combining primitives using point set or blend operations that are the basis of, respectively, CSG, [13], and Blobby models, [4]. The implicit descriptio...

This paper presents a complete design environment that explores the modeling capabilities of convolution surfaces and puts them into practice. The design system includes a number of implicit primitives and modeling techniques, that allow objects to be created by sculpturing their surfaces at all levels of detail. All techniques are illustrated using models of marine life forms and other objects of organic origin. Implementation and efficiency issues are discussed. 1 Introduction Convolution surfaces were introduced by Bloomenthal and Shoemake [8] as a generalization of the `blobby models ' developed for computer graphics in [4], [19], [28]. Being a superset of these models, convolution surfaces inherit their valuable properties, such as an ability to form smooth blends and free-form shapes. At the same time, convolution surfaces demonstrate much greater modeling flexibility, allowing a designer to create objects using skeletal elements of various shapes and sizes. This advantage was c...