Implicit surfaces (IS) are commonly used in image creation, modeling environments,
modeling objects, and scientific data visualization. In this article, we present a survey of …

Abstract Concepts of functionally based geometric modeling including sets of objects,
operations, and relations are discussed. Transformations of a defining real function are …

In the past few years, there have been key advances in the three main approaches to the
visualization of volumetric data: isosurfacing, slicing and volume rendering, which together …

Implicit definition and description of geometric objects and surfaces plays a critical role in the
appearance and manipulation of computer graphics. In addition, the mathematical definition …

We present a novel method that reconstructs surfaces from volume data using a dual
marching cubes approach without lookup tables. The method generates quad only meshes …

Functionally (implicitly) defined 3D objects allow us to quite easily model parts with complex
topology such as lattices and organic-like structures with a high level of flexibility. Previous …

Surface creases provide us with important information about the shapes of objects and can
be intuitively defined as curves on a surface along which the surface bends sharply. Our …

This paper introduces a unified and general tesselation algorithm for parametric and implicit
surfaces. The algorithm produces a hierarchial mesh that is adapted to the surface geometry …

An approach to modeling heterogeneous objects as multidimensional point sets with
multiple attributes (hypervolumes) is presented. Attributes given at each point represent …

In this article, we have developed an open system architecture and Web-based shape-
modeling applications using HyperFun, a high-level programming language for specifying …