Distance fields on unstructured grids: Stable interpolation, assumed gradients, collision detection and gap function

Continuous Collision Detection Between Points and Signed Distance Fields

We present an algorithm for fast continuous collision detection between points and signed distance fields. Such robust queries are often needed in computer animation, haptics and virtual reality applications, but have so far only been investigated for polygon (triangular) geometry representations. We demonstrate how to use an octree subdivision of the distance field for fast traversal of distan...

compactifications and function spaces on weighted semigruops

chapter one is devoted to a moderate discussion on preliminaries, according to our requirements. chapter two which is based on our work in (24) is devoted introducting weighted semigroups (s, w), and studying some famous function spaces on them, especially the relations between go (s, w) and other function speces are invesigated. in fact this chapter is a complement to (32). one of the main fea...

Distance Fields for Rapid Collision Detection in Physically Based Modeling

In this paper we address the problem of rapid distance computation between rigid objects and highly deformable objects, which is important in the context of physically based modeling of e.g hair or clothing. Our method is in particular useful when modeling deformable objects with particle systems—the most common approach to simulate such objects. We combine some already known techniques about d...

Transonic Turbulent Flow Computations on Unstructured Triangular Grids

Approximate distance fields with non-vanishing gradients

For a given set of points S, a Euclidean distance field is defined by associating with every point p of Euclidean space Ed a value that is equal to the Euclidean distance from p to S. Such distance fields have numerous computational applications, but are expensive to compute and may not be sufficiently smooth for some applications. Instead, popular implicit modeling techniques rely on various a...