D-Forms, Space deformations for close form collisions

Abstract:

We present a new group of deformations that allow to move a subset of

R^3 along a path, with the following properties: locality, second

order continuity, foldover-free, reversibility and topology

preservation. We illustrate this method in a virtual clay modeler.

The deformations are really intuitive: the control parameters are

simply defined by the movement of a non-deformable tool's shape

(union of points, segments, volumes) that collides with the surface.

Because we use space reversible foldover-free deformations, the

surface mathematical definition is precise, and when sampled,

aliasing is locally controlled. The clay is represented in a tree.

Branches can be collapsed by sampling the clay with a mesh and the

tool with a BSP. To avoid parsing cost while modeling, a sampled clay

is maintained. Moreover the user can create his own tools by drying

pieces of clay. The deformation algorithm complexity is O(N * log{M})

when applied to a mesh (where N is the number of samples of the clay,

M the constant number of samples of the tool).

Keywords:

object representations, interactive modeling, free form deformation