D-Forms, Space deformations for close form collisions

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).

object representations, interactive modeling, free form deformation