Enhancing Spatial Deformation for Virtual Sculpting
The task of computer-based free-form shape design is fraught with practical and
conceptual difficulties. Incorporating elements of traditional clay sculpting
has long been recognised as a means of shielding a user from the complexities
inherent in this form of modelling. The premise is to deform a
mathematically-defined solid in a fashion that loosely simulates the physical
moulding of an inelastic substance, such as modelling clay or silicone putty.
Virtual sculpting combines this emulation of clay sculpting with interactive
Spatial deformations are a class of powerful modelling techniques well suited
to virtual sculpting. They indirectly reshape an object by warping the
surrounding space. This is analogous to embedding a flexible shape within a
lump of jelly and then causing distortions by flexing the jelly. The user
controls spatial deformations by manipulating points, curves or a volumetric
hyperpatch. Directly Manipulated Free-Form Deformation (DMFFD), in particular,
merges the hyperpatch- and point-based approaches and allows the user to pick
and drag object points directly.
This thesis embodies four enhancements to the versatility and validity of
1. We enable users to specify deformations by manipulating the normal vector
and tangent plane at a point. A first derivative frame can be tilted, twisted
and scaled to cause a corresponding distortion in both the ambient space and
inset object. This enhanced control is accomplished by extending previous work
on bivariate surfaces to trivariate hyperpatches.
2. We extend DMFFD to enable curve manipulation by exploiting functional
composition and degree reduction. Although the resulting curve-composed DMFFD
introduces some modest and bounded approximation, it is superior to previous
curve-based schemes in other respects. Our technique combines all three forms
of spatial deformation (hyperpatch, point and curve), can maintain any desired
degree of derivative continuity, is amenable to the automatic detection and
prevention of self-intersection, and achieves interactive update rates over the
entire deformation cycle.
3. The approximation quality of a polygon-mesh object frequently degrades under
spatial deformation to become either oversaturated or undersaturated with
polygons. We have devised an efficient adaptive mesh refinement and decimation
scheme. Our novel contributions include: incorporating fully symmetrical
decimation, reducing the computation cost of the refinement/decimation trigger,
catering for boundary and crease edges, and dealing with sampling problems.
4. The potential self-intersection of an object is a serious weakness in
spatial deformation. We have developed a variant of DMFFD which guards against
self-intersection by subdividing manipulations into injective (one-to-one)
mappings. This depends on three novel contributions: analytic conditions for
identifying self-intersection, and two injectivity tests (one exact but
computationally costly and the other approximate but efficient).