An efficient but approximate injectivity test which is a sufficient condition only. This expands the range of possible deformations without sacrificing the speed of the approximate test. 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 feedback.
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. 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.