The idea behind Virtual Sculpting is to make the process of designing shapes on computer as close to real world clay sculpting as possible (without the disadvantages of being unable to rectify your mistakes). To do this we use a spatial deformation (also referred to variously as Space Deformation, Space Warping and Free-Form Deformation) approach.
We have worked on allowing changes in topology (creating holes and merging parts), preventing self-intersection (where one part of a surface interpenetrates another), remeshing (because the initial lump of virtual clay can become very distorted and poorly sampled) and a variety of sculpting tools (including volumetric fields and tangent frames)
Patrick Marais, Neil Dodgson, Barry Steyn, Ilan Angel, Dominique Bechmann
Gain, J. and Bechmann, D., “A Survey of Spatial Deformation from a User-Centered Perspective”, ACM Transactions on Graphics, Vol. 27, No. 4, October 2008, pp. 1-21.
Gain, J. and Marais, P., "Warp Sculpting", IEEE Transactions on Visualization and Computer Graphics,Vol. 11 , No. 2 , March/April 2005, pp. 217-227.
Steyn, B. and Gain, J., "Topology Alteration for Virtual Sculpting using Spatial Deformation", AFRIGRAPH 2003, Cape Town, South Africa, 3-5 Febraury 2003, ACM Press, pp. 63-68.
J. and Dodgson, N., Preventing Self-Intersection under Free-Form Deformation,
IEEE Transactions on Visualization and Computer Graphics, Vol. 7, No. 4,
Oct.-Dec. 2001, pp. 289-298.
Gain, J. and Dodgson, N., Adaptive Refinement and Decimation under Free-Form Deformation, Eurographics UK '99, Cambridge (UK), 13-15 April 1999.
Video of Warp Sculpting (19Mb MPEG)