Constrained Multiresolution Geometric Modeling

Freeform curves, surface and solids are generally represented in B-spline basis. Various geometric quantities, such as control points, knots and weights have to be specified. Controlling the shape of an object under complex deformations by manipulating the control points directly is often difficult. The movement of control points gives an indication of the resulting deformation, but being extraneous to the object, the control points do not allow for precise control of the shape. In addition, large deformations of complex objects with many details to be preserved become nearly impossible without any ”higher level” control mechanisms. User-friendly shape-control tools, therefore, generally make use of modeling techniques that integrate constraints. The present paper surveys the state-of-the-art of geometric modeling techniques that integrate constraints, including direct shape manipulation, physics-based modeling, solid modeling and freeform deformations as well as implicit surface modeling. In particular, we will focus on recent advances of multiresolution modeling of shapes under constraints. Going beyond the limits of traditional modeling techniques, they allow for editing of complex objects while automatically preserving the details.