Simple Constrained Deformations for Geometric Modeling and Interactive Design

Deformations are a powerful tool for shape modeling and design. We present a new model for producing controlled spatial deformations, which we term Simple Constrained Deformations 1994. The user defines a set of constraint points, giving a desired displacement and radius of influence for each. Each constraint point determines a local B-spline basis function centered at the constraint point, falling to zero for points beyond the radius. The deformed image of any point in space is a blend of these basis functions, using a projection matrix computed to satisfy the constraints. The deformation operates on the whole space regardless of the representation of the objects embedded inside the space. The constraints directly influence the final shape of the deformed objects, and this shape can be fine-tuned by adjusting the radius of influence of each constraint point. The computations required by the technique can be done very efficiently, and real-time interactive deformation editing on current workstations is possible.