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Simple Constrained Deformations for Geometric Modeling and 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 (Scodef). *
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.

* ACM Transactions on Graphics, * 13(2):137-155, 1994.