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The goal of this research is to develop and improve design methodology for free-form surfaces capable of intuitively defining sculptured shapes with minimum input.
A method is being developed for defining free-form surfaces using geometric and physical constraints. Physical constraints allow surface behavior to be defined independently of the large number of degrees of freedom in mathematical representation.
The research deals with parametric surfaces such as Non Uniform B-Splines (NURBS) surfaces. Such surfaces provide a powerful tool for representing free-form shapes. With this new approach, internal deformations and other physical quantities can be incorporated into parametric surfaces. Through application of simulated forces and local and global shape constraints, surfaces are moved and deformed in a physically intuitive way in response to the user's direct manipulations .
Optimizing algorithms are being developed derived from geometric and physical constraints operating on surfaces. Non-linear equations describing geometric and physical constraints are solved through numerical methods in order to find the deformed surface. This technique can be used to simulate forces and imitate surface behavior. Variable magnitude and direction forces.
P. Kagan, "Surface Design
with Geometrical and Physical Constraints," (M.Sc. Thesis, Mechanical Engineering,
Technion, July 1997.