Study and application of physics-based deformable curves and surfaces

Physics-based deformable curve and surface modeling techniques are presented. The new approach is efficient and easy to use in many aspects of geometric design. Its applications include the construction of N-sided patches, surface smooth joining, curve and surface fairing, etc. The equations of motion for the deformable curves and surfaces are derived using the Lagrangian mechanics and are solved by the finite element method. The constraints, such as the position of points on curves or surfaces, the tangent plane and cross-derivative of surface are implemented through the penalty function methods.