Deformation Calculation of Curve under Constraints

A new approach is proposed in the paper on the B-spline curve deformation controlled by global geometric constraints. When a CAD software environment is involved, curve deformation has to accurately meet some geometric constraints often associated with the functional requirements. Here the deformation method is called parametric deformation technique, and the expression of the deformed curve apart from that of initial curve represents a curve called displacement curve. By minimizing the energy of displacement curve under linear constraints, the deformation formula is obtained, and the formula is used as a foundation in calculating the deformation under non-linear constraints. The method proposed in this paper can be used in a 2D parametric design system.