摘要
Engineering design and geometric modeling often require the ability to modifythe shape of parametric curves and surfaces so that their shape satisfy some given geometricconstraints, including point, normal vector, curve and surface. Two approaches are presented todirectly manipulate the shape of B-spline surface. The former is based on the least-square, whereasthe latter is based on minimizing the bending energy of surface. For each method, since unified andexplicit formulae are derived to compute new control points of modified surface, these methods aresimple, fast and applicable for CAD systems. Algebraic technique is used to simplify the computationof B-spline composition and multiplication. Comparisons and examples are also given.
Engineering design and geometric modeling often require the ability to modifythe shape of parametric curves and surfaces so that their shape satisfy some given geometricconstraints, including point, normal vector, curve and surface. Two approaches are presented todirectly manipulate the shape of B-spline surface. The former is based on the least-square, whereasthe latter is based on minimizing the bending energy of surface. For each method, since unified andexplicit formulae are derived to compute new control points of modified surface, these methods aresimple, fast and applicable for CAD systems. Algebraic technique is used to simplify the computationof B-spline composition and multiplication. Comparisons and examples are also given.
基金
This project is supported by Teaching and Research Award Program for Outstanding Young Professors in Higher Education Institute, Ministry of Education, China.
