Title: Dynamic evaluation of free-form curves and surfaces
Free-form curves and surfaces defined by control points together with various varieties of basis functions are frequently used in Computer Aided Geometric Design. Efficient evaluation of points and derivatives of free-form curves and surfaces plays important roles for interactive rendering or CNC machining. In this presentation we show that almost all free-form curves used in CAGD are the solutions of linear differential systems. By employing typical numerical methods for solving the differential systems, points and derivatives of free-form curves and surfaces can be computed in a dynamical way. There are two advantages of the proposed technique for evaluating free-form curves and surfaces than other known methods. First, the proposed method is universal and efficient for evaluating free-form curves and surfaces. Second, the evaluation needs only arithmetic operations even when the free-form curves and surfaces are defined using some transcendental functions. (This is a joint work with Jialin Hong from CAS.)
Brief Bio: Xunnian Yang is now an associate professor at the school of mathematical sciences, Zhejiang University. He obtained a PhD in Zhejiang University in 1998. His major research interests include spans of CAGD, particularly spline and subdivision based techniques for shape representation and geometric modeling. Recently, he also studies differential geometry, ODE and PDE based methods for shape modeling and geometric processing.