Implicitization using moving planes and moving quadrics

In this talk, I will first review some recent work on constructing moving quadrics from moving planes that follow a tensor product surface with no base points, assuming that there are no moving planes of low degree following the surface. The I will discuss the possibility of extending the results to more general cases.Non UBCUnreviewedAuthor affiliation: University of Science and Technology of ChinaFacult

Degree reduction of disk Bézier curves

A disk Bézier curve is a Bézier curve whose control points are disks in a plane. It can be viewed as a parametric curve with error tolerances. In this paper, we discuss the problem of degree reduction of disk Bézier curves, that is, bounding disk Bézier curves with lower degree disk Bézier curves. We propose an efficient method to solve this problem. The algorithm starts by finding an optimal approximation to the center curve of the original disk Bézier curve, which is served as the center curve of the degree reduced disk Bézier curve. Then the radius of the degree reduced disk Bézier curve is computed by solving some linear programming problems, and for which analytic solutions are obtained. Finally, we analyze the bounding errors for the degree reduction algorithm and provide some examples to show the effectiveness of the proposed algorithm

Geometric Computation

Ouvrage (éditeur).The book comprises three closely related parts: the first is devoted mainly to curve and surface modeling, and contains one general survey on theoretical and practical applications of algebraic methods and three specialized surveys on surface blending, parametrization, and implicitization, followed by four research papers. The second part is concentrated on geometric reasoning, with one tutorial survey on Clifford algebra approaches, another on automated deduction in real geometry, and one research article. The last part is highlighted by a chapter that outlines a theory of real approximation, based on a generalization of the central idea of exact geometric computation. The book ends with one paper on A-resultant quotients and another on face recognition, which show how computer algebra and artificial intelligence meet geometry in the era of computation