Subdivision Surfaces And Their Application In Product Design

In recent years Subdivision Surface Modeling is becoming more and more important for the researchers and the practitioners in the fields of computer graphics and computer animation owing to the following reasons:(1) Arbitrary Topology:(2) Uniformity of Representation(3) The algorithms are simple and easy to implement.(4) Levels of DetailSo Subdivision Surface Modeling is widely used in geometric designing and commercial software. This article first discusses the mathematic theory used in the subdivision surface. As the basis for subdivision surface, we discuss the curve's refinement processing such as Chaikin's cut corner curve, Uniform Quadratic B-Spline Curve and Uniform Cubic B-Spline Curve. Then we extend the curve refinement schemes to surface subdivision. We elaborate on four surface subdivision schemes. They are Loop subdivision, Modified Butterfly Subdivision, Doo-Sabin Subdivision and Catmull-Clark subdivision. We also use matrix methods to explain these methods' convergence and limitation properties. After that we detail how to apply these methods in product development and designing. Finally we present the piece-wise surface subdivision method and the solution for boundary's problem. With these methods we can create Geometric models with sharp properties.