Subdivision surfaces were applied to the entire meshes in order to produce smooth surfaces refinement from coarse mesh. Several schemes had been introduced in this area to provide a set of rules to converge smooth surfaces. However, to compute and render all the vertices are really inconvenient in terms of memory consumption and runtime during the subdivision process. It will lead to a heavy co...

Normal Doo-Sabin subdivision surfaces are based on uniform quadratic B-splines. This makes it somewhat more difficult to produce an object with sharp creases or corners using normal Doo-Sabin subdivision. Non-Uniform Subdivision Surfaces on the other hand, allow for the possibility of creating an object that will keep specific points sharp based on the knot intervals that a particular edge is a...

In this paper, we provide formal definitions for object space, space subdivision and ray tracing. We also introduce concept models such as ordered space subdivisions and ordered visualization. From these works, we can evaluate the correctness and performance of our space subdivision scheme for volume visualization. With these definitions, we also analyze some established space subdivision appro...

1, Department of Mathematics, University of Sargodha, Sargodha, Pakistan Department of Mathematics, COMSATS Institute of Information Technology, Sahiwal, Pakistan [email protected]; [email protected]; [email protected] ABSTRACT. This paper presents the general formula for surface subdivision scheme to subdivide quad meshes by using Lagrange interpolating polynomial. We can see t...

The length Λ of a given rational Bézier curve is efficiently estimated. Since a rational Bézier function is nonlinear, it is usually impossible to evaluate its length exactly. The length is approximated by using subdivision and the accuracy of the approximation Λn is investigated. In order to improve the efficiency, adaptivity is used with some length estimator. A rigorous theoretical analysis ...