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...

ACKNOWLEDGEMENTS In the name of Allah, Most Gracious, Most Merciful All praise and glory to Almighty Allah (Subhanahu Wa Taalaa) who gave me courage and patience to carry out this work. Peace and blessing of Allah be upon last Prophet Muhammad (Peace Be Upon Him). Acknowledgment is due to King Fahd University of Petroleum & Minerals for supporting this research. My unrestrained appreciation goe...

In volume-rendering applications, an appropriate resampling filter can be chosen by making a compromise between quality and efficiency. For realtime volume visualization, usually the trilinear filter is used, since its evaluation is directly supported by the recent GPUs. Although higher-order filters (e.g. quadratic or cubic filters) ensure much higher image quality, due to their larger support...

Introduction 3D reconstruction of an object from its 2D cross-sections (slices) has many applications in different fields of sciences such as medical physics and biomedical engineering. In order to perform 3D reconstruction, at first, desired boundaries at each slice are detected and then using a correspondence between points of successive slices surface of desired object is reconstructed. Mate...

In this study, a modeling study was carried out on the weekly average values of henna partridge egg production. For purpose, yields 148 days from herd consisting 320 breeders were taken and cubic spline, Gompertz, Logistic, Richard, Schunute, Quadratic Spline, McNally Gamma equations used in modeling. comparison goodness fit equations, Determination Coefficient〖(R〗^2), Mean Square Error (MSE), ...

Spline quasi-interpolants are local approximating operators for functions or discrete data. We consider the construction of discrete and integral spline quasi-interpolants on uniform partitions of the real line having small infinite norms. We call them near minimally normed quasi-interpolants: they are exact on polynomial spaces and minimize a simple upper bound of their infinite norms. We give...

Uniform cubic B-spline functions have been used for mapping functions in various areas such as image warping and morphing, 3D deformation, and volume morphing. The injectivity (one-to-one property) of a mapping function is important to obtain good results in these areas. This paper considers the local injectivity conditions of 2D and 3D uniform cubic B-spline functions. We propose a geometric i...

We characterize of the Bernstein-Bezier (BB) form of an implicitly deened bivariate polynomial over a triangle, such that the zero contour of the polynomial deenes a smooth and single sheeted real algebraic curve segment. We call a piecewise G k-continuous chain of such real algebraic curve segments in BB-form as an A-spline (short for algebraic spline). We prove that the degree n A-splines can...

We study the curvature variation functional, i.e., the integral over the square of arc-length derivative of curvature, along a planar curve. With no other constraints than prescribed position, slope angle, and curvature at the endpoints of the curve, the minimizer of this functional is known as a cubic spiral. It remains a challenge to effectively compute minimizers or approximations to minimiz...