C-Bézier and C-B-spline curves, as the trigonometric extensions of cubic uniform spline curves are well-known in geometric modeling. These curves depend on a shape parameter α in a way that α → 0 yields the cubic polynomial curves. The geometric effect of the alteration of this parameter is discussed in this paper by the help of relative parametrization and linear approximation.

We present serial and parallel algorithms for interactive rendering of large-scale NURBS models. The algorithm converts the NURBS surfaces to B ezier surfaces, tessellates each B ezier surface into triangles and renders them using the triangle rendering capabilities common to current graphics systems. This paper explains how to derive tight bounds for good quality tessellation of B ezier surfac...

A class of single-valued curves in polar coordinates, which we refer to as p-B ezier curve, has been recently presented by SS anchez-Reyes and independently discovered by P.de Casteljau. From their deenition and expression in terms of the Fourier basis it is obvious that every curve of degree n can be expressed as a curve of degree kn, for any natural value k. In this paper, we provide a formul...

We give an eecient algorithm for evaluating B ezier and B-spline tensor products for both positions and normals. The algorithm is an extension of a method for computing the position and tangent to a B ezier curve, and is asymptotically twice as fast as the standard bilinear algorithm. Many applications, such as rendering a surface using Phong shading, require evaluating both the value and deriv...

A new kind of quasi-quartic trigonometric polynomial base functions with a shape parameter λ over the space Ω=span {1, sint, cost, sint2t, cos2t} is presented, and the corresponding quasi-quartic trigonometric Bézier curves and surfaces are defined by the introduced base functions. The quasi-quartic trigonometric Bézier curves inherit most of properties similar to those of quartic Bézier curves...

Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of higher dimensional (rational) curves and (hybrid) multivariate surfaces determined by coordinate functions that are exclusively given either by traditional trigonometric or hyperbolic polynomials in each of their variable...

Recently, in the eld of entertainment, the metamorphosis of 2-D images, as it is an attractive technique, has come to be used in movies and television commercials. This technique is referred to as morphing. In the proposed method, B ezier or B-spline nets are overlapped onto digital images, and their deformation is performed by moving the control points of the nets on the images. The method pro...

abstract L-bases and B-bases are two important classes of polynomial bases used for representing surfaces in CAGD. The B ezier and multinomial bases are special cases of both L-bases and B-bases. We establish that certain proper subclasses of bivariate Lagrange and Newton bases are L-bases and certain proper subclasses of power and Newton dual bases are B-bases. A geometric point-line duality b...