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We present a new method of surface generation from prescribed boundaries based on the elliptic partial differential operators. In particular, we focus on the study of the so-called harmonic and biharmonic Bézier surfaces. The main result we report here is that any biharmonic Bézier surface is fully determined by the boundary control points. We compare the(More)
In this paper we present a method for generating Bézier surfaces from the boundary information based on a general 4th-order PDE. This is a generalisation of our previous work on harmonic and biharmonic Bézier surfaces whereby we studied the Bézier solutions for Laplace and the standard biharmonic equation, respectively. Here we study the Bézier solutions of(More)
Interactive design of practical surfaces using the partial differential equation (PDE) method is considered. The PDE method treats surface design as a boundary value problem (ensuring that surfaces can be defined using a small set of design parameters). Owing to the elliptic nature of the PDE operator, the boundary conditions imposed around the edges of the(More)
—One of the challenging problems in geometric modeling and computer graphics is the construction of realistic human facial geometry. Such geometry are essential for a wide range of applications, such as 3D face recognition, virtual reality applications, facial expression simulation and computer based plastic surgery application. This paper addresses a(More)
We propose the use of Partial Differential Equations (PDEs) for shape modelling within visual cyberworlds. PDEs, especially those that are elliptic in nature, enable surface modelling to be defined as boundary-value problems. Here we show how the PDE based on the Bihar-monic equation subject to suitable boundary conditions can be used for shape modelling(More)