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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)
This paper extends the PDE method of surface generation. The governing partial differential equation is generalised to sixth order to increase its flexibility. The PDE is solved analytically, even in the case of general boundary conditions, making the method fast. The boundary conditions, which control the surface shape, are specified interactively,(More)
  • Hassan Ugail
  • 2003
The spine of an object is an entity that can characterise the object's topology and describes the object by a lower dimension. It has an intuitive appeal for supporting geometric modelling operations. The aim of this paper is to show how a spine for a PDE surface can be generated. For the purpose of the work presented here an analytic solution form for the(More)