We discuss rational parameterizations of surfaces whose support functions are rational functions of the coordinates specifying the normal vector and of a given non-degenerate quadratic form. The class of these surfaces is closed under offsetting. It comprises surfaces with rational support functions and non-developable quadric surfaces, and it is a subset of the class of rational surfaces with ...

We present a reverse engineering method for constructing a surface approximation scheme whose input is a set of unorganized noisy points in space and whose output is a set of quadric patches. The local surface properties, necessary for the subsequent segmentation, are estimated directly from the data using a simple and efficient data structure the neighborhood graph. Our segmentation scheme, ba...

We consider projective rational strong Calabi dream surfaces: smooth surfaces which admit a constant scalar curvature Kähler metric for every class. show that there are only two such surfaces, namely the plane and quadric surface. In particular, we all other than those destabilising slope test configuration some polarisation, as introduced by Ross Thomas. further Hirzebruch surface with Picard ...

A line symmetric motion is the motion obtained by reflecting a rigid body in the successive generator lines of a ruled surface. In this work we review the dual quaternion approach to rigid body displacements, in particular the representation of the group SE(3) by the Study quadric. Then some classical work on reflections in lines or half-turns is reviewed. Next two new characterisations of line...

In this paper we review the derivation of implicit equations for non-degenerate quadric patches in rational Bézier triangular form. These are the case of Steiner surfaces of degree two. We derive the bilinear forms for such quadrics in a coordinate-free fashion in terms of their control net and their list of weights in a suitable form. Our construction relies on projective geometry and is groun...

This paper describes an efficient representation for real-time mapping and rendering of surface details onto arbitrary polygonal models. The surface details are informed as depth maps, leading to a technique with very low memory requirements and not involving any changes of the model’s original geometry (i.e., no vertices are created or displaced). The algorithm is performed in image space and ...

I was a graduate student at the Mas-sachusetts Institute of Technology. The rst three years of these studies were supported by an NSF Graduate Student Fellowship. My research there led to a Ph.D. thesis entitled \Noncommutative ruled surfaces." My thesis research describes certain classes of graded rings which arise as homogeneous coordinate rings of noncommutative quantizations of algebraicall...