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Interactive Rendering of Parametric Spline Surfaces
, 1996
"... This dissertation presents techniques for fast rendering of parametric spline surfaces. It presents algorithms and data structures needed to support the thesis that realtime display of surfaces (represented parametrically) is indeed possible on current graphics systems that are optimized to display ..."
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This dissertation presents techniques for fast rendering of parametric spline surfaces. It presents algorithms and data structures needed to support the thesis that realtime display of surfaces (represented parametrically) is indeed possible on current graphics systems that are optimized to display triangles. It analyzes the sources of bottleneck in surface rendering and derives techniques to display tens of thousands of B'ezier surfaces, 10 \Gamma 20 times a second, by efficiently utilizing the graphics hardware. In a more general framework, this work demonstrates the effectiveness of using higherorder surfaces, as opposed to polygons. Analytic representation of surfaces retains information that is often lost in a static translation to polygons. We meaningfully use this analytic information to obtain better images than those generated from purely polygonal models. On the other hand, since current graphics systems are optimized for displaying triangles, we perform online triangulati...
Modeling and Animation of Generalized Cylinders with Variable Radius Offset Space Curves
 THE JOURNAL OF VISUALIZATION AND COMPUTER ANIMATION
, 1994
"... A method is presented for the modeling and animation of generalized cylinders with variable radius offset space curves. The boundary surface of a generalized cylinder is constructed: either as a translational sweep of crosssectional curves along the skeleton curve, or as a rotational sweep of profi ..."
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Cited by 6 (0 self)
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A method is presented for the modeling and animation of generalized cylinders with variable radius offset space curves. The boundary surface of a generalized cylinder is constructed: either as a translational sweep of crosssectional curves along the skeleton curve, or as a rotational sweep of profile curves around the skeleton curve. The crosssectional curves are computed as the variable radius offset curves of a circle in the normal plane, and the profile curves are computed as the variable radius offset space curves of the skeleton curve. The offset curves are approximated by spline curves, and the boundary surface of a generalized cylinder is approximated by the tensor product surface patches of the offset spline curves.
A Methodology for Piecewise Linear Approximation of Surfaces
, 1997
"... We discuss the problem of adaptive polygonization of regular surfaces of the euclidean 3D space, and present effective algorithms for computing optimal polygonizations of surfaces described in parametric or implicit form. Keywords: Surface approximation, polygonization, parametric surfaces, implici ..."
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Cited by 3 (2 self)
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We discuss the problem of adaptive polygonization of regular surfaces of the euclidean 3D space, and present effective algorithms for computing optimal polygonizations of surfaces described in parametric or implicit form. Keywords: Surface approximation, polygonization, parametric surfaces, implicit surfaces, geometric modeling. 1 Introduction The polygonization of surfaces is a classical problem in computer graphics and geometric modeling that has many practical applications. The problem is computing a piecewise linear approximation for a smooth surface described either in parametric or implicit form. In this paper, we present a conceptual framework for the piecewise linear approximation of surfaces and also a methodology for computing good polygonal approximations while keeping the number of polygons low. Based on the general principles in this methodology, we describe two specific new algorithms for the adaptive polygonization of parametric and implicit surfaces. 1.1 Importance...
Optimal Adaptive Polygonal Approximation of Parametric Surfaces
 In Proceedings of SIBGRAPI '96 (Brazilian Symposium on Computer Graphics and Image Processing
, 1996
"... We present a new method for adaptive polygonization of parametric surfaces. The method combines recursive simplicial subdivision of the domain and point sampling along curves on the surface. We avoid cracks in the polygonal mesh by determining the optimal sampling rate along the edges of a cell be ..."
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We present a new method for adaptive polygonization of parametric surfaces. The method combines recursive simplicial subdivision of the domain and point sampling along curves on the surface. We avoid cracks in the polygonal mesh by determining the optimal sampling rate along the edges of a cell before subdividing it. The method is suitable for surfaces with low variations, such as bicubic patches, as well as for surfaces with high variations, such as height fields.
NorthHolland Surface algorithms using bounds on derivatives
, 1987
"... Abstract. This paper generalizes three very important algorithms for surfaces which previously only worked well with polynomials. The algorithms are calculation of piecewise linear approximations, minmax boxes, and surface/surface intersections. The class of surfaces that can be handled are all par ..."
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Abstract. This paper generalizes three very important algorithms for surfaces which previously only worked well with polynomials. The algorithms are calculation of piecewise linear approximations, minmax boxes, and surface/surface intersections. The class of surfaces that can be handled are all parametric C 2 surfaces. All the algorithms are related by theorems from approximation theory which give information about the maximum deviation an approximation to a surface can have if bounds on partial derivatives are known. We generalize these theorems to work with parametric geometry, and we also show how to obtain the necessary bounds.