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A Unified Approach for Hierarchical Adaptive Tesselation of Surfaces
 ACM Transactions on Graphics
, 2000
"... This paper introduces a unified and general tesselation algorithm for parametric and implicit surfaces. The algorithm produces a hierarchical mesh that is adapted to the surface geometry and has a multiresolution and progressive structure. This representation can be exploited with advantages in seve ..."
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Cited by 9 (0 self)
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This paper introduces a unified and general tesselation algorithm for parametric and implicit surfaces. The algorithm produces a hierarchical mesh that is adapted to the surface geometry and has a multiresolution and progressive structure. This representation can be exploited with advantages in several applications.
Efficient and Accurate Tessellation of Implicit Sweep Objects
 In Constructive Solid Geometry
, 1998
"... The isosurface model, in which a 3D implicit object is created by computing the isosurface of a potential field generated by a set of sources, is considered by several authors [4, 18] as a superset of the CSG model, because it allows the user to define soft blending operators in addition to the mo ..."
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Cited by 7 (2 self)
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The isosurface model, in which a 3D implicit object is created by computing the isosurface of a potential field generated by a set of sources, is considered by several authors [4, 18] as a superset of the CSG model, because it allows the user to define soft blending operators in addition to the more usual boolean combinations. The isosurface model preserves many advantages of the CSG model (storage compactness, inside/outside function, arbitrary topology) but unfortunately also its main drawback, that is the difficulty to generate an efficient and accurate tessellation of the surface, in order to use hardware rendering and texturing algorithms. This paper proposes a solution to achieve this goal for a specific (but very large) subset of isosurfaces: implicit sweeps. The implicit sweep model that we presented in [8] provides high level primitives (i.e. generalized sweeps) that can be used to build freeform implicit objects. One interesting characteristic of implicit sweeps is that ...
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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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...
A Unified Approach for Hierarchical Adaptive Tesselation of Surfaces
 ACM Transactions on Graphics
, 1999
"... ..."
Robust Adaptive Polygonal Approximation of Implicit Curves
"... We present an algorithm for computing a robust adaptive polygonal approximation of an implicit curve in the plane. The approximation is adapted to the geometry of the curve because the length of the edges varies with the curvature of the curve. Robustness is achieved by combining interval arithmet ..."
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Cited by 1 (0 self)
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We present an algorithm for computing a robust adaptive polygonal approximation of an implicit curve in the plane. The approximation is adapted to the geometry of the curve because the length of the edges varies with the curvature of the curve. Robustness is achieved by combining interval arithmetic and automatic differentiation.
Modelling and Sampling Ramified Objects with SubstructureBased Method
"... Abstract. This paper describes a technique that speeds up both the modelling and the sampling processes for a ramified object. By introducing the notion of substructure, we divide the ramified object into a set of ordered substructures, among which only a part of basic substructures is selected fo ..."
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Abstract. This paper describes a technique that speeds up both the modelling and the sampling processes for a ramified object. By introducing the notion of substructure, we divide the ramified object into a set of ordered substructures, among which only a part of basic substructures is selected for implicit modelling and point sampling. Other substructures or even the whole object can then be directly instantiated and sampled by simple transformation and replication without resorting to the repetitive modelling and sampling processes. 1
A Methodology for Piecewise
"... 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. ..."
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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.
Implicit Linear Interval Estimations
, 2002
"... Visualization and collision detection are two of the most important problems connected with implicit objects. Enumeration algorithms can be used either directly or as preprocessing step for many algorithms solving these problems. In general, enumeration algorithms based on recursive space subdivisio ..."
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Visualization and collision detection are two of the most important problems connected with implicit objects. Enumeration algorithms can be used either directly or as preprocessing step for many algorithms solving these problems. In general, enumeration algorithms based on recursive space subdivision are reliable tools to encounter those parts in space, where the object might be located. But the bad performance and the huge number of computed enclosing cells, if high precision is required, are grave drawbacks. Implicit Linear Interval Estimations (ILIEs) introduced in this paper are implicit interval (hyper)planes providing oriented tight bounds of the object within given cells. It turns out that the use of ILIEs highly improves the performance of the classical enumeration algorithm and the quality of the results. The theoretical background as well as a fast and simple technique to compute ILIEs are presented. The applicability of ILIEs is demonstrated by means of a modified enumeration algorithm that has been implemented and tested for implicit surfaces.