G1 rational blend interpolatory schemes: A comparative study
Interpolation of triangular meshes is a subject of great interest in many computer graphics related applications, as, for example, gaming and realtime rendering. One of the main approaches to interpolate the positions and normals of the mesh vertices is the use of parametric triangular Bezier patche...
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| Published in | Graphical models Vol. 74; no. 1; pp. 29 - 49 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
Amsterdam
Elsevier
01.01.2012
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| Subjects | |
| Online Access | Get full text |
| ISSN | 1524-0703 |
| DOI | 10.1016/j.gmod.2011.11.002 |
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| Abstract | Interpolation of triangular meshes is a subject of great interest in many computer graphics related applications, as, for example, gaming and realtime rendering. One of the main approaches to interpolate the positions and normals of the mesh vertices is the use of parametric triangular Bezier patches. As it is well known, any method aiming at constructing a parametric, tangent plane (G1) continuous surface has to deal with the vertex consistency problem. In this article, we propose a comparison of three methods appeared in the nineties that use a particular technique called rational blend to avoid this problem. Together with these three methods we present a new scheme, a cubic Gregory patch, that has been inspired by one of them. Our comparison includes an analysis of their computational costs on CPU and GPU, a study of their capabilities of approximating analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use. |
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| AbstractList | Interpolation of triangular meshes is a subject of great interest in many computer graphics related applications, as, for example, gaming and realtime rendering. One of the main approaches to interpolate the positions and normals of the mesh vertices is the use of parametric triangular Bezier patches. As it is well known, any method aiming at constructing a parametric, tangent plane (G1) continuous surface has to deal with the vertex consistency problem. In this article, we propose a comparison of three methods appeared in the nineties that use a particular technique called rational blend to avoid this problem. Together with these three methods we present a new scheme, a cubic Gregory patch, that has been inspired by one of them. Our comparison includes an analysis of their computational costs on CPU and GPU, a study of their capabilities of approximating analytic surfaces and their response to different surface interrogation methods on arbitrary triangle meshes with a low triangle count that actually occur in their real-world use. |
| Author | Albrecht, Gudrun Romani, Lucia Boschiroli, Maria Fünfzig, Christoph |
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| Cites_doi | 10.1016/0010-4485(95)00046-1 10.1016/j.cag.2010.09.011 10.1016/0010-4485(88)90012-7 10.1016/0167-8396(87)90003-3 10.1016/j.cagd.2005.01.004 10.1145/263834.263849 10.1145/1457515.1409094 10.1016/0097-8493(95)00005-W 10.1145/1071866.1071882 10.1007/BF01888155 |
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| Keywords | Plane surface Rational approximation Gregory patch Shape interrogation G Free form blending Image rendering Real time Image analysis Bézier curve Graphic processing unit Computer graphics local interpolation Triangular mesh Cubics Tiling Surface fitting Bézier triangle Central unit Rational blend |
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| SubjectTerms | Applied sciences Artificial intelligence Bezier patches Blends Computational efficiency Computer science; control theory; systems Exact sciences and technology Finite element method Interrogation Mathematical models Pattern recognition. Digital image processing. Computational geometry Rendering Triangles |
| Title | G1 rational blend interpolatory schemes: A comparative study |
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