LEVY, B., AND MALLET, J. Non-distorted texture mapping for sheared triangulated meshes. In Computer Graphics (SIGGRAPH 98 Proceedings) (1998), pp. 343 -- 352.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of original mesh data onto simple planar regions. Recently, there has been a bout of interest in surface mesh parameterization algorithms targeting surface texturing [3] 4] geometry approximation with semi regular approximations [5] 6] as well as general mesh parameterization techniques [7][8]. In this paper we introduce a modification to a wellknown shape preserving parameterization scheme of Michael Floater [9] We work in a setting useful to traditional remeshing algorithms that split the original surface mesh into topologically simple patches, and map each patch onto a simple ....

Levy B., Mallet J. "Non-Distorted Texture Mapping for Sheared Triangulated Meshes." Proceedings of SIGGRAPH, pp. 343--352, 1998

....atlas, mesh partitioning, parameterization, surface flattening, texture mapping, 3D painting 1 Introduction Low distortion parameterization of triangulated surfaces is a fundamental problem in computer graphics. Such parameterizations are essential for operations such as texture mapping [1, 6, 9, 11, 14, 21], texture synthesis on surfaces [17, 19, 20] interactive 3D painting [7] remeshing and multi resolution analysis [2, 8, 18] mesh compression [4, 16] and digital geometry processing [5] Since in 3D computer graphics surfaces are 2D entities (2 manifolds) embedded in 3D space, a ....

....equations whose solution provably exists, always yielding a valid planar map. However, the predefined planar boundary used by this method may yield significant distortions in the resulting parameterizations, when the parameterized surface is complex and exhibits high curvatures. Levy and Mallet [9] extend Floater s approach by defining a set of non linear constraints on the mapping that ensures local orthogonality and even spacing of isoparametric curves. The non linear system can be reduced to a set of linear systems by fixing one of the two coordinates in the plane and solving a linear ....

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Bruno Levy and Jean-Laurent Mallet. Non-distorted texture mapping for sheared triangulated meshes. Proceedings of SIGGRAPH 98, pages 343--352, July 1998.

....cost compared to other approaches which makes it particularly suitable for real time applications. However, this technique has a number of drawbacks. These are texture distortion, lack of continuity preservation and a lack of three dimensionality (application specific solutions have been published [9] [10] In addition, texture mapping can only be used for synthesis and there is no direct link to the analysis of volumetric texture. Solid texture is a more suitable approach if we are con L.Blot and R. Zwiggelaar are with the School of Information System, University of East Anglia, Norwich, ....

B. Levy and J-L. Mallet, "Non-distorted texture mapping for sheared triangulated meshes," Computer Graphics (A CM Siggraph Annual Conference Series), pp. 343-52, 1998.

....with as little distortion as possible. Our idea is to compute a (u,v) texture parameterization for both the source and destination regions, and use this mapping for the clone brush. 4. 1 Non distorted parameterization Our parameterization optimization is based on the work by Levy et al. LM98, Mal89] with three important differences: Our approach is local around the clone brushed regions, has no boundary condition, and needs to run in real time. We first quickly review the key points of their method in order to describe the specifics of our floodfill adaptation. This overview is ....

....real time. We first quickly review the key points of their method in order to describe the specifics of our floodfill adaptation. This overview is presented in our specific context, where each pixel is seen as a vertex connected to its 4 neighbors. We refer the reader to their article for details [LM98, Mal89] Levy et al. propose to minimize two classes of distortions: angular (preserve orthogonal angles) and iso parametric distance (make isolines equidistant) The former requires that the gradient of u and v be orthogonal, and the latter requires constant magnitude for their gradients. ....

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B. Levy and JL Mallet. Non-distorted texture mapping for sheared triangulated meshes. In Proc. of SIGGRAPH, 1998.

....in non distorted texture mapping fixes this problem by assigning texture coordinates such that the resulting u map is as close to similarity as possible, consisting, at least locally, of little else than rotations, translations and uniform scales. 10] 2] textcitemaillot93 and more recently [9] devised global optimization methods that assigned texture coordinates that minimized a distortion metric whereas others such as [23] instead reduced distortion by flattening the polygons onto a cube surrounding the object. We assume the u map is locally affine in that it affinely maps model ....

B. Levy and J.-L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. Proc. SIGGRAPH 98, pages 343--352, July 1998.

....algorithms begin from multiple 2D textures and require consistent statistics over these multiple views; therefore they can model only textures without large scale structures. Texture Mapping: Another body of related work is texture mapping algorithms. However, globally consistent texture mapping [14] is difficult. Often, either distortions or discontinuities, or both, will be introduced. 17] addressed this problem by patching the object with continuously textured triangles. However, this approach works only for isotropic textures, and it requires careful preparation of input texture ....

B. Levy and J.-L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. Proceedings of SIGGRAPH 98, pages 343--352, July 1998.

....triangle mesh typically comes without canonical parameterization and hence in order to derive divided difference operators we first have to find parameter values for the mesh vertices. In general, this is a hard problem if certain quality requirements for the parameterization have to be satisfied [28]. In our case, however, the problem is not as difficult since we only need local parameterizations for the construction of divided difference operators. Assume we want to compute second order partial derivatives then we have to compute a quadratic local interpolant. The interpolation problem is ....

B. Levy and J. Mallet, Non-Distorted Texture Mapping for Sheared Triangulated Meshes, SIGGRAPH 98 Proceedings, 343 -- 352

....is required. As a consequence, there will necessarily be discontinuities of the texture somewhere on the surface if the object is closed or has a higher topologic order. Moreover, the texture may be highly distorted if the object has an arbitrary geometry. Optimization techniques such as those in [1, 11] can be used to reduce distortions, either locally, or by allowing the introduction of cracks , i.e. discontinuities. Entirely suppressing distortions by editing the mapping is impossible, except if the object s surface can be unfolded onto a plane (such as a cloth) This is not the case for ....

....we have developed a specific method, described below, for assigning u;v local coordinates to mesh vertices that lie on a texture patch without producing excessively large texture distortions. Alternative (and possibly better) solutions for implementing this part of the process can be found in [10, 4, 11]. 3.2 Computing texture coordinates for mesh points The texture mesh may have been designed at either a smaller or a larger resolution than the geometric mesh that describes the object. In the latter case, the local part of the surface that falls into a patch of the texture mesh (i.e. between ....

Bruno Levy and Jean-Laurent Mallet. Non-distorted texture mapping for sheared triangulated meshes. In Michael Cohen, editor, SIGGRAPH 98 Conference Proceedings, pages 343--352. ACM SIGGRAPH, Addison Wesley, July 1998.

....triangles, edges and nodes are classified according to their belonging to a surface (S 1 or S 2 ) to the limit of the region (#S 1 or #S 2 ) or to the intersection (S 1 # S 2 ) Once the region of interest has been identified, the slip surface is locally parameterized. Parameterization [LM98,Mal01] consists in defining a bijective application : # # # x , giving the coordinates ) v u of any point ) z y x on the surface, with the minimum distortion. As any manifold surface is locally parameterizable, our method can handle closed surfaces, provided that the area of influence is ....

....coming from its star of triangles. This algorithm has been chosen because it is very fast, but it is not proven that it always ends up in a valid parameterization. In practice, we have not seen cases where the algorithm fails, but it might be interesting to use a numerical approach such as in [LM98, Lev01]. 3.2 Interactive manipulation Mouse cursor consistency In order to get a consistent 3D position from the 2D mouse cursor coordinates, a generalization of snap dragging [Bie90] has been defined for triangulated surfaces. Starting from an initial triangle (containing the previous input point) ....

B. Levy and J.L. Mallet. Non-Distorted Texture Mapping for Sheared Triangulated Meshes. In Computer Graphics (SIGGRAPH Conf. Proc.). ACM, July 1998.

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LEVY, B., AND MALLET, J. Non-distorted texture mapping for sheared triangulated meshes. In Computer Graphics (SIGGRAPH 98 Proceedings) (1998), pp. 343 -- 352.

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Bruno Levy and Jean-Laurent Mallet. Non-Distorted Texture Mapping for Sheared Triangulated Meshes. Proceedings of SIGGRAPH 98, pages 343--352, July 1998.

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Levy, "Non-Distorted Texture Mapping for Sheared Triangulated Meshes", Proceedings of Siggraph, July 1998, pp. 343-352.

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Bruno Levy and Jean-Laurent Mallet. Non-Distorted Texture Mapping for Sheared Triangulated Meshes. Proceedings of SIGGRAPH 98, pages 343--352, July 1998.

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B. Levy and J. L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. In Proc. of Compuer Graphics, Annual Conference Series, pages 343--352, 1998.

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B. Levy and J.L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. In SIGGRAPH 98, pages 343--352.

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Bruno Levy and Jean-Laurent Mallet. Non-distorted texture mapping for sheared triangulated meshes. In Proc. SIGGRAPH 98, pages 343--352, July 1998.

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Levy, B. and Mallet, J. L. Non-distorted Texture Mapping for Sheared Triangulated Meshes, In Proceedings of SIGGRAPH '98, pages 343--352, 1998.

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B. Levy and J.-L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. In M. Cohen, editor, Proceedings of SIGGRAPH 98, Computer Graphics Proceedings, Annual Conference Series, pages 343--352. Addison Wesley, July 1998.

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B. Levy and J.-L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. In Proceedings of ACM SIGGRAPH 98, pages 343--352. ACM Press, 1998.

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Levy, B., and Mallet, J. L. Non-distorted texture mapping for sheared triangulated meshes. In SIGGRAPH 98 (1998), Addison Wesley.

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B. Levy and J-L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. Proc. of SIGGRAPH, July 1998.

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B. Levy and J. L. Mallet. Non-distorted texture mapping for sheared triangulated meshes. Computer Proc. of Siggraph'98), pp. 343-352, 1998.

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Bruno Lvy and Jean-Laurent Mallet. Non-Distorted Texture Mapping for Sheared Triangulated Meshes. In Proceedings of ACM SIGGRAPH 98, August 1998.

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B. Levy and J. L. Mallet, Non-Distorted Texture Mapping for Sheared Triangulated Meshes, Computer Graphics (SIGGRAPH '98 Conference Proceedings), pp. 343-352, 1998.

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