## Texture mapping progressive meshes (2001)

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Citations: | 214 - 6 self |

### BibTeX

@INPROCEEDINGS{Sander01texturemapping,

author = {Pedro V. Sander and John Snyder and Steven J. Gortler},

title = {Texture mapping progressive meshes},

booktitle = {},

year = {2001},

pages = {409--416},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

Given an arbitrary mesh, we present a method to construct a progressive mesh (PM) such that all meshes in the PM sequence share a common texture parametrization. Our method considers two important goals simultaneously. It minimizes texture stretch (small texture distances mapped onto large surface distances) to balance sampling rates over all locations and directions on the surface. It also minimizes texture deviation (“slippage ” error based on parametric correspondence) to obtain accurate textured mesh approximations. The method begins by partitioning the mesh into charts using planarity and compactness heuristics. It creates a stretch-minimizing parametrization within each chart, and resizes the charts based on the resulting stretch. Next, it simplifies the mesh while respecting the chart boundaries. The parametrization is re-optimized to reduce both stretch and deviation over the whole PM sequence. Finally, the charts are packed into a texture atlas. We demonstrate using such atlases to sample color and normal maps over several models. Additional Keywords: mesh simplification, surface flattening, surface parametrization, texture stretch.

### Citations

514 | Multiresolution analysis of arbitrary meshes
- Eck, DeRose, et al.
- 1995
(Show Context)
Citation Context ...es in a PM using various parametrization schemes. The curve labeled “uniform” corresponds to uniform edge-spring parametrization followed by simplification minimizing texture deviation. (The harmo=-=nic [4] and-=- Floater [5] parametrizations typically have even greater stretch than the uniform parametrization.) The curve labeled “min-stretch param.” replaces the initial parametrization with our scheme of ... |

254 | Parametrization and smooth approximation of surface triangulations
- FLOATER
- 1997
(Show Context)
Citation Context ...o produce an embedding. Eck et al. [4] propose the harmonic map, which weights edge springs non-uniformly. The weights can sometimes be negative, in which case an embedding is not guaranteed. Floater =-=[5] -=-proposes a similar scheme with a different edge-spring weighting that guarantees embedding for convex boundaries. For either method, the parametrization can be found by solving a linear system. Lévy ... |

207 | Fitting smooth surfaces to dense polygon meshes
- Krishnamurthy, Levoy
- 1996
(Show Context)
Citation Context ...rface parametrization for all LODs. 2. Previous work Mesh partitioning into charts. Several authors have proposed methods for parametrizing meshes by partitioning into charts. Krishnamurthy and Levoy =-=[17]-=- describe an interactive system in which the user manually lays out chart boundaries by tracing curves. Maillot et al. [21] partition mesh faces according to a bucketing of face normals. Eck et al. [4... |

138 | Fast and memory efficient polygonal simplification
- Lindstrom, Turk
- 1998
(Show Context)
Citation Context ... and isoparametric terms in their metric. To solve the resulting nonlinear optimization, they iteratively fix one texture component (s or t) and solve for the other using a linear optimization. As in =-=[20]-=-, a term is added which must be sufficiently weighted to guarantee an embedding. Hormann and Greiner [11] propose the MIPS parametrization, which roughly attempts to preserve the ratio of singular val... |

133 | Interactive Texture Mapping
- Maillot, Yahia, et al.
- 1993
(Show Context)
Citation Context ...or parametrizing meshes by partitioning into charts. Krishnamurthy and Levoy [17] describe an interactive system in which the user manually lays out chart boundaries by tracing curves. Maillot et al. =-=[21]-=- partition mesh faces according to a bucketing of face normals. Eck et al. [4] use a Voronoi-based partition. These last two algorithms make little effort to adapt charts to surface geometry, so the c... |

132 | Appearance-Preserving Simplification
- Cohen, Olano, et al.
(Show Context)
Citation Context ...on for the entire PM sequence. Chartcompliance can be obtained by first defining the charts on the original mesh, and then constraining a simplification sequence to comply with those chart boundaries =-=[3]-=-. Therefore, our problem is the following: given an arbitrary mesh, parametrize it onto a texture atlas, and create a PM sequence compliant with the atlas charts. In doing so, we have two goals: - Min... |

122 | Hierarchical face clustering on polygonal surfaces
- Garland, Willmott, et al.
(Show Context)
Citation Context ...rst partition the mesh using a greedy chart-merging approach. It is similar to simplification schemes based on the greedy growth of “superfaces” [9][15], and to the independent work by Garland et =-=al. [6]-=-. Initially, each face is assigned to be its own chart. For each pair of adjacent charts, we consider the operation of merging the two charts into one, and enter this candidate operation into a priori... |

108 | Non-distorted texture mapping for sheared triangulated meshes
- Lévy, Mallet
- 1998
(Show Context)
Citation Context ... similar scheme with a different edge-spring weighting that guarantees embedding for convex boundaries. For either method, the parametrization can be found by solving a linear system. Lévy and Mallet=-= [19]-=- combine orthogonality and isoparametric terms in their metric. To solve the resulting nonlinear optimization, they iteratively fix one texture component (s or t) and solve for the other using a linea... |

96 |
Geometric Optimization
- Hinker, Hansen
- 1993
(Show Context)
Citation Context ...ition. Clearly this is intractable. In our system we first partition the mesh using a greedy chart-merging approach. It is similar to simplification schemes based on the greedy growth of “superfaces=-=” [9]-=-[15], and to the independent work by Garland et al. [6]. Initially, each face is assigned to be its own chart. For each pair of adjacent charts, we consider the operation of merging the two charts int... |

79 | A general framework for mesh decimation
- Kobbelt, Campagna, et al.
- 1998
(Show Context)
Citation Context ...o the vertex. Our PM is based on the half-edge collapse operaM tion (v1 , v2) � v1 which affects the neighborhood of v2 as shown on the right and leaves the position v2 and attributes of v1 unchange=-=d [16]-=-. We prefer the half-edge to the full-edge collapse to avoid writes v1 to the vertex buffer during runtime LOD changes. Therefore, (s,t) texture coordinates at any vertex must be the same at all LOD l... |

63 | Rectangle-Packing-Based Module Placement
- Murata, Fujiyoshi, et al.
- 1995
(Show Context)
Citation Context ...e long axis of the rectangle with the vertical direction. The problem then becomes that of rectangle packing, which is still NP-hard, but for which there exist good heuristic approximations (e.g. [14]=-=[24]-=-). We develop our own simple heuristic, which works as follows. We sort the rectangles by height. In order of decreasing height, we place the rectangles sequentially into rows in alternating leftto-ri... |

57 |
MIPS: An efficient global parametrization method
- HORMANN, GREINER
- 1999
(Show Context)
Citation Context ... fix one texture component (s or t) and solve for the other using a linear optimization. As in [20], a term is added which must be sufficiently weighted to guarantee an embedding. Hormann and Greiner =-=[11]-=- propose the MIPS parametrization, which roughly attempts to preserve the ratio of singular values over the parametrization. However, the metric disregards absolute stretch scale over the surface, wit... |

52 |
A Texture-Mapping Approach for the Compression of Colored 3D
- Rioux, Soucy, et al.
- 1996
(Show Context)
Citation Context ...ioned into a set of charts. Each chart is parametrized by a region of a texture domain, and these parametrizations collectively form an atlas (see Figure 4c). For instance, several schemes [2][22][25]=-=[27]-=- simplify a mesh and then construct a texture image chart over each simplified face by sampling attributes (e.g. normals) from the original mesh. For a PM, one might then consider re-using chart image... |

35 |
Maps: multiresolution adaptive parametrization of surfaces
- Lee, Sweldens, et al.
- 1998
(Show Context)
Citation Context ... Voronoi-based partition. These last two algorithms make little effort to adapt charts to surface geometry, so the chart boundaries can hinder simplification, leading to poor LOD approximations. MAPS =-=[18]-=- and Normal Meshes [8] map edges of the simplified base domain back to the original mesh. While the resulting charts adapt to surface geometry, their boundaries cut across faces of original mesh, requ... |

35 | Rotational polygon containment and minimum enclosure using only robust 2d constructions
- Milenkovic
- 1999
(Show Context)
Citation Context ...en presented for the special case of packing 3-sided charts [2][22][25][27]. However, our chart boundaries can be arbitrary polygons. The general problem is known as the NP-hard pants packing problem =-=[23]-=-. We simplify the problem by conservatively approximating each chart polygon with the least-area rectangle that encloses it. This rectangle is found efficiently by considering each edge of the polygon... |

34 | Adaptive unwrapping for interactive texture painting
- Igarashi, Cosgrove
- 2001
(Show Context)
Citation Context ...n the long axis of the rectangle with the vertical direction. The problem then becomes that of rectangle packing, which is still NP-hard, but for which there exist good heuristic approximations (e.g. =-=[14]-=-[24]). We develop our own simple heuristic, which works as follows. We sort the rectangles by height. In order of decreasing height, we place the rectangles sequentially into rows in alternating leftt... |

27 |
Hierarchical parametrization of triangulated surfaces
- Hormann, Greiner, et al.
- 1998
(Show Context)
Citation Context ...etrization approach to other multiresolution frameworks such as those using subdivision. • Speeding up the parametrization optimization of Section 3 using a hierarchical coarse-to-fine approach as i=-=n [12]. ��-=-� Given a known texture, optimizing the parametrization to consider local texture frequency content, as in [13][26]. • Addressing the problems involved when mip-mapping texture images containing mul... |

25 |
Superfaces: Polyhedral approximation with bounded error
- KALVIN, TAYLOR
- 1994
(Show Context)
Citation Context ...on. Clearly this is intractable. In our system we first partition the mesh using a greedy chart-merging approach. It is similar to simplification schemes based on the greedy growth of “superfaces”=-= [9][15]-=-, and to the independent work by Garland et al. [6]. Initially, each face is assigned to be its own chart. For each pair of adjacent charts, we consider the operation of merging the two charts into on... |

19 | Importance driven texture coordinate optimization
- Sloan, M, et al.
- 1998
(Show Context)
Citation Context ...ation optimization of Section 3 using a hierarchical coarse-to-fine approach as in [12]. • Given a known texture, optimizing the parametrization to consider local texture frequency content, as in [1=-=3][26]. ��-=-� Addressing the problems involved when mip-mapping texture images containing multiple charts. • Considering out-of-core execution for complex models. Acknowledgments We would like to thank the MIT ... |

18 |
A General Method for Recovering Attribute Values on Simplified Meshes
- CIGNONI, MONTANI, et al.
- 1998
(Show Context)
Citation Context ...t be partitioned into a set of charts. Each chart is parametrized by a region of a texture domain, and these parametrizations collectively form an atlas (see Figure 4c). For instance, several schemes =-=[2]-=-[22][25][27] simplify a mesh and then construct a texture image chart over each simplified face by sampling attributes (e.g. normals) from the original mesh. For a PM, one might then consider re-using... |

15 |
Generating a Texture Map from Object-Surface Texture Data
- Maruya
- 1995
(Show Context)
Citation Context ...e partitioned into a set of charts. Each chart is parametrized by a region of a texture domain, and these parametrizations collectively form an atlas (see Figure 4c). For instance, several schemes [2]=-=[22]-=-[25][27] simplify a mesh and then construct a texture image chart over each simplified face by sampling attributes (e.g. normals) from the original mesh. For a PM, one might then consider re-using cha... |

14 | Uniform frequency images: adding geometry to images to produce space-efficient textures
- Hunter, Cohen
- 2000
(Show Context)
Citation Context ...trization optimization of Section 3 using a hierarchical coarse-to-fine approach as in [12]. • Given a known texture, optimizing the parametrization to consider local texture frequency content, as i=-=n [13][26]-=-. • Addressing the problems involved when mip-mapping texture images containing multiple charts. • Considering out-of-core execution for complex models. Acknowledgments We would like to thank the ... |

9 |
Progressive Meshes", SIGGRAPH
- Hoppe
- 1996
(Show Context)
Citation Context ...trization, texture stretch. 1. Introduction The progressive mesh (PM) representation encodes an arbitrary mesh as a simple base mesh M 0 and a sequence of n refinement operations called vertex splits =-=[10]. -=-It defines an array {M 0 …M n } of level-of-detail (LOD) approximations, and supports geomorphs and progressive transmission [1]. Unlike multiresolution frameworks based on subdivision, the meshes i... |