Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009...
-
Upload
christine-lisa-young -
Category
Documents
-
view
214 -
download
0
Transcript of Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009...
![Page 1: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/1.jpg)
Mesh Quilting For Geomet-ric Texture Synthesis
Kun Zhou et al.In SIGGRAPH 2006
발표 이성호2009 년 4 월 15 일
![Page 2: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/2.jpg)
2
Abstract
• Mesh quilting– Geometric texture synthesis algorithm– 3D texture sample given in the form of a triangle
• inside a thin shell around an arbitrary surface
• Allow interactive and versatile editing and animation
• Based on stitching together 3D geometry elements
• On curved surfaces– Reduce distortion of geometry elements
• inside the 3D space of the thin shell
– Low-distortion parameterization
![Page 3: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/3.jpg)
3
Introduction
• Today’s commodity video cards– Exquisite details can be purely geometrically
modeled
• Modeling such complex geometric de-tails– A tedious process
• Creating mesh-based 3D geometric tex-tures– Remains challenging
![Page 4: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/4.jpg)
4
Mesh quilting
• To synthesize geometric details by stitching together small patches – of an input geometric texture sample
• Tools to further edit and animate – these geometric details
![Page 5: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/5.jpg)
5
![Page 6: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/6.jpg)
6
Related work
• Modeling of Geomet-ric Detail on Surfaces– Fur• [Kajiya and Kay 1989]
– Rendering fur with three dimensional textures.
– In Proceedings of SIG-GRAPH 89
– Volume textures• [Neyret 1998]
![Page 7: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/7.jpg)
7
• More versatile repre-sentations– Geometric textures• [Elber 2005]
– Shell map• [Porumbescu et al.
2005]
![Page 8: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/8.jpg)
8
• Limitations– Periodic textures
• Mesh-based creation – Of geometric textures on arbitrary
meshes– [Fleischer et al. 1995]–Mostly restricted to the dissemination • Of simple texture elements over the surface
![Page 9: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/9.jpg)
9
Example-based Texture Syn-thesis
• Synthesis based on per-pixel non-parametric sampling– [Turk 2001;Wei and Levoy 2001; Ying et
al. 2001; Tong et al. 2002; Zelinka and Garland 2003]
• Based on the L2-norm– a relatively poor measure
• of perceptual similarity,
– such algorithms are not applicable • to a large spectrum of textures.
![Page 10: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/10.jpg)
10
• Textures by directly copying small parts – of an input texture sample– alpha-blending [Praun et al. 2000]– quilting
• [Efros and Freeman 2001; Liang et al. 2001; Soler et al. 2002; Magda and riegman 2003; Kwatra et al. 2003; Wu and Yu 2004; Zhou et al. 2005]
• Searching for the “min-cut” seams– further enhance the smoothness across the
seams• [Efros and Freeman 2001; Kwatra et al. 2003; Zhou et
al. 2005]
![Page 11: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/11.jpg)
11
• Feature matching– [Wu and Yu 2004]– Human visual system is so sensitive
• to edges, corners and other high-level features in tex-tures
• Parallel controllable texture synthesis on GPU– [Lefebvre and Hoppe 2005]
• Texture synthesis using Expectation Maximiza-tion optimization– [Kwatra et al. 2005]
![Page 12: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/12.jpg)
12
Graphcut textures
![Page 13: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/13.jpg)
13
![Page 14: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/14.jpg)
14
![Page 15: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/15.jpg)
15
Shell map
![Page 16: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/16.jpg)
16
![Page 17: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/17.jpg)
17
![Page 18: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/18.jpg)
18
Challenges
• Little work to provide tool – for 3D geometric texture synthesis.• [Bhat et al. 2004; Lagae et al. 2005]
[Lagae et al. 2005]
![Page 19: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/19.jpg)
19
• [Bhat et al. 2004] – voxel-based approach
• [Lagae et al. 2005] – used distance fields
[Bhat et al. 2004]
![Page 20: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/20.jpg)
20
Challenges
• Irregular mesh– The input texture sample
• is not a regular array of pixel values
• Geometry elements– Each being truly a small 3D object identified
• As a connected component in 3D
• Quilting is performed on curved surfaces– Severe distortion in the 3D space
![Page 21: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/21.jpg)
21
Contributions
• Mesh-based geometric texture synthesis– Synthesized over the base mesh.
• Triangle meshes– Both the input geometry and output geometry
• Integrity– Maintains the integrity of geometry elements
• In the synthesized texture• Texture editing and texture animation
– can be easily performed
![Page 22: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/22.jpg)
22
• Aligns elements – through local deformation– And merges elements to connect texture
patches
• Mesh quilting on curved surfaces– Low-distortion parameterization • of the shell space
![Page 23: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/23.jpg)
23
Mesh Quilting Synthesis
• Setup & Nomenclature
![Page 24: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/24.jpg)
24
Algorithm Overview
• Seed Finding– Find a seed region R from which to grow the output mesh texture
further out
• Geometry Matching– Find the best patch placement around region R using geometry
matching to minimize mismatch between the new and the old patch
• Element Correspondences– Find correspondences between elements in the new patch and
those in the old patch
• Element Deformation– Align the corresponding elements through local deformation
• Element Merging– Expand the output texture by merging the new patch into the
output texture space
![Page 25: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/25.jpg)
25
![Page 26: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/26.jpg)
26
Seed Finding
• Grid-based approach– The bounding boxes of both Mout and Min are subdi-
vided in finer regular grids
• These grids are only two-dimensional• Initially, the cells of Mout are tagged unprocessed
• Each time we wish to grow out the current mesh Mout, – we look for an unprocessed cell with the largest
number of adjacent cells that are already processed• this will be the seed cell that we will try to process next.
![Page 27: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/27.jpg)
27
Geometry Matching
• Find how to complete the mesh tex-ture in the seed cell– and possibly add to its surroundings too.
Using the nearby existing mesh texture available near the seed cell
– Find a portion of the original swatch Min best matching this surrounding to ex-tend Mout .
![Page 28: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/28.jpg)
28
![Page 29: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/29.jpg)
29
![Page 30: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/30.jpg)
30
• Restrict the translation t to be in – grid unit
• Element deformation described in Section 2.6 – will compensate for an imperfect ele-
ment alignment
• Octree data structure for the input texture– Significant speed-up
![Page 31: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/31.jpg)
31
Element Correspon-dences
• the overlapping region is usually larger than the small sub-patch Pout – since the input mesh texture covers Pout
completely.
![Page 32: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/32.jpg)
32
![Page 33: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/33.jpg)
33
Element Deformation
![Page 34: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/34.jpg)
34
![Page 35: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/35.jpg)
35
![Page 36: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/36.jpg)
36
Element Merging
• Every element (either from Cout or Cin) without correspondence – directly added to Mout .
• For every established correspondence (Cout ,Cin)– If Cout is entirely within the overlapping re-
gion, Cout is ignored • and Cin is instead added to the final results
– if Cin is entirely within the overlapping region,• Cin is ignored and Cout is added to Mout .
![Page 37: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/37.jpg)
37
In all other cases
• stitch parts of Cin and Cout– to get a singly-connected, combined element– seek a cut path in each element– the graph cut algorithm
• [Boykov et al. 2001]
![Page 38: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/38.jpg)
38
![Page 39: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/39.jpg)
39
![Page 40: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/40.jpg)
40
![Page 41: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/41.jpg)
41
Mesh Quilting Over Curved Surfaces
• Setup– Let Mbase be the base mesh that we wish
to enhance with added geometric de-tails.
–Min the geometric texture mesh • used as a swatch
– seamlessly tile the base mesh
– S• the scale of the geometric details
![Page 42: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/42.jpg)
42
From Planar to Curved
• 2D grid -> base mesh– Quilting process will stop
• Only when there are no more unprocessed triangles
• Define a local surface patch – By starting from the chosen triangle – Growing the region
• Using breadth-first traversal – Until we reach a certain depth– Or when the total area of the patch exceeds a user-
defined threshold
![Page 43: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/43.jpg)
43
• Position of vertices located with re-spect to the base mesh
• Location of a vertex v – over a triangle Tbase – is defined by the barycentric coordinates – of its orthogonal projection • on Tbase
– along with the orthogonal distance (i.e., height) » from the triangle to v
![Page 44: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/44.jpg)
44
discrete conformal map-ping
• surface patch is flattened over the 2D plane – using a discrete conformal mapping• DCM [Desbrun et al. 2002]
![Page 45: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/45.jpg)
45
• Local operations – Described for planar mesh quilting– Can be performed • Over this parameterization plane
• Position of the newly synthesized vertices–Will be reprojected • Onto the local mesh-based coordinate sys-
tem
![Page 46: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/46.jpg)
46
in very curved regions
• If the area distortion induced – by the local parameterization is too
large– Reduce the area of the surface patch• This will decrease
– the size of the output-sub-patch Pout
![Page 47: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/47.jpg)
47
Final Mesh Embedding
• Convert the vertex positions– Stored in local coordinates for now– Into a stand-alone, common embedding
• Self-intersections can be created• Build a texture atlas for Mbase
– Convert the above local representation of vertex positions to locations • in a geometry texture space
• Then, construct a shell space around Mbase– Mapping the vertices
• from the geometry texture space to the shell space– will fix the location of the vertices in 3D space
![Page 48: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/48.jpg)
48
![Page 49: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/49.jpg)
49
![Page 50: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/50.jpg)
50
Shell Mapping
• Porumbescu et al. [2005]– Creates large distortion in curved re-
gions
• We alleviate this!– By optimizing a stretch metric on this
tetrahedral mesh– A natural extension of • low-distortion parameterization
– of triangle meshes
• [Sander et al. 2001]
![Page 51: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/51.jpg)
51
![Page 52: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/52.jpg)
52
![Page 53: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/53.jpg)
53
Minimization Algorithm
• Only update the u and v texture co-ordinates of the vertices on the offset surface
• Optimization of the stretch metric – along a randomly chosen search direc-
tion – in the (u, v) plane – as in [Sander et al. 2001].
![Page 54: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/54.jpg)
54
![Page 55: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/55.jpg)
55
![Page 56: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/56.jpg)
56
![Page 57: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/57.jpg)
57
![Page 58: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/58.jpg)
58
Discussions
• Regions with very high curvature can be badly handled– parametric distortion of small surface
patches may be high
• Cannot always achieve perfect matching – if the swatch is untileable
• even with major element deformation
– Postprocessing step is performed • to remove those visually-displeasing elements• Figure 5(b)
![Page 59: Mesh Quilting For Geometric Texture Synthesis Kun Zhou et al. In SIGGRAPH 2006 발표 이성호 2009 년 4 월 15 일.](https://reader035.fdocument.pub/reader035/viewer/2022062519/5697bfbf1a28abf838ca3307/html5/thumbnails/59.jpg)
59
Conclusions
• Mesh-based 3D texture synthesis al-gorithm