Decimation of Triangle Meshes
description
Transcript of Decimation of Triangle Meshes
![Page 1: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/1.jpg)
visualization and graphics research group
CIPIC
Decimation of Triangle Meshes
William J. Schroeder, Jonathan A. Zarge, William E. Lorensen
Presented by
Alden ChewSerban Porumbescu
![Page 2: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/2.jpg)
visualization and graphics research group
CIPIC
What is the Problem?
• Want to visualize data interactively• Too many triangles• Too little hardware
![Page 3: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/3.jpg)
visualization and graphics research group
CIPIC
High Level Approach
• Characterize the local vertex geometry and topology
• Evaluate decimation criteria for vertex removal
• Triangulate the resulting hole
![Page 4: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/4.jpg)
visualization and graphics research group
CIPIC
Vertex Classification
•Feature edge: dihedral angle greater than user specified feature angle
•An interior edge vertex is a vertex with two feature edges
•A corner has one, three, or more feature edges
![Page 5: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/5.jpg)
visualization and graphics research group
CIPIC
Vertex Removal
• Based on user specified distance to plane or distance to edge (boundary vertex)
![Page 6: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/6.jpg)
visualization and graphics research group
CIPIC
Vertex Removal
• Removal of vertex creates a hole in the mesh– Triangulate
• Removal of feature edge:– Create a new feature edge– If two non-overlapping loops can be created,
triangulate the two loops
![Page 7: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/7.jpg)
visualization and graphics research group
CIPIC
Triangulate Resulting Hole
• Triangulate using a recursive loop splitting procedure
• The stencil of the hole is called a loop• Loops are divided into two parts by a
split line • Split line
– A line between two non-adjacent vertices in the loop
![Page 8: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/8.jpg)
visualization and graphics research group
CIPIC
Split Plane
• Split plane– The plane orthogonal to the average plane
through a split line
• Used for half space comparisons
![Page 9: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/9.jpg)
visualization and graphics research group
CIPIC
Loop Splitting Procedure
• Need to create two non-overlapping loops
• A valid loop is entirely on one side of the split plane ….
• If the loop contain more than three vertices, recurse
• If the loop has three vertices, form a triangle
![Page 10: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/10.jpg)
visualization and graphics research group
CIPIC
Split Line Selection
• Many split lines to choose from• Choose line that maximizes the aspect
ratio• The aspect ratio is the minimum
distance of the loop vertices to the split plane divided by the length of the split line
![Page 11: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/11.jpg)
visualization and graphics research group
CIPIC
Special Cases
• Want to preserve topology • Don’t create duplicate triangles and
triangle edges
![Page 12: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/12.jpg)
visualization and graphics research group
CIPIC
Sample Run From VTK (US Patent Number 5,559,388)
![Page 13: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/13.jpg)
visualization and graphics research group
CIPIC
Skull
![Page 14: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/14.jpg)
visualization and graphics research group
CIPIC
Blade
![Page 15: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/15.jpg)
visualization and graphics research group
CIPIC
Hawaii
![Page 16: Decimation of Triangle Meshes](https://reader036.fdocuments.us/reader036/viewer/2022062422/56813c5b550346895da5dc7e/html5/thumbnails/16.jpg)
visualization and graphics research group
CIPIC
Mars