1 / 22

Meshes

Meshes. faces. vertices. Triangular Mesh (or mesh). A mesh is a set of adjacent triangles. edges. Topological properties of a mesh. Two Manifold or not yes if each edge is shared by max 2 faces two manifold = good not two manifold = bad

caine
Télécharger la présentation

Meshes

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Meshes

  2. faces vertices Triangular Mesh (or mesh) • A mesh is a set of adjacent triangles edges

  3. Topological properties of a mesh • Two Manifold or not • yes if each edge is shared by max 2 faces • two manifold = good • not two manifold = bad • most algorithms on meshes assume it is two-manifold NO YES

  4. Topological properties of a mesh • Closed or open • When closed, each edge is shared by exactly two faces

  5. Topological properties of a mesh • Coherent orientation • Is it possible to assign to each face an orientation so that the overall assignment is coherent? • Coherent orientation = coherent normals! A 1 1 3 D 2 3 2 C B Opposite direction, coherent edge

  6. How can we define a mesh? • A mesh is a set of adjacent triangles • How can we define it? • Direct way: • An array of triangles • and for each triangle three vertices • and for each vertex three coordinate

  7. How can we define a mesh? • Indexed mode • Ordered list of vertices • for each vertex its position • Ordered list of faces • for each face, 3 indices to vertices

  8. What about the attributes? • Can be defined: • per vertex • Define an attribute for each vertex • per face • Define an attribute for each face • per wedge (vertex of face) • Define three attributes for each face • Most common attributes: • color • Texture coordinates • Normals

  9. Example: PLY format • Digital format for meshes • Can be either binary, or ASCII (text) • binary: more compact and easy to machine-read • ascii: human-readable with a text-editor • In both cases, it starts with an ASCII header.

  10. Example: PLY format cube.ply ply format ascii 1.0 comment a simple cube element vertex 8 property float x property float y property float z element face 12 property list uchar int vertex_indices end_header

  11. # faces # edges # vertices first face: 4 vertices: with indices 3,2, 1 and 0 index 0 x,y,z 2nd vertex index 1 index 2 index 3 Example: OFF format LetterL.off OFF12 10 400 0 03 0 03 1 01 1 01 5 00 5 00 0 13 0 13 1 11 1 1 1 5 10 5 14 3 2 1 04 5 4 3 04 6 7 8 94 6 9 10 114 0 1 7 64 1 2 8 74 2 3 9 84 3 4 10 94 4 5 11 104 5 0 6 11

  12. Mesh: common tasks • Given a mesh: compute the bounding box • Very useful in many applications, e.g. collisions • How to compute it? • We cycle on the vertices: compute the max and the min of all x, y and z

  13. Mesh: common tasks • Given a mesh: compute the normals per vertex • How? • 1 Set all the vertex normals to 0 • 2 cycle on each face: • compute the normal • normalize it • add it to the vertex normal • 3 cycle on each vertex: • normalize the normal

  14. More difficult tasks • Compute a Bounding sphere • Stripification • Parametrize • Automated simplification • Detail recovery • ...

  15. More difficult tasks • Stripification • Organize the triangles in triangle strips • As long as possible

  16. More difficult tasks • Parameterization • assign a pair of texture coordinates to each wedge • When there are seams (lines appearing in two separate images) • replicate the vertices • Save the texture coordinates for each wedge v

  17. More difficult tasks • Automated simplification • Parameters: A maximal error or a given number of faces automatically mesh originale 500K triangles mesh semplificata 2K triangles

  18. Automated simplification p e r f o r m a n c e q u a l i t y

  19. Automated simplification A hierarchy of Levels of Detail LOD 2 LOD 3 LOD 4 LOD 1 To be used when viewer is far away To be used when viewer is nearby

  20. Detail preservation (or texture for geometry) • Idea: • Synthesize a texture • To compensate for the detail lost during simplification

  21. Ad-hoc created TEXTURE detail recovery rendering 2k triangles, with texture mapping 500k triangles Automated simplification 2k triangles

  22. simplified but textured 2K triangles originale 500K triangles simplified 2K triangles

More Related