Applying background part 3

Applying background part 3 - triangle mesh: 3F 2E under...

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33 Polygonal Meshes: Shared Vertex Data Structure (cont) vertex list (V vertices) normal list (N normal vectors) x V-1 , y V-1 , z V-1 V-1 x 1 , y 1 , z 1 1 x 0 , y 0 , z 0 0 coordinates vertex nx N-1 , ny N-1 , nz N-1 N-1 nx 1 , ny 1 , nz 1 1 nx 0 , ny 0 , nz 0 0 coordinates normal vector 34 Polygonal Meshes: Shared Vertex Data Structure (cont) face table (F faces) note that numbers in vertices and normals columns are for example only the normal vector associated with each of the vertices the vertices of the face in counterclockwise order F-1 5, 1, 9 3, 6, 9 1 0, 1, 2 (array indices into normal list) 0, 4, 5 (array indices into vertex list) 0 vertex normals vertices face
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35 Polygonal Meshes: Shared Vertex Data Structure (cont) storage requirements? need relationship between number of vertices and number of faces if the mesh has no holes (e.g. not a doughnut or torus), and if every edge is shared by exactly two polygons Euler’s formula: V – E + F = 2 # vertices – # edges + # faces = 2
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Unformatted text preview: triangle mesh: 3F 2E under these assumptions: 2 / 2 2 / 2 2 / 3 2 F V F V F F V F E V + = + 36 Polygonal Meshes: Shared Vertex Data Structure (cont) what about the number of normal vectors? impossible to say in general, but assume N V the storage requirements are: this is half the storage requirement of the first simple data structure F F F F V F V V F N V 9 6 3 6 6 6 3 3 6 3 3 = + + = + + + + 37 Polygonal Meshes: Shared Vertex Data Structure Example S x , S y , S z S R x , R y , R z R Q x , Q y , Q z Q P x , P y , P z P coordinates vertex c x , c y , c z c d x , d y , d z d b x , b y , b z b a x , a y , a z a coordinates normal d, d, d Q, P, S 3 c, c, c R, S, P 2 b, b, b R, Q, S 1 a, a, a P, Q, R normal vertex face...
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Applying background part 3 - triangle mesh: 3F 2E under...

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