3 Meshes. Strips, Fans, Indexed Face Sets. Display Lists, Vertex Buffer Objects, Vertex Cache

Transcription

1 3 Meshes Strips, Fans, Indexed Face Sets Display Lists, Vertex Buffer Objects, Vertex Cache

2 Intro generate geometry triangles, lines, points glbegin(mode) starts primitive then stream of vertices with glvertex( ) vertices interpreted according to mode mode can be:

3 Intro primitive assembly: how to interpret stream of incident vertices? glbegin(gl_triangles); glvertex(0,0,0); glvertex(1,0,0); glvertex(1,1,0); glend(); vertex shader vertex stream primitive assembly vertex stream geometry shader rasterizer pixel stream

4 Triangle meshes isolated triangles: glbegin(gl_triangles); glvertex(v1); tri 1 glvertex(v2); glvertex(v3); glvertex(v4); glvertex(v5); glvertex(v6); glend(); tri 2 v1 v6 v3 v2 3n vertices for n triangles 3n vertices processed by geometry stage v5 v4

5 Triangle meshes triangle fans glbegin(gl_triangle_fan); glvertex(v1); glvertex(v2); glvertex(v3); glvertex(v4); glvertex(v5); glvertex(v6); glvertex(v2); glend(); v2 v6 v1 v3 v5 v4 n+2 vertices for n triangles three times less work for geometry stage!

6 Triangle meshes triangle strips v2 v4 v6 v8 v10 v1 v3 v5 glbegin(gl_triangle_strip); glvertex(v1); glvertex(v2); tri 1 glvertex(v3); tri 2 glvertex(v4); tri 3 glvertex(v5); for n triangles, n+2 vertices must pass geometry stage v7 v9 v11

7 Triangle meshes triangle strips v2 v4 v6 v8 v10 v1 v3 v5 v7 v9 v11 in OpenGL: vertices v1, v2, v3... triangles: (v1,v2,v3), (v2,v3,v4), (v3,v4,v5),...

8 Triangle meshes general triangle strips v9 v10 v2 v4 v6 v8 v1 v3 v5 v7 triangles:... (v6,v7,v8), (v6,v8,v9), (v8,v9,v10)... not directly supported by OpenGL

9 Triangle meshes v9 v10 general triangle strips v2 v4 v6 v8 conversion: v1,v2,v3,v4,v5,v6,v7,v6,v8,v9,v10 delivers:...(v5,v6,v7), (v6,v7,v6), (v7,v6,v8), (v6,v8,v9),... v1 dummy triangle v3 v5 v7

10 Triangle meshes indexed face sets in OpenGL provide vertex data in an array float pos[n] = { x1,y1,z1, x2,y2,z2,...}; glvertexpointer(pos); also normal, texture coordinates, color arrays possible: float norm[n] = { nx1,ny1,nz1, nx2,ny2,nz2,...}; glnormalpointer(norm); draw entire stream by providing index list int index[m] = {0,1,2, 1,2,3, 1,3,5,...}; gldrawelements(gl_triangles,m,index);

11 Vertex Buffer Objects (VBOs) remaining problem with glvertexpointer(): data still on client side (main memory) must be transfered to video memory for rendering (in fast streaming mode) Vertex Buffer Object: abstraction for access to video memory can hold vertex data (vertex array with position, normal, ) can hold triangle indices (element array) as fast as display lists memory manager: if data does not entirely fit to video memory swap in and out transparently

12 Vertex Buffer Objects glgenbuffer() generate Vertex Buffer Object returns ID for new object glbindbuffer() from now on, all calls to glvertexpointer(), glxxxpointer() refer to buffer pointers are now relative to this buffer, i.e. they start with 0 glbufferdata() load data into currently bound VBO glmapbuffer(), glunmapbuffer() map VBO to main memory CPU can access data via normal pointer unmap maps changes back to video memory

13 Vertex Buffer Objects example (from NeHe tutorials) // Generate And Bind The Vertex Buffer // Get A Valid Name glgenbuffersarb( 1, &m_nvbovertices ); // Bind The Buffer glbindbufferarb( GL_ARRAY_BUFFER_ARB, m_nvbovertices ); // Load The Data glbufferdataarb( GL_ARRAY_BUFFER_ARB, m_nvertexcount*3*sizeof(float), m_pvertices, GL_STATIC_DRAW_ARB ); // bind buffer glbindbufferarb( GL_ARRAY_BUFFER_ARB, m_nvbovertices); // Set The Vertex Pointer To The Vertex Buffer glvertexpointer( 3, GL_FLOAT, 0, (char *) NULL );

14 Batches sending a complete mesh via glvertex is very expensive due to the large number of function calls display lists are better best way to go nowadays: vertex buffer objects remaining bottle neck: batch number (= number of gldrawelements calls) we can submit about batches per second (CPU bound) 10 or triangles per batch makes no real difference see: Batch, Batch, Batch: What Does It Really Mean

15 Triangle meshes acceleration techniques Stripification: convert mesh to triangle strips Vertex Cache: cache for processed vertices

16 Stripification we need mesh as Indexed Face Set with Neighborhood vertex list per vertex: (x,y,z) coordinate triangle list per triangle: vertex indices, neighbor indices example: vertex list v1...v5 triangle list: T1: v1,v3,v5; T2,NIL,T3 T2: v3,v4,v5; NIL,T1,NIL T3: v1,v2,v3; NIL,T1,NIL v2 v4 v3 T2 T3 T1 v5 v1

17 Stripification goal: search optimal decomposition into triangle strips reduced work for vertex unit memory efficient way to store topology (1+ε indices / triangle) increase cache coherence complexity: NP complete, i.e. generally not doable for typical meshes with thousands of vertices

18 Stripification most simple approach 1. random select of unused triangle 2. start a triangle strip along one edge until the boundary or a used triangle is reached 3. continue triangle strip in opposite direction 4. continue with step 1, until all triangles are used

19 Stripification SGI approach (from SGI demo): more intelligent selection of start triangle: search triangle with least unused neighbors if not unique: select triangle whose neighbors have the least unused neighbors motivation: triangles with few neighbors can quickly get isolated and then result in bad strips of lenght 1

20 Stripification Example: selection first triangle all boundary triangles have two neighbors

21 Stripification Example: Selection first triangle all boundary triangles have two neighbors four of them have neighbors with also only two neighbors

22 Stripification Example: Selection first triangle all boundary triangles have two neighbors four of them have neighbors with also only two neighbors select one of them

23 Stripification Example: Selection first triangle all boundary triangles have two neighbors four of them have neighbors with also only two neighbors select one of them

24 Stripification Example: Selection second triangle select on of the four candidates

25 Stripification Example: Selection second triangle select on of the four candidates continue strip

26 Stripification Example: selection third triangle continue strip

27 Vertex Cache indexed face sets in OpenGL provide vertex data in an array float pos[n] = { x1,y1,z1, x2,y2,z2,...}; glvertexpointer(pos); also normal, texture coordinates, color arrays possible: float norm[n] = { nx1,ny1,nz1, nx2,ny2,nz2,...}; glnormalpointer(norm); draw entire stream by providing index list int index[m] = {0,1,2, 1,2,3, 1,3,5,...}; gldrawelements(gl_triangles,m,index);

28 Vertex Cache graphics stores the vertex program result of the last n vertices reuse cached results if possible typical vertex cache size: 24 Example: Indizes 0,1,2, 3,2,5, 1,3,4, 4,2,3, 6,7,8,... Misses & Hits: 0,1,2, 3,2,5, 1,3,4, 4,2,3, 6,7,8

29 Vertex Cache Properties: optimal ratio triangles / vertices is 2, i.e. from n vertices, 2n triangles are generated! only possible with indexed face sets find cache entries by index comparison optimization for vertex cache tricky Demo NVTriStrips (

30 Cache Oblivious Mesh Layout more general way to improve cache coherence Yoon et al., Siggraph 2005 (see webpage: following slides from this website given is arbitrary triangle mesh as indexed face set search optimal order for indices that minimizes cache misses general idea: metric for cache coherent vertex order of meshes optimize vertex order

31 Cache Oblivious Mesh Layout overview vb va vc vd Input graph Multilevel optimization va vb vd vc Cache-oblivious metric Local permutations Result 1D layout

32 Cache Oblivious Mesh Layout Undirected graph, G = (V, E) Represents access patterns of applications Vertex can be mesh triangle or can be mesh vertex Edge Connects two vertices if they are likely to be accessed sequentially if vertices are mesh triangles: sort triangle list cache friendly if vertices are mesh vertices: sort vertex list cache friendly vb va vc vd

33 Cache Oblivious Mesh Layout Vertex layout of G = (V, E) One to one mapping of vertices to indices in the 1D layout ϕ : { 1,..., V } V vb va vd va vb vd vc vc ϕ Compute a that minimizes the expected number of cache misses

34 Cache Oblivious Mesh Layout Optimization by swapping vertex orders Vertex layout here: v_c is used in triangle abc, so it should be close to a and b swapping 4th and 5th vertex (v_c and v_e) decreases probability of cache misses

35 Cache Oblivious Mesh Layout How can we formalize this? edge span of (va, vb) = ϕ( v ) ϕ( v ) a b ϕ( v ) = a 1 Layout mapping ϕ( v ) ϕ( v ) = a c 4 ϕ( v ) = c 5

36 Cache Oblivious Mesh Layout E i Set of edges having edge span i in the layout 44 ( v, v ) E a c 4

37 Cache Oblivious Mesh Layout Edge span distribution Ei where i is in [1, n] E 1 = E 1 2 = E 1 3 = E 4 = Number of edges Edge span 1

38 Cache Oblivious Mesh Layout Probability of a cache miss for a given edge span i Cache miss ratio = Probability to have a cache miss 1 0 p i i Edge span 1 n-1

39 Cache Oblivious Mesh Layout Estimated by multiplying two factors Runtime edge span distribution CMRF Runtime edge span distribution CMRF ( p 2 + p 4 + p 2 ) = (2,1) (p 2,p 4 ) Edge span 2 Edge span 4 Edge span 2 1D Layout:

40 Cache Oblivious Mesh Layout Approximate runtime edge span distribution with one of the layout The number of vertices Edge span distribution of the layout n 1 i= 1 E p i i

41 Cache Oblivious Metric Decides if a local permutation reduces number of cache misses Probabilistic formulation Reduces to geometric volume computation

42 Does a Local Permutation Decrease Cache Misses? n 1 i= 1 n? E p > i i i= 1 1 ( E i +Δ E i ) p i Ei E + Δ E i i

43 Does a Local Permutation Decrease Cache Misses? n 1 i= 1 n E p > i i = i 1 1 ( E i +Δ E i ) p i n 1 i=1 Δ E p i i < 0

44 Monotonocity of CMRF, pi Assume CMRF is a monotonically increasing function of edge span Cache miss ratio 1 0 p i 1 i Edge span

45 Exact Cache Oblivious Metric n 1 i=1 Δ E p i i where All the possible cache configurations < 0 Monotonicity of CMRF 0 p p... p p 1 2 n 2 n 1 1

46 Geometric Formulation Half hyperspace n 1 Δ E p i i < 0 p 2 i=1 where 0 p 1 0 p p... p p 1 2 n 2 n 1 Closed hyperspace R n 1 1 p 2 0 p 1

47 Geometric Volume Computation Assume each CMRF to be equally likely n 1 i=1 Δ E i p i < 0 where 0 p p2... p n 2 pn 1 1 Half hyperspace (blue area) Space of CMRFs that reduce cache misses 1 p 2 0 p 1

48 Cache Oblivious Mesh Layout optimize by deciding about local permutations Exact: O(n n +1) [Lasserre and Zeron 01] Appr.: O(n 5 ) [Kannan et al. 97] practical algorithm in paper Process 70 million vertices per hour Takes 2.6 hours to lay out St. Matthew model (372 million triangles) 2.4GHz of Pentium 4 PC with 1 GB main memory

49 Cache Oblivious Mesh Layout Peak performance: 145 M tri / s on GeForce 6800 Ultra Models # of Tri. Our layout Simplification layout [Yoon et al. 04] St. Matthew 372M 106 M/s 23 M/s 4.5X Isosurface 100M 90 M/s 20 M/s Double Eagle Tanker 2.1X 82M 47 M/s 22 M/s

50 video (quicktime) Cache Oblivious Mesh Layout