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Date: Wed, 18 Jun 97 14:15:41 -0700 From: Robert ZakoSubject: Speed Tests on Mesh, Polyhedron and Trimesh Geometries INTRODUCTION At Artifice, Inc., we have also just completed extensive tests on rendering speeds using mesh, polyhedron and trimesh geometries. We rendered using the wire frame renderer, the interactive renderer with Apple hardware acceleration, and the interactive renderer without hardware acceleration. We also measured binary 3DMF files sizes and file reading/writing times. METHODOLOGY We generated test files consisting of 2-dimensional arrays of 1x1x1 blocks. Each test file contained 1, 100, 1000, 3000 or 10000 blocks that were identical except for their positions. By testing files with different numbers of blocks, we could distinguish the fixed rendering overhead time from the variable per object rendering time. We generated test files using several different kinds of blocks: solid, textured and tunneled. (See the detailed descriptions below and the sample 3DMF files, available on request. Please contact support@artifice.com.) Each solid block had 8 vertices and 6 square faces. For the polyhedron and trimesh geometries, each square face was represented by 2 triangles created by dividing the square along its diagonal. Thus each polyhedron or trimesh geometries had 12 triangles. Using TQ3PolyhedronEdgeMask values, the diagonals in the polyhedron blocks were made invisible. The trimesh geometry does not support invisible edges. Each textured block had 14 vertices and 6 square faces. The additional vertices were duplicates required to get the surface UV parametrization correct. See Figure 4-5 in "3D Graphics Programming With QuickDraw 3D 1.5" and join the 6 faces together to form a "T". For the polyhedron and trimesh geometries, all faces were triangulated as for the solid blocks. Each textured block had its own surface UV parametrization vertex attributes, but the texture shader was applied globally to the entire model. Each tunneled block was a solid block with a square hole cut from the front face through to the back face. As a result, the front and back faces were ring-shaped and the tunnel added 4 rectangular faces. Thus each tunneled block had 16 vertices, 4 square faces, 4 rectangular faces, and 2 ring-shaped faces. For the polyhedron and trimesh geometries, each square or rectangular faces was represented by two triangles; each ring-shaped face was represented by 8 triangles. Thus each polyhedron or trimesh geometry had 32 triangles. Note that rendering times vary due to caching. We repeated each measurement several times and used the MINIMUM rendering time, which appeared to be the most stable value. We ran our tests on a Power Mac 8600/200 with 64M of RAM and an Apple graphics accelerator card. All files were opened with a version of DesignWorkshop that logs timing data. RESULTS All times are in ticks (1 tick = 1/60 second). A smaller time is better. The rate is the number of objects rendered per second after adjusting for the fixed rendering overhead time. The rate was computed using a linear regression through the data points. The rate is reported in 1000's of objects per second. Thus "4.1" means 4100 objects per second. A larger rate is better. WIRE FRAME RENDERER Total Number of Objects Kind Geometry 1 100 1000 3000 10000 Rate -------- ---------- -- --- ---- ---- ----- ---- solid mesh 2 4 17 46 n/a 4.1 " polyhedron 2 3 6 12 32 20.3 " trimesh 2 3 7 15 41 15.7 textured mesh 2 5 26 74 n/a 2.5 " polyhedron 2 3 6 12 n/a 18.4 " trimesh 2 3 7 16 n/a 13.0 tunneled mesh 2 7 48 134 n/a 1.4 " polyhedron 2 3 9 21 60 10.4 " trimesh 2 4 13 32 95 6.5 Looking at the rates, observe that the polyhedron geometry is somewhat faster than the trimesh geometry. This makes sense when you realize that the trimesh geometries are rendering diagonal lines whereas the polyhedron geometries are not. It is more difficult to understand why the meshes are so slow: After all, the wire frame renderer is merely drawing lines. For any geometry, it is only necessary to transform the vertices from local to window coordinates and then draw lines between them. Also observe that the polyhedron geometry is 5-7 times faster than the mesh geometry, which does not seem to make sense. After all, the wire frame renderer is merely drawing lines. For any geometry, it is only necessary to transform the vertices from local to window coordinates and then draw lines between them. Why should meshes be so much slower here? Finally, note that rendering tunneled blocks takes 2-3 times longer, in proportion to the added topological complexity. Similarly, adding textures slows down the rendering somewhat, which is probably due to the added topological complexity since the textures are not actually rendered by the wire frame renderer. INTERACTIVE RENDERER (WITH APPLE ACCELERATOR CARD) Total Number of Objects Kind Geometry 1 100 1000 3000 10000 Rate -------- ---------- -- --- ---- ---- ----- ---- solid mesh 5 5 26 71 n/a 2.7 " polyhedron 4 4 13 32 93 6.8 " trimesh 4 4 9 22 63 10.1 textured mesh 5 7 41 118 n/a 1.6 " polyhedron 4 6 25 67 n/a 2.9 " trimesh 4 5 15 31 n/a 6.6 tunneled mesh 6 10 67 186 n/a 1.0 " polyhedron 6 6 28 75 233 2.6 " trimesh 6 6 19 47 138 4.5 Looking at the rates, observe that the trimesh geometry is 1.5-2.5 times faster than the polyhedron geometry and 3.5-4.5 times faster than the mesh geometry. As expected, adding textures or tunnels slows down the rendering time, in line with the added topological and/or textural complexity. INTERACTIVE RENDERER (SOFTWARE) Total Number of Objects Kind Geometry 1 100 1000 3000 10000 Rate -------- ---------- -- --- ---- ---- ----- ---- solid mesh 15 18 38 83 n/a 2.7 " polyhedron 15 16 24 39 93 7.7 " trimesh 15 16 21 32 72 10.6 textured mesh 15 20 50 125 n/a 1.6 " polyhedron 15 18 37 76 n/a 3.0 " trimesh 15 17 26 40 n/a 7.3 tunneled mesh 15 22 77 188 n/a 1.0 " polyhedron 15 16 36 77 216 3.0 " trimesh 15 16 27 50 128 5.3 Again, the trimesh geometry is 1.5-2.5 times faster than the polyhedron geometry and 3.5-5.5 times faster than the mesh geometry. Surprisingly, for large models, the interactive renderer is hardly slower and in some cases even faster without hardware acceleration than with hardware acceleration. Looking at the column for models with only 1 object, we see that it takes 15 ticks (1/4 second) to render small models. This seems like an a long time considering that the renderer has to do little other than copy bits to a buffer and then to the screen: There is so little geometry that the computation time should be negligible. Lastly, we also looked at file sizes and file reading/writing times. The file size rate is in bytes/object. The reading/writing rates are in 1000's of objects per second. The reading/writing rates adjust for any fixed overhead time and only reflect the variable time per object. BINARY 3DMF FILE Size Read Write Kind Geometry Rate Rate Rate -------- ---------- ---- ---- ---- solid mesh 236 0.2 0.4 " polyhedron 308 1.9 0.5 " trimesh 192 2.2 0.6 textured mesh 792 0.03 0.1 " polyhedron 864 0.1 0.2 " trimesh 412 1.3 0.5 tunneled mesh 452 0.06 0.4 " polyhedron 724 0.9 0.4 " trimesh 348 1.5 0.5 Note that binary files with trimesh geometries are the smallest; binary files with polyhedron geometries are the largest. Note that solid and tunneled trimesh files read slightly faster than corresponding polyhedron files. In contrast, textured trimesh files read 9 times faster than textured polyhedron files. The large difference is probably due to the more efficient handling of attributes by trimeshes. Even more dramatic, trimesh files read 13 or more times faster than corresponding mesh files. The greatest difference is for textured files (which contain attributes). Why does it take so excruciatingly long to open files with meshes? Trimesh files also write faster than polyhedron or mesh files, although the differences are much less dramatic than for reading. CONCLUSIONS By most measures, trimeshes outperform polyhedra which outperform meshes. One notably exception: With the wire frame renderer, polyhedra render faster than trimeshes (assuming that some internal lines are made invisible) and for some applications look much better.

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