1. ALGORITHMS FOR POLYGON REDUCTION Author: Ing. Roman Schulz FIT VUT, 2008

2. Purpose of work It is not possible to display all models in scene in full detail, because their rendering takes too much gpu time. Detail view requires a quality model Far objects may use much lower level of detail It is expensive to create objects with lower detail by hand

3. Object simplification Simplified object may create Graphic designer – hard work, he may to do more important and interesting work. Advantage of such simplification is that only a graphic designer knows, which parts of object are important and needs more detail. Independent application – It is necessary to select only an algorithm and a quality, and then verify a simplified object. It is also possible to simplify many models by script to save time and money.

4. Selecting of edge to remove Simplification is done by removing of edges, which are at least important Selection of that edge is done by used metric size of edge – Importance of each edge is done by its length. This metric is very fast. error quadrics – fast and good quality edge andles – Metric was described in Game Developer's Magazine – It is quite slow, but perfect quality progressive meshes

5. Edge remove Select at least important edge and remove it. It also removes two triangles adjacent with edge and one point. Process of removing edge uv – Remove all triangles which contains both points u and v (ie. edge uv )‏ – Update all other triangles which contains point u to use point v instead of point u – Remove point u

6. Quality of metrics We have done thousands of tests on various 3d models Quadric error metrics produces the best results But it is possible to try all metrics and select the highest quality model

7. Application structure Modular design makes it possible to include any block into existing project (program or game). It is also possible to add new file format support One of most important features is 3ds file format support, which is commonly used for 3d file exchange

8. Program control Settings of all features is done by command line parameters. This way is useful for batch processing of many models at a time by script../reducer.exe -i - Input file -o - Output file -q - quality settings 0-100 -a - algorithm settings -b – Preserve borders of object -j – Preserve borders between materials...and others(see parameter --help)‏

9. Example – Reduction of object with 60.000 polygons to 50%, 25% and 10% of original size

10. References [1] David Luebke, Martin Reddy, Jonathan Cohen. Level of Detail for 3D Graphics. Morgan Kaufmann Publishers, 2003 [2] Stan Melax. A Simple, Fast and Effective Polygon Reduction Algorithm. Game Developer Magazine, November 1998 [3] P. Lindstrom, G. Turk. Fast and memory efficient polygonal simplification. IEEE Visualization 98 Conference Proceedings, 1998. [4] M. Garland, P. Heckbert. Surface simplification using quadric error metrics. SIGGRAPH 97 Conference Proceedings, 1997 [5] William Schroeder, Jonathan Zarge, William Lorensen. Decimation of triangle meshes. SIGGRAPH 92 Conference Proceedings, 1992 [6] Hugues Hoppe, Tony DeRose. Mesh Optimization. Proceedings of SIGGRAPH 93. 1993

11. Questions?