Interaction with Geometry video now public on GDC Vault
Posted: Sun May 03, 2015 11:05 pm
My 2013 Math Tutorial video on GDC Vault is now publicly accessible:
http://www.gdcvault.com/play/1017654/Ma ... nteraction
I suspect most people here on the Bullet Physics forum are probably very competent with math and geometry already. Nonetheless, being the last Math Tutorial session of the day, after the first 15 minutes of easy material, I did delve into some advanced topics - including some tidbits that, to the best of my knowledge, haven't been covered elsewhere. Perhaps interesting or educational to some people here.
At the 16 minute mark, the talk describes convex hull generation including the simple approach of adding tetrahedrons and deleting back-to-back triangles and also explains how to overcome the numerical robustness issues.
At the 24m:20s mark begins a section about about boolean operations and leads up to a plane quantization trick that avoids numerical precision robustness issues when doing geomod/destruction. The technique isn't dependent on a particular type of spatial structures, hence I didn't get into BSP merging (not enough time anyways).
At 34 minutes, talk dives into the derivation of the formulas behind tetrahedral summation approach for computing the inertia tensor.
At 46 minutes, the focus shifts to soft-body/cloth and shows the trade-offs between force-based implicit integration methods and iterative position projection approaches. Unfortunately, didn't have time to go into detail about the remaining compression instability that Baraff and Witkin describe in section 7 in their 1998 siggraph paper. The slide at 55 minutes includes a tiny sidenote about a better way to avoid this problem without resorting to adaptive time stepping.
Enjoy.
-stan
http://www.gdcvault.com/play/1017654/Ma ... nteraction
I suspect most people here on the Bullet Physics forum are probably very competent with math and geometry already. Nonetheless, being the last Math Tutorial session of the day, after the first 15 minutes of easy material, I did delve into some advanced topics - including some tidbits that, to the best of my knowledge, haven't been covered elsewhere. Perhaps interesting or educational to some people here.
At the 16 minute mark, the talk describes convex hull generation including the simple approach of adding tetrahedrons and deleting back-to-back triangles and also explains how to overcome the numerical robustness issues.
At the 24m:20s mark begins a section about about boolean operations and leads up to a plane quantization trick that avoids numerical precision robustness issues when doing geomod/destruction. The technique isn't dependent on a particular type of spatial structures, hence I didn't get into BSP merging (not enough time anyways).
At 34 minutes, talk dives into the derivation of the formulas behind tetrahedral summation approach for computing the inertia tensor.
At 46 minutes, the focus shifts to soft-body/cloth and shows the trade-offs between force-based implicit integration methods and iterative position projection approaches. Unfortunately, didn't have time to go into detail about the remaining compression instability that Baraff and Witkin describe in section 7 in their 1998 siggraph paper. The slide at 55 minutes includes a tiny sidenote about a better way to avoid this problem without resorting to adaptive time stepping.
Enjoy.
-stan