| No | curve | equation 1 | supports | # mixed subdivisions | Enum by reverse search (sec) 2 | TOPCOM point2alltriang (sec) 3 | TOPCOM point2triang(sec) 4 | # mixed cell configurations | # extreme terms | # all terms |
|---|---|---|---|---|---|---|---|---|---|---|
| 1. | astroid | acos(t)^3,asin(t)^3 | supports | 289 | 193.62 | 0.048 | 0.452 | 289 | 35 | 454 |
| 2. | cardioid | a(2cos(t)-cos(2t)),a(2sin(t)-sin(2t)) | supports | 37 | 6.52 | 0.005 | 0.024 | 37 | 10 | 33 |
| 3. | circle | cos(t),sin(t) | supports | 5 | 0.004 | 0.016 | 0.004 | 5 | 3 | 4 |
| 4. | conchoid | a+cos(t),ah+sin(t) | supports | 12 | 0.84 | 0.003 | 0.008 | 12 | 4 | 6 |
| 5. | ellipse | acos(t),bsin(t) | supports | 5 | 0.15 | 0.001 | 0.004 | 5 | 3 | 4 |
| 6. | folium of descartes | 3ah/(1+h^3),3ah^2/(a_h^3) | supports | 14 | 0.94 | 0.004 | 0.008 | 14 | 6 | 10 |
| 7. | involute of a circle | a(cos(t)+t(sin(t)),a(sin(t)-tcos(t)) | supports | 14 | 1.00 | 0.001 | 0.007 | 14 | 6 | 7 |
| 8. | nephroid | a(3cos(t)-cos(3t)),a(3sin(t)-sin(3t)) | supports | 289 | 195.27 | 0.004 | 0.240 | 289 | 35 | 454 |
| 9a. | plateau curve | asin(3t)/sin(t),2asin(2t) | supports | 94 | 33.02 | 0.012 | 0.064 | 94 | 15 | 55 | 9b. | plateau curve | asin(6t)/sin(2t),2asin(4t) | supports | 42168 | halt | 25.934 | 85.597 | 42168 | 495 | not computed |
| 10. | talbot's curve | (a^2 - 2f^2 + (f^2)sin(t)^2)sin(t)/b | supports | 1944 | 3948.80 | 0.416 | 2.356 | 1944 | 84 | 1600 |
| 11. | tricuspoid | a(2cos(t)+cos(2t)),a(2sin(t)-sin(2t)) | supports | 37 | 6.20 | 0.008 | 0.024 | 37 | 10 | 33 |
| 12. | witch of agnesi | ah,a/(1 + h^2) | supports | 2 | 0.03 | 0.007 | 0.004 | 2 | 2 | 2 |
| 13. | circle (3 systems) | -t^2 + 1/s, 2t/s, t^2 -s + 1 | supports | 26 | 6.00 | 0.020 | 0.052 | 26 | 6 | 7 |
| No | surface | equation 1 | supports | # mixed subdivisions | Enum by reverse search (sec) 2 | TOPCOM point2alltriang (sec) 3 | TOPCOM point2triang(sec) 4 | # mixed cell configurations | # extreme terms | # all terms |
|---|---|---|---|---|---|---|---|---|---|---|
| 1. | cylinder | cos(t),sin(t),s | supports | 5 | 0.24 | 0.003 | 0.006 | 5 | 3 | 4 |
| 2. | cone | scos(t),ssin(t),s | supports | 122 | 73.45 | 0.192 | 0.288 | 98 | 8 | 14 |
| 3. | paraboloid | scos(t),ssin(t),s^2 | supports | 122 | 71.60 | 0.192 | 0.296 | 98 | 8 | 37 |
| 4. | surface of revolution | scos(t),ssin(t),cos(s) | supports | 122 | 71.80 | 0.193 | 0.288 | 98 | 8 | 37 |
| 5. | sphere | sin(t)cos(s),sin(t)sin(s),cos(t) | supports | 104148 | halt | 19496.602 | 714.161 | 43018 | 21 | 186 |
| 6. | sphere2 | cos(t)cos(s),sin(t)cos(s),sin(s) | supports | 76280 | halt | 4492.977 | 397.157 | 32076 | 95 | 776 |
| 7. | stereographic shpere | 2t/(1+t^2+s^2),2s/(1+t^2+s^2),(t^2+s^2-1)/(1+t^2+s^2) | supports | 3540 | 7112.54 | 25.402 | 11.025 | 3126 | 22 | 283 |
| 8. | twisted shpere | a(cos(t)+t(sin(t)),a(sin(t)-tcos(t)) | supports | >1812221 | not computed | not computed | not computed | not computed | not computed | not computed |
1. Many thanks to Tatjana Kalinka for providing this list of surfaces.
2. This is the computation time of enumeration of regular triangulations algorithm using reverse search. I would like to thank very much Fumihiko TAKEUCHI for running the experiments and providing this results. Experiments were done on a Blade 100, 550Mhz, 2GB memory with SunOS 5.9.
3. This is the computation time of points2alltriangs client of TOPCOM package. Experiments were done on a Intel(R) Pentium(R) 4 CPU 3.20GHz, 1.5GB memory with x86_64 Debian GNU/Linux.
4. This is the computation time of points2triangs client of TOPCOM package. Experiments were done on a Intel(R) Pentium(R) 4 CPU 3.20GHz, 1.5GB memory with x86_64 Debian GNU/Linux.