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kurse:efcomputergrafik:kw7 [2020/02/12 10:08] Ivo Blöchliger |
kurse:efcomputergrafik:kw7 [2020/02/12 10:50] Ivo Blöchliger |
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| Schön und gut, aber die Gleichungen sind nichtlinear... z.B. sieht die letzte Gleichung etwa so aus: |
| $${{\left(\left(3\,{\it ri}_{1}-3\,\xi_{1}\right)\,\left(6\,\xi_{2}- |
| 12\,{\it ri}_{2}+6\,{\it lip}_{2}\right)-\left(6\,\xi_{1}-12\, |
| {\it ri}_{1}+6\,{\it lip}_{1}\right)\,\left(3\,{\it ri}_{2}-3\, |
| \xi_{2}\right)\right)\,\left(6\,{\it xip}_{3}-6\,\xi_{3}+18\, |
| {\it ri}_{3}-18\,{\it lip}_{3}\right)+\left(\left(6\,\xi_{1}-12\, |
| {\it ri}_{1}+6\,{\it lip}_{1}\right)\,\left(3\,{\it ri}_{3}-3\, |
| \xi_{3}\right)-\left(3\,{\it ri}_{1}-3\,\xi_{1}\right)\,\left(6\, |
| \xi_{3}-12\,{\it ri}_{3}+6\,{\it lip}_{3}\right)\right)\,\left(6\, |
| {\it xip}_{2}-6\,\xi_{2}+18\,{\it ri}_{2}-18\,{\it lip}_{2}\right)+ |
| \left(\left(3\,{\it ri}_{2}-3\,\xi_{2}\right)\,\left(6\,\xi_{3}-12\, |
| {\it ri}_{3}+6\,{\it lip}_{3}\right)-\left(6\,\xi_{2}-12\, |
| {\it ri}_{2}+6\,{\it lip}_{2}\right)\,\left(3\,{\it ri}_{3}-3\, |
| \xi_{3}\right)\right)\,\left(6\,{\it xip}_{1}-6\,\xi_{1}+18\, |
| {\it ri}_{1}-18\,{\it lip}_{1}\right)}\over{\left(\left(3\, |
| {\it ri}_{2}-3\,\xi_{2}\right)\,\left(6\,\xi_{3}-12\,{\it ri}_{3}+6 |
| \,{\it lip}_{3}\right)-\left(6\,\xi_{2}-12\,{\it ri}_{2}+6\, |
| {\it lip}_{2}\right)\,\left(3\,{\it ri}_{3}-3\,\xi_{3}\right)\right) |
| ^2+\left(\left(6\,\xi_{1}-12\,{\it ri}_{1}+6\,{\it lip}_{1}\right)\, |
| \left(3\,{\it ri}_{3}-3\,\xi_{3}\right)-\left(3\,{\it ri}_{1}-3\, |
| \xi_{1}\right)\,\left(6\,\xi_{3}-12\,{\it ri}_{3}+6\,{\it lip}_{3} |
| \right)\right)^2+\left(\left(3\,{\it ri}_{1}-3\,\xi_{1}\right)\, |
| \left(6\,\xi_{2}-12\,{\it ri}_{2}+6\,{\it lip}_{2}\right)-\left(6\, |
| \xi_{1}-12\,{\it ri}_{1}+6\,{\it lip}_{1}\right)\,\left(3\, |
| {\it ri}_{2}-3\,\xi_{2}\right)\right)^2}}={{\left(\left(3\,\xi_{1}-3 |
| \,{\it li}_{1}\right)\,\left(6\,\xi_{2}+6\,{\it rim}_{2}-12\, |
| {\it li}_{2}\right)-\left(6\,\xi_{1}+6\,{\it rim}_{1}-12\, |
| {\it li}_{1}\right)\,\left(3\,\xi_{2}-3\,{\it li}_{2}\right)\right) |
| \,\left(-6\,{\it xim}_{3}+6\,\xi_{3}+18\,{\it rim}_{3}-18\, |
| {\it li}_{3}\right)+\left(\left(6\,\xi_{1}+6\,{\it rim}_{1}-12\, |
| {\it li}_{1}\right)\,\left(3\,\xi_{3}-3\,{\it li}_{3}\right)-\left(3 |
| \,\xi_{1}-3\,{\it li}_{1}\right)\,\left(6\,\xi_{3}+6\,{\it rim}_{3}- |
| 12\,{\it li}_{3}\right)\right)\,\left(-6\,{\it xim}_{2}+6\,\xi_{2}+ |
| 18\,{\it rim}_{2}-18\,{\it li}_{2}\right)+\left(\left(3\,\xi_{2}-3\, |
| {\it li}_{2}\right)\,\left(6\,\xi_{3}+6\,{\it rim}_{3}-12\, |
| {\it li}_{3}\right)-\left(6\,\xi_{2}+6\,{\it rim}_{2}-12\, |
| {\it li}_{2}\right)\,\left(3\,\xi_{3}-3\,{\it li}_{3}\right)\right) |
| \,\left(-6\,{\it xim}_{1}+6\,\xi_{1}+18\,{\it rim}_{1}-18\, |
| {\it li}_{1}\right)}\over{\left(\left(3\,\xi_{2}-3\,{\it li}_{2} |
| \right)\,\left(6\,\xi_{3}+6\,{\it rim}_{3}-12\,{\it li}_{3}\right)- |
| \left(6\,\xi_{2}+6\,{\it rim}_{2}-12\,{\it li}_{2}\right)\,\left(3\, |
| \xi_{3}-3\,{\it li}_{3}\right)\right)^2+\left(\left(6\,\xi_{1}+6\, |
| {\it rim}_{1}-12\,{\it li}_{1}\right)\,\left(3\,\xi_{3}-3\, |
| {\it li}_{3}\right)-\left(3\,\xi_{1}-3\,{\it li}_{1}\right)\,\left(6 |
| \,\xi_{3}+6\,{\it rim}_{3}-12\,{\it li}_{3}\right)\right)^2+\left( |
| \left(3\,\xi_{1}-3\,{\it li}_{1}\right)\,\left(6\,\xi_{2}+6\, |
| {\it rim}_{2}-12\,{\it li}_{2}\right)-\left(6\,\xi_{1}+6\, |
| {\it rim}_{1}-12\,{\it li}_{1}\right)\,\left(3\,\xi_{2}-3\, |
| {\it li}_{2}\right)\right)^2}}$$ |
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