Geometric Algebra Computing Mathematical Introduction Dr. Dietmar Hildenbrand
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1 Gomtri Algr Computing Mthmtil Introdution 6..0 Dr. Ditmr Hildnrnd Thnish Univrsität Drmstdt
2 Montg, 9..0 fällt di Üung us -> individull Bsprhungstrmin 6..0 Thnish Univrsität Drmstdt Ditmr Hildnrnd
3 Nhtrg Shnitt von Kugl und Kris Ws pssirt, wnn dr Kris uf dr Kugl ligt? (KuglMlKris.lu) 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd
4 Nhtrg (CLUCl) 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 4
5 Nhtrg Zwi idntish Kugln? Kugln mit idntishm Mittlpunkt, r untrshidlihn Rdin? 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 5
![Litrtur [] Christin Prwss nd Ditmr Hildnrnd Aspts of Gomtri Algr in Eulidn, Projtiv nd Conforml Sp, Tutoril uf dr DAGM 00, Stnd 4. Jn.](/docs-images/91/105762797/images/6-1.jpg "004 Chptr An Intrtiv Introdution to Gomtri Algr Kpitl Introdutions to Clifford Algr und Gomtris [] Christin Prwss, Gomtri Algr with Applitions in Enginring, Springr 009 [] John Vin Gomtri Algr: An")
6 Litrtur [] Christin Prwss nd Ditmr Hildnrnd Aspts of Gomtri Algr in Eulidn, Projtiv nd Conforml Sp, Tutoril uf dr DAGM 00, Stnd 4. Jn. 004 Chptr An Intrtiv Introdution to Gomtri Algr Kpitl Introdutions to Clifford Algr und Gomtris [] Christin Prwss, Gomtri Algr with Applitions in Enginring, Springr 009 [] John Vin Gomtri Algr: An Algri Systm for Computr Gms nd Animtion, Springr, 009 Chptr Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 6
7 Ovrviw Clultions in D ulidn GA Th sin rul Clultions in 5D onforml GA D 5D Rfltion/projtion in oth sps 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 7
8 DAGM-Tutoril Strt.lu 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 8
9 Clultions in D Eulidn GA 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 9
10 Th lds of D ulidn gomtri lgr 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 0
11 Th min produts of gomtri lgr Outr Produt vtor ivtor trivtor Innr Produt Gomtri Produt 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd
12 Proprtis of th outr produt 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd
13 Proprtis of th outr produt Not: th outr produt n usd s msur of prlllnss 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd
14 Exmpl ivtore.lu 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 4
15 Computtion xmpl 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 5
16 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 6 Th outr produt of vtors in D ) ( ) ( ) ( ) ( ) ( = = = =
17 trivtore.lu 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 7
18 trivtore.lu 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 8
19 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 9 Th outr produt of vtors in D ) ( ) ( ) ( ) ( ) ( ) ( = = = Not : linrly dpndnt vtors -> th outr produt is 0
20 Th innr produt of two vtors Innr produt = Slr produt is tru only for vtors! For vtor nd ivtor: Gnrl rul in [] pg Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 0
21 Rvrs, norm of susps A = with ~ A = k ~ A A... Exmpl: In CLUCl: 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd
22 Th innr produt nd prpndiulrity 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd
23 Th gnrl innr produt Innr produt not only dfind for vtors! Exmpl: Not: - th rsulting vtor is prpndiulr to x InnrProdutE.lu - th innr produt is grd drsing 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd
24 Thnks for your ttntion 6..0 Thnish Univrsität Drmstdt Computr Sin Dprtmnt Ditmr Hildnrnd 4
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