{VERSION 5 0 "HP RISC UNIX" "5.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 256 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 257 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE " " 0 258 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 259 1 {CSTYLE "" -1 -1 "" 1 24 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 } {PSTYLE "" 0 260 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 261 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 262 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 1 0 0 0 0 0 0 0 0 1 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }{PSTYLE "" 0 263 1 {CSTYLE "" -1 -1 "Helvetica" 1 18 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }3 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 259 "" 0 "" {TEXT -1 24 "Orthogonale Projektionen " }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 8 "resta rt:" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 146 "with(plots, display):\nDick e := 5: # Strichdicke, mit der Vektoren gezeichnet werden\nWinkel \+ := Pi/8: # (halber) \326ffnungswinkel der Vektorpfeile" }}{PARA 0 "> \+ " 0 "" {MPLTEXT 1 0 927 "v := proc(Anfang, Ende, Farbe)\n# zeichnet ei nen Vektor von Anfang nach Ende in Farbe\nglobal Dicke, Winkel;\nlocal dx, dy, phi, phi1, phi2, l1, l2, r1, r2;\ndx := Ende[1] - Anfang[1]; \ndy := Ende[2] - Anfang[2];\nif (abs(dy) > abs(dx)) then\n phi := P i/2 - arctan(dx/dy)\nelif (abs(dx) > 0) then\n phi := arctan(dy/dx) \nelse return(plot([Anfang[1], Anfang[2]], color=Farbe))\nfi;\n phi1 := phi + Winkel;\n phi2 := phi - Winkel;\n l1 := Ende[1] - 0.2*si gn(dy)*cos(phi1);\n l2 := Ende[2] - 0.2*sign(dy)*sin(phi1);\n r1 : = Ende[1] - 0.2*sign(dy)*cos(phi2);\n r2 := Ende[2] - 0.2*sign(dy)*s in(phi2);\n plots[display]([\n plot([[Anfang[1], Anfang[2]], [Ende [1], Ende[2]]], color=Farbe,\n thickness=Dicke, scaling=constraine d),\n plot([[l1, l2], [Ende[1], Ende[2]]], color=Farbe,\n thickn ess=Dicke, scaling=constrained),\n plot([[r1, r2], [Ende[1], Ende[2] ]], color=Farbe,\n thickness=Dicke, scaling=constrained)]);\nend: " }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 430 "pfeil := proc(P,Q, Farbe)\nloc al v, e, a, alpha;\ne := vector([0,0,1]);\nv := vector(Q-P);\nalpha := linalg[angle](e, v);\na := linalg[crossprod](e, v);\nif linalg[equal] (a, vector([0$3])) then a := vector([0,0,1]) fi;\nplots[display]([PLOT 3D(CURVES([P,Q], THICKNESS(5))),\nplottools[translate](\nplottools[rot ate](plottools[cone]([0,0,0],0.1,-0.3, style=patchnogrid), alpha, [[0$ 3],convert(a, list)]),\nQ[1],Q[2],Q[3])], color=Farbe);\nend:" }}} {EXCHG {PARA 260 "" 0 "" {TEXT -1 54 "Orthogonale Projektion eines dre idimensionalen Vektors" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 169 "plots[display3d]([\npfeil([5,4,0], [5,4,3], green), \npfeil([0,0,0], [5,4,0], blue),\npfeil([0,0,0], [5,4,3], red)],\norie ntation=[-95, 80], scaling=constrained, axes=boxed);" }}}{EXCHG {PARA 261 "" 0 "" {TEXT -1 54 "Orthogonale Projektion eines dreidimensionale n Objekts" }{MPLTEXT 1 0 0 "" }}{PARA 262 "" 0 "" {TEXT -1 27 "zun\344 chst das Objekt selbst:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 1402 "T1 := [0,0,0]: T2 := [1,0,0]: T3 := [1,1,0]: T4 := \+ [0,1,0]:\nS1 := [1, -2, 0]: S2 := [11,-2,0]: S3 := [11,3,0]: S4 := [1, 3,0]:\nTS := [0.5,0.5,11]:\nSD1 := [1,0.5,6]: SD2 := [11,0.5,6]:\nfor \+ i to 4 do\nT||(i+4) := [T||i[1], T||i[2],10]:\nS||(i+4) := [S||i[1], S ||i[2],4]:\nT||(i+8) := TS + 1.2*(T||(i+4)-TS):\nod:\nS9 := SD1 + 1.2* (S5-SD1): S10 := SD2 + 1.2*(S6-SD2):\nS12 := SD1 + 1.2*(S8-SD1): S11 : = SD2 + 1.2*(S7-SD2):\nr := 1.75:\nfor i from 0 to 12 do\nA||i := eval f([11 + r*sin(Pi*(i-0)/12), 0.5 + r*cos(Pi*(i-0)/12), 0]):\nB||i := ev alf([11 + r*sin(Pi*(i-0)/12), 0.5 + r*cos(Pi*(i-0)/12), 3.5]):\nAS := \+ [11, 0.5, 5]: AZ := [11, 0.5, 0]:\nC||i := AS + 1.2*(B||i-AS):\nod:\n \ndemo := proc(proj, titel)\nlocal p;\np := L -> map(proj, L);\nplots[ display]([\nCURVES(p([T1,T2,T3,T4,T1]),p([T5,T6,T7,T8,T5]),p([T1,T5,T6 ,T2,T1]),\np([T2,T6,T7,T3,T2]),p([T3,T7,T8,T4,T3]),p([T4,T8,T5,T1,T4]) ,\np([T5,T6,TS,T5]),p([T6,T7,TS,T6]),p([T7,T8,TS,T7]),p([T8,T5,TS,T8]) ,\np([S1,S2,S3,S4,S1]),p([S5,S6,S7,S8,S5]),p([S1,S5,S6,S2,S1]),\np([S2 ,S6,S7,S3,S2]),p([S3,S7,S8,S4,S3]),p([S4,S8,S5,S1,S4]),\np([S5,S6,SD2, SD1,S5]),p([S7,S8,SD1,SD2,S7]),\n'p([A||i, B||i, B||(i+1), A||(i+1), A ||i])' $ 'i'=0..11,\n'p([C||i, C||(i+1), AS, C||i])' $ 'i'=0..11, COLO R(RGB,0,0,0),\nTHICKNESS(2))],\nscaling=CONSTRAINED, axes=NONE, title= titel, titlefont=[HELVETICA, 24]):\nend:\nproj1 := P -> [P[1], P[2]]: \nproj2 := P -> [P[2], P[3]]:\nproj3 := P -> [P[1], P[3]]:\n" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 653 "plots[display3d]([\nPOLYGONS([T1,T2,T3,T 4],[S1,S2,S3,S4],\n'[A||i, A||(i+1), AZ]' $ 'i'=0..11, COLOR(RGB,1,1,1 )),\nPOLYGONS([T1,T5,T6,T2],[T2,T6,T7,T3],[T3,T7,T8,T4],[T4,T8,T5,T1], \nCOLOR(RGB,0.65,0.7,0.4)),\nPOLYGONS([T9,T10,TS],[T10,T11,TS],[T11,T1 2,TS],[T12,T9,TS],\n[S9,S10,SD2,SD1],[S11,S12,SD1,SD2],\n'[C||i, C||(i +1), AS]' $ 'i'=0..11 ,COLOR(RGB,0.8,0.2,0.2)),\nPOLYGONS([S1,S5,S6,S2 ],[S2,S6,S7,S3],[S3,S7,S8,S4],[S4,S8,S5,S1],\n[S6,SD2,S7],[S5,SD1,S8], '[A||i, B||i, B||(i+1), A||(i+1)]' $ 'i'=0..11,\nCOLOR(RGB,0.8,0.8,0.1 ))], scaling=CONSTRAINED, orientation=[-55,80],\nlight = [50,30,1$3], \+ light=[165,-20,0.7$3], ambientlight=[0.2$3],\nstyle=patchnogrid);" }}} {EXCHG {PARA 256 "" 0 "" {TEXT -1 9 "Grundri\337:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "demo(proj1, \"Grundriss\");" }}} {EXCHG {PARA 257 "" 0 "" {TEXT -1 7 "Aufri\337:" }{MPLTEXT 1 0 0 "" }} {PARA 0 "> " 0 "" {MPLTEXT 1 0 23 "demo(proj2, \"Aufriss\");" }}} {EXCHG {PARA 258 "" 0 "" {TEXT -1 9 "Kreuzri\337:" }{MPLTEXT 1 0 0 "" }}{PARA 0 "> " 0 "" {MPLTEXT 1 0 25 "demo(proj3, \"Kreuzriss\");" }}} {EXCHG {PARA 263 "" 0 "" {TEXT -1 43 "K\374rzester Abstand von einem U ntervektorraum" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 265 "plots[display3d]([\npfeil([5,4,0], [5,4,3], cyan),\n pfeil([0,0,0], [5,4,0], blue),\npfeil([0,0,0], [5,8,0], navy),\npfeil( [5,8,0], [5,4,3], green),\npfeil([5,8,0], [5,4,0], black),\npfeil([0,0 ,0], [5,4,3], red)],\norientation=[-105, 85], scaling=constrained, axe s=framed);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}}{MARK "1 0 0" 8 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }