{VERSION 4 0 "HP RISC UNIX" "4.0" } {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 "Helvetica" 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 "" 0 257 1 {CSTYLE "" -1 -1 " " 1 13 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 "" 0 258 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 }} {SECT 0 {EXCHG {PARA 256 "" 0 "" {TEXT -1 27 "Perspektivische Abbildun gen" }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 258 "" 0 "" {TEXT -1 138 "Dies es worksheet zeigt verschiedene Bilder des W\374rfels unter perspektiv ischen Abbildungen, teilweise als Animationen mit bewegtem Zentrum." } {MPLTEXT 1 0 0 "" }}{PARA 257 "" 0 "" {TEXT -1 120 "This worksheet sho ws several perspectivic projections of the unit cube, some of them as \+ animations with a moving center." }{MPLTEXT 1 0 0 "" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 859 "restart;\n\nproj := proc(P)\nglobal z, n ; local a;\na := evalm(\n(linalg[dotprod](z, n)*P - linalg[dotprod](ve ctor(P), n)*z)\n/(linalg[dotprod](z, n) - linalg[dotprod](vector(P), n )));\n[a[1], a[2]]\nend: \n\nwuerfel := proc(z1, z2, z3, n1, n2, n3)\n global W, z, n;\nlocal w, i;\nz := vector(3, [z1, z2, z3]);\nn := vect or(3, [n1, n2, n3]);\nfor i to 8 do\nw[i] := proj(W[i]); od;\nplots[di splay]([\nplot([[w[1], w[2]], [w[2], w[3]], [w[3], w[4]], [w[4], w[1]] ,\n[w[2], w[6]], [w[3], w[7]], [w[4], w[8]],\n[w[8], w[7]], [w[7], w[6 ]]], color=black, thickness=5),\nplot([[w[5], w[1]], [w[5], w[6]], [w[ 5], w[8]]],\ncolor=black, thickness=5)], scaling=constrained):\nend:\n \ndrehe := proc(c, a)\nlocal s;\ns := sqrt(1 - c^2);\nconvert(evalm(ma trix([[c, -s],[s, c]]) &* vector(a)), list);\nend:\n\nW := [[-1,-1,1], [-1,1,1], [1,1,1], [1,-1,1],\n [-1,-1,-1], [-1,1,-1], [1,1,-1], \+ [1,-1,-1]]:" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 231 "plots[displ ay]([seq(\nplots[display]([wuerfel(0,0,20-i,0,0,1),\nplots[textplot]([ 2.0, 2.1, sprintf(\"Zentrum = (%1d, %1d, %1d)\",\nz[1], z[2], z[3])],f ont=[HELVETICA, 24], align=LEFT)]), i=0..18)],\ninsequence=true, scali ng=CONSTRAINED);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 236 "plots[ display]([seq(\nplots[display]([wuerfel(0,-2+i/5,3,0,0,1),\nplots[text plot]([1.5, 2.3, sprintf(\"Zentrum = (%1d, %03.1f, %1d)\",\nz[1], z[2] , z[3])],font=[HELVETICA, 24], align=LEFT)]), i=0..30)],\ninsequence=t rue, scaling=CONSTRAINED);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 236 "plots[display]([seq(\nplots[display]([wuerfel(-2+i/5,0,5,0,0,1), \nplots[textplot]([1.5, 2.3, sprintf(\"Zentrum = (%03.1f, %1d, %1d)\", \nz[1], z[2], z[3])],font=[HELVETICA, 24], align=LEFT)]), i=0..30)],\n insequence=true, scaling=CONSTRAINED);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "wuerfel(0,0,3,1,2,3);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 332 "Fx := [-9, 0]: Fy := [0,-4]: Fz := [0, 0]:\nplots[di splay]([wuerfel(0,0,3,1,2,3),\nplot([[proj(W[1]), Fx], [proj(W[2]), Fx ],\n[proj(W[5]), Fx], [proj(W[6]), Fx],\n[proj(W[1]), Fy], [proj(W[4]) , Fy],\n[proj(W[5]), Fy], [proj(W[8]), Fy],\n[proj(W[5]), Fz], [proj(W [6]), Fz],\n[proj(W[7]), Fz], [proj(W[8]), Fz]],\ncolor=black, thickne ss=1)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "plots[display] ([wuerfel(0,0,3,1,2,3),\nplot([[proj(W[1]), Fx], [proj(W[2]), Fx],\n[p roj(W[5]), Fx], [proj(W[6]), Fx],\n[proj(W[1]), Fy], [proj(W[4]), Fy], \n[proj(W[5]), Fy], [proj(W[8]), Fy],\n[proj(W[5]), Fz], [proj(W[6]), \+ Fz],\n[proj(W[7]), Fz], [proj(W[8]), Fz]],\ncolor=black, thickness=1), \nplot([[Fx, Fy], [Fy, Fz],[Fz, Fx]], color=red, thickness=3)]);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 21 "wuerfel(3,4,3,1,2,3);" }}} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 333 "Fx := [-17, 4]: Fy := [3,-6 ]: Fz := [3, 4]:\nplots[display]([wuerfel(3,4,3,1,2,3),\nplot([[proj(W [1]), Fx], [proj(W[2]), Fx],\n[proj(W[5]), Fx], [proj(W[6]), Fx],\n[pr oj(W[1]), Fy], [proj(W[4]), Fy],\n[proj(W[5]), Fy], [proj(W[8]), Fy], \n[proj(W[5]), Fz], [proj(W[6]), Fz],\n[proj(W[7]), Fz], [proj(W[8]), \+ Fz]],\ncolor=black, thickness=1)]);" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 350 "plots[display]([wuerfel(3,4,3,1,2,3),\nplot([[proj(W [1]), Fx], [proj(W[2]), Fx],\n[proj(W[5]), Fx], [proj(W[6]), Fx],\n[pr oj(W[1]), Fy], [proj(W[4]), Fy],\n[proj(W[5]), Fy], [proj(W[8]), Fy], \n[proj(W[5]), Fz], [proj(W[6]), Fz],\n[proj(W[7]), Fz], [proj(W[8]), \+ Fz]],\ncolor=black, thickness=1),\nplot([[Fx, Fy], [Fy, Fz],[Fz, Fx]], color=red, thickness=3)]);" }}}}{MARK "2 0 0" 9 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }