{VERSION 5 0 "IBM INTEL NT" "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 }{CSTYLE "2D Math" -1 2 "Times" 0 1 0 0 0 0 0 0 2 0 0 0 0 0 0 1 }{CSTYLE "2D Input" 2 19 "" 0 1 255 0 0 1 0 0 0 0 0 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 "Heading 1" 0 3 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 0 0 0 0 0 0 0 1 }1 0 0 0 6 6 0 0 0 0 0 0 -1 0 }{PSTYLE "Heading 2" 3 4 1 {CSTYLE "" -1 -1 "" 1 14 0 0 0 0 0 0 0 0 0 0 0 0 0 1 }0 0 0 -1 4 4 0 0 0 0 0 0 -1 0 }{PSTYLE "Maple Plot" 0 13 1 {CSTYLE "" -1 -1 "" 0 1 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 "Title" 0 18 1 {CSTYLE "" -1 -1 "" 1 18 0 0 0 0 0 1 1 0 0 0 0 0 0 1 }3 0 0 -1 12 12 0 0 0 0 0 0 19 0 }} {SECT 0 {EXCHG {PARA 18 "" 0 "" {TEXT -1 26 "B\351zierova bikubick\341 plocha" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 13 "Implementacia" }}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 32 "Ber nsteinove polynomy stupna 'k'" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Bernstein := proc(k, i, t)\n combinat[binomial](k, i) * t^i * (1-t )^(k-i)\nend:" "6#>%*BernsteinGf*6%%\"kG%\"iG%\"tG7\"6\"F+*(-&%)combin atG6#%)binomialG6$F'F(\"\"\")F)F(F3),&F3F3F)!\"\",&F'F3F(F7F3F+F+F+" } }}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 26 "Suradnice riadiacich bodov" }} {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 150 "mx := linalg[matrix](4, 4, \+ \n [[0., 80., 160., 240.], \n [0., 80., 160., 240.],\n \+ [0., 80., 160., 240.],\n [0., 80., 160., 240.]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 157 "my := linalg[matrix](4, 4,\n \+ [[0., 0., 0., 0.],\n [80., 80., 80., 80.],\n [160 ., 160., 160., 160.],\n [240., 240., 240., 240.]]):" }}}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 151 "mz := linalg[matrix](4, 4, \n \+ [[0., 80., 80., 0.],\n [80., 160., 160., 80.],\n [80., 160., 160., 80.],\n [0., 80., 80., 0.]]):" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 13 "Urcujuca siet" }}{EXCHG {PARA 0 "> " 0 " " {XPPEDIT 19 1 "siet1 := PLOT3D(seq( CURVES([seq( [mx[i, j], my[i, j] , mz[i, j]], i=1..4)], COLOR(RGB, 0, 0, 0)), j = 1..4)):" "6#>%&siet1G -%'PLOT3DG6#-%$seqG6$-%'CURVESG6$7#-F)6$7%&%#mxG6$%\"iG%\"jG&%#myG6$F5 F6&%#mzG6$F5F6/F5;\"\"\"\"\"%-%&COLORG6&%$RGBG\"\"!FEFE/F6;F?F@" }}} {EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "siet2:= PLOT3D(seq( CURVES([se q( [mx[i, j], my[i, j], mz[i, j]], j=1..4)], COLOR(RGB, 0, 0, 0)), i \+ = 1..4)):" "6#>%&siet2G-%'PLOT3DG6#-%$seqG6$-%'CURVESG6$7#-F)6$7%&%#mx G6$%\"iG%\"jG&%#myG6$F5F6&%#mzG6$F5F6/F6;\"\"\"\"\"%-%&COLORG6&%$RGBG \"\"!FEFE/F5;F?F@" }}}}{SECT 0 {PARA 4 "" 0 "" {TEXT -1 43 "Vypocet kr ivky Q pre hodnoty parametra u, v" }}{EXCHG {PARA 0 "> " 0 "" {XPPEDIT 19 1 "Q := proc(u, v)\nlocal i, j, t, nx, ny, nz;\n nx := 0; \+ ny := 0; nz := 0;\n for i from 1 to 4 do\n for j from 1 to 4 do\n t := Bernstein(3, i-1, u) * Bernstein(3, j-1, v);\n nx := nx + mx[i, \+ j] * t;\n ny := ny + my[i, j] * t;\n nz := nz + mz[i, j] * t;\n o d;\n od;\n[nx, ny, nz]\nend:" "6#>%\"QGf*6$%\"uG%\"vG7(%\"iG%\"jG%\"tG %#nxG%#nyG%#nzG6\"F0C'>F-\"\"!>F.F3>F/F3?(F*\"\"\"F7\"\"%%%trueG?(F+F7 F7F8F9C&>F,*&-%*BernsteinG6%\"\"$,&F*F7F7!\"\"F'F7-F?6%FA,&F+F7F7FCF(F 7>F-,&F-F7*&&%#mxG6$F*F+F7F,F7F7>F.,&F.F7*&&%#myG6$F*F+F7F,F7F7>F/,&F/ F7*&&%#mzG6$F*F+F7F,F7F77%F-F.F/F0F0F0" }}}}}{SECT 0 {PARA 3 "" 0 "" {TEXT -1 18 "Vykreslenie krivky" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 128 "graf := plot3d(Q(u, v), u=0..1, v=0..1, title=`B\351zierova b ikubick\341 plocha`):\n#Zobrazenie\nplots[display3d](\{siet1, siet2, g raf\});" }}{PARA 13 "" 1 "" {GLPLOT3D 310 281 281 {PLOTDATA 3 "6,-%'CU RVESG6$7&7%$\"\"!F)F(F(7%F($\"#!)F)F+7%F($\"$g\"F)F+7%F($\"$S#F)F(-%&C OLORG6&%$RGBGF)F)F)-F$6$7&7%F+F(F+7%F+F+F.7%F+F.F.7%F+F1F+F3-F$6$7&7%F .F(F+7%F.F+F.7%F.F.F.7%F.F1F+F3-F$6$7&7%F1F(F(7%F1F+F+7%F1F.F+7%F1F1F( F3-F$6$7&F'F:FAFHF3-F$6$7&F*F;FBFIF3-F$6$7&F-F