DERIVE for Windows version 5.02 DfW file saved on 23 Nov 2002 ver(v, w):=VECTOR(v™i + w, i, 1, DIM(v)) z_streck(v, x, y, l):=VECTOR(M_k·v™i + [(1 - l)·x, (1 - l)·y], i, 1, DIM(v)) BILD:=[22, -14; 20, -14; 20, -18; 18, -18; 18, -20; 20, -20; 20, -22; 16, -22; 16, -24; 22, -24; 22, -14] Bild:=[22, -14; 20, -14; 20, -18; 18, -18; 18, -20; 20, -20; 20, -22; 16, -22; 16, -24; 22, -24; 22, -14] Bild_O:=[5, 5; 10, 5; 10, 15; 15, 15; 15, 20; 10, 20; 10, 25; 20, 25; 20, 30; 5, 30; 5, 5] Bild_Ur:=[-2, -2; -4, -2; -4, -6; -6, -6; -6, -8; -4, -8; -4, -10; -8, -10; -8, -12; -2, -12; -2, -2] M_k:=[-2, 0; 0, -2] Orig:=[1, 1; 2, 1; 2, 3; 3, 3; 3, 4; 2, 4; 2, 5; 4, 5; 4, 6; 1, 6; 1, 1] Z:=[8, -4] hCross:=APPROX(22) k:=-2 vCross:=APPROX(- 8666666666666667/1250000000000000) x_Z:=8 y_Z:=-4 zx:= zy:= ÿÿCTextObj bsÿ™{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2\fcharset1 Californian FB;}{\f4\fswiss\fprq2 News Gothic MT;}{\f5\fswiss\fprq2\fcharset1 Courier New;}{\f6\fswiss\fprq2\fcharset1 ZapfCalligr BT;}} {\colortbl\red0\green0\blue0;} \deflang1031\pard\plain\f4\fs28\cf0\b Zentrische Streckungen mit Matrizen\plain\f4\fs40\cf0 \par \plain\f4\fs22\cf0 \par \plain\f4\fs22\cf0\b Das Original\plain\f4\fs22\cf0 , eingegeben als nx2 - Matrix. Hintergrund: Nur so kann Derive plotten. Au\'dferdem funktioniert sonst (also in "querschreibweise") die Verschiebung nicht - s.u. \par } ÿÿCExpnObj8¸{Benutzerð¿IOrig:=[[1,1],[2,1],[2,3],[3,3],[3,4],[2,4],[2,5],[4,5],[4,6],[1,6],[1,1]]€‡bÃÿ4{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2\fcharset1 Californian FB;}{\f4\fswiss\fprq2 News Gothic MT;}{\f5\fswiss\fprq2\fcharset1 Courier New;}{\f6\fswiss\fprq2\fcharset1 ZapfCalligr BT;}} {\colortbl\red0\green0\blue0;} \deflang1031\pard\plain\f4\fs22\cf0\b Das Streckzentrum.\plain\f4\fs22\cf0 Um einen Zugriff auf die Koordinaten des Streckzentrums zu haben, werden diese einzen eingegeben und Z dan \'fcber diese Eingaben definiert.\plain\f4\fs22\cf0\b \par } €8ÏxÛBenutzerð¿x_Z:=8€8ç€óBenutzerð¿y_Z:=-4€8ÿ° Benutzerð¿ Z:=[x_Z,y_Z]€0h#Simp(Benutzer)[8,-4]€/bAÿ~{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2\fcharset1 Californian FB;}{\f4\fswiss\fprq2 News Gothic MT;}{\f5\fswiss\fprq2\fcharset1 Courier New;}{\f6\fswiss\fprq2\fcharset1 ZapfCalligr BT;}} {\colortbl\red0\green0\blue0;} \deflang1031\pard\plain\f4\fs22\cf0\b Der Streckfaktor: \par } €8MpYBenutzerð¿k:=-2€ebwÿ~{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2\fcharset1 Californian FB;}{\f4\fswiss\fprq2 News Gothic MT;}{\f5\fswiss\fprq2\fcharset1 Courier New;}{\f6\fswiss\fprq2\fcharset1 ZapfCalligr BT;}} {\colortbl\red0\green0\blue0;} \deflang1031\pard\plain\f4\fs22\cf0\b Die Streckmatrix: \par } €8ƒ°§Benutzerð¿M_k:=[[k,0],[0,k]]€ ³p×Simp(Benutzer)[[-2,0],[0,-2]]€ãb5ÿÖ{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2\fcharset1 Californian FB;}{\f4\fswiss\fprq2 News Gothic MT;}{\f5\fswiss\fprq2\fcharset1 Courier New;}{\f6\fswiss\fprq2\fcharset1 ZapfCalligr BT;}} {\colortbl\red0\green0\blue0;} \deflang1031\pard\plain\f4\fs22\cf0\b Die gestreckte Originalfigur mit dem Ursprung als Streckzentrum\plain\f4\fs22\cf0 . Zun\'e4chst wird \plain\f5\fs22\cf0\b Orig\plain\f4\fs22\cf0 transponiert, sodass die Matrizenmultiplikation durch \plain\f5\fs22\cf0\b M_k \plain\f4\fs22\cf0 m\'f6glich wird. Im Anschluss an diese Multiplikation wird die Ergebnismatrix ihrerseits zur\'fccktransponiert - s.o. \par } €8AðMBenutzerð¿ Bild_Ur:=(M_k*Orig`)`€ YxUSimp(Benutzer)ü©ñÒMb`? ][[-2,-2],[-4,-2],[-4,-6],[-6,-6],[-6,-8],[-4,-8],[-4,-10],[-8,-10],[-8,-12],[-2,-12],[-2,-2]]€ab²ÿd{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2\fcharset1 Californian FB;}{\f4\fswiss\fprq2 News Gothic MT;}{\f5\fswiss\fprq2\fcharset1 Courier New;}{\f6\fswiss\fprq2\fcharset1 ZapfCalligr BT;}} {\colortbl\red0\green0\blue0;} \deflang1031\pard\plain\f4\fs22\cf0\b Zentrische Streckung mit beliebigem Zentrum. \plain\f4\fs22\cf0 Zun\'e4chst wird Abbildung definiert f\'fcr beliebige Streckzentren und beliebige Streckfaktoren [ver(v,x,y,l)], danach wird ver(*,*,*,*) auf die gew\'fcnschten Vorgaben angewandt: \plain\f5\fs22\cf0\b Orig\plain\f4\fs22\cf0 , \plain\f5\fs22\cf0\b Z\plain\f4\fs22\cf0 in Form von \plain\f5\fs22\cf0\b x_Z \plain\f4\fs22\cf0 und \plain\f6\fs22\cf0\b y_Z\plain\f4\fs22\cf0 , sowie den Streckfaktor \plain\f5\fs22\cf0\b k\plain\f4\fs22\cf0 . \par } €8¾ ÖBenutzerð¿ Cz_streck(v,x,y,l):=VECTOR(M_k*v SUB i+[(1-l)*x,(1-l)*y],i,1,DIM(v))€8âPîBenutzerð¿ d[[22,-14],[20,-14],[20,-18],[18,-18],[18,-20],[20,-20],[20,-22],[16,-22],[16,-24],[22,-24],[22,-14]]€ úxöSimp(Benutzer) d[[22,-14],[20,-14],[20,-18],[18,-18],[18,-20],[20,-20],[20,-22],[16,-22],[16,-24],[22,-24],[22,-14]]€b,ÿð{\rtf1\ansi\deff0\deftab720{\fonttbl{\f0\fswiss MS Sans Serif;}{\f1\froman\fcharset2 Symbol;}{\f2\fswiss\fprq2 System;}{\f3\fswiss\fprq2\fcharset1 Californian FB;}{\f4\fswiss\fprq2 News Gothic MT;}{\f5\fswiss\fprq2\fcharset1 Courier New;}{\f6\fswiss\fprq2\fcharset1 ZapfCalligr BT;}} {\colortbl\red0\green0\blue0;} \deflang1031\pard\plain\f4\fs22\cf0\b Plotten im Graphikfenster.\plain\f4\fs22\cf0 Es werden \plain\f5\fs22\cf0\b Orig, Bild_Ur\plain\f4\fs22\cf0 und \plain\f5\fs22\cf0\b Bild\plain\f4\fs22\cf0 gezeigt. Das folgende Ergebnis erh\'e4lt man durch "Einbetten". Wer genau hinsieht, erkennt sogar das ebendfalls geplottete Sterckzentrum \plain\f5\fs22\cf0\b Z[8,-4)]\plain\f3\fs22\cf0 \plain\f4\fs22\cf0 als schwarzes Quadrat. \par } ÿÿCPlotObjÌ8žÿÿ C2DPlotViewÿÿCPointListPlotÿ  ð? ð? @ ð? @ @ @ @ @ @ @ @ @ @ @ @ @ @ ð? @ ð? ð?€ÿ  À À À À À À À À À  À À  À À $À  À $À  À (À À (À À À €ÿ  6@ ,À 4@ ,À 4@ 2À 2@ 2À 2@ 4À 4@ 4À 4@ 6À 0@ 6À 0@ 8À 6@ 8À 6@ ,À €  @ 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