[math]E_\vec{n}: n_1\cdot x+n_2\cdot y+n_3\cdot z=d[/math][br][br][table] [tr][br] [td]Der [b]Normalenvektor[/b] [math]\vec{n}=\left(n_1,n_2,n_3\right)^T[/math] steht senkrecht auf der Ebene! Aus einer Parameterform [math]Ep(\lambda,\mu)=> E:\vec{x}=\vec{p}+\lambda\cdot\vec{r_1}+\mu\cdot\vec{r_2}[/math] erhalte ich den Normalenvektor durch das Vektorprodukt der Richtungsvektoren [math]\vec{n}=\vec{r_1}\otimes\vec{r_2}[/math]. Aus einer Koordinatenform E1(x,y,z) berechne ich den [b]Normalenvektor[/b] n[sub]k[/sub] durch Aufsammeln der Faktoren der Koordinatenvariablen x,y,z [[i]n:=PerpendicularVector( )[/i]]. [br]Der Normalenvektor kann unterschiedlich lang ausfallen (vielfache des n) und auf verschiedenen "Seiten" der Ebene gezeichnet werden ([math]n_k=-3n[/math]).[br][br]Die [b]Hesse’sche Normalengleichung[/b] Eh(x,y,z) mit normiertem Normalenvektor [math]\vec{n}[/math] [br]Länge [math]\vec{n}[/math] = 1 -> |[math]\vec{n}[/math]|= 1[br][br][/td][br] [td][img]data:image/png;base64,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[/img][br][/td][br][/tr][br][/table]Der Normalenvektor [math]\vec{n}[/math] führt zur Normalenform/[b]Normalengleichung[/b][br][math]Nf:\vec{n}\left(\vec{x}-\vec{o}\right)=0[/math][br]mit [math]\vec{o}[/math] Vektor zu einem Punkt O der Ebene und .[math]\vec{x}=\left(\begin{matrix}x\\y\\z\end{matrix}\right)[/math] .[br][br]Die Schnittpunkte der Ebene mit den Koordinatenachsen (Spurpunkte) führen zur Achsenabschnittform: [br][math]E_{sp}:\frac{x}{s_x}+\frac{y}{s_y}+\frac{z}{s_z}=1[/math] mit den Achsenabschnitten, Spurpunkten [math]{\left(\begin{matrix}s_x\\0\\0\end{matrix}\right)},{\left(\begin{matrix}0\\s_y\\0\end{matrix}\right)},{\left(\begin{matrix}0\\0\\s_z\end{matrix}\right)}[/math].

[table][tr][td]Mathe[/td][td]Eingabe            [br][/td][td]Ausgabe[/td][/tr][tr][td][math]E1:-x+2y-2z=-1[/math][br][/td][td][color=#1155Cc][size=85][/size][color=#e69138][size=85]Koordinantenform[/size][/color][size=85][size=50][br]1[/size] E1(x, y, z):= -x+2y-2z+1[br][size=50]2[/size] E_1:=E1(x,y,z)=0 [/size][/color][/td][td][math]{E1(x, y, z) \, := \, - \; x + 2 \; y - 2\; z + 1}[/math][br][math]{E_1: \, - \; x + 2 \; y - 2 z +1 = 0}[/math][br][size=85]Zeichnen von [math]E_1[/math][/size][br][/td][/tr][tr][td][math]\vec{x}=\left(\begin{matrix}1\\-1\\-1\end{matrix}\right)+r\left(\begin{matrix}0\\6\\5\end{matrix}\right)+s\left(\begin{matrix}2\\3\\3\end{matrix}\right)[/math][br][/td][td] [color=#1155Cc][size=50][color=#e69138][size=85]Paramterform[/size][/color][br]3 [/size][size=85]Ep(r,s):= (1,-1,-1) + r (0,6,5) +s (2,3,3)[br] [/size][/color][/td][td][math]{Ep(r,s) \, := \, \left( \begin{tabular}{r}2 \; r + 1\\6 \; r + 3 \; s - 1\\ 5 \; r + 3 \; s - 1\\ \end{tabular} \right)[/math][br][size=85]Zeichnen von Ep[/size][br][/td][/tr][tr][td][math]\left(\begin{matrix}0\\6\\5\end{matrix}\right)\times\left(\begin{matrix}2\\3\\3\end{matrix}\right)=\left(\begin{matrix}3\\-6\\6\end{matrix}\right)[/math][br][/td][td][color=#1155Cc][size=85][/size][color=#e69138][size=85]Richtungsvektoren und Normalenvektor aus Parameterform[/size][/color][size=85][size=50][br]4[/size] r_1:=[color=#1155Cc][size=85]Ep(1,0)-Ep(0,0)[/size][/color][br][size=50]5[/size] r_2:=[/size][color=#1155Cc][size=85]Ep(0,1)-Ep(0,0)[/size][/color] [br][size=50]6 [/size][size=85]n:=Kreuzprodukt[ r_1 , r_2 ])[/size] [/color][/td][td][math]{n \, := \, \left( \begin{tabular}{r}3\\-6\\ 6\\ \end{tabular} \right) [/math][br][/td][/tr][tr][td][br][math]-1 x+2 y - 2 z = -1 [/math][br][br][/td][td][color=#1155Cc][size=50][size=85][size=100][/size][/size][color=#e69138][size=85][size=100][/size]Normalenvektor aus Koordinatenform[/size][/color][br]7[/size][size=85] n_k:=(E1(1,0,0),E1(0,1,0),E1(0,0,1)) - (1,1,1)*E1(0,0,0))[br][/size][/color][/td][td][math]{n_k \, := \, \left( \begin{tabular}{r}-1\\2\\ -2\\ \end{tabular} \right)[/math][br][/td][/tr][tr][td][math]\vec{n}\left(\vec{x}-Q\right)=0[/math][br][/td][td][color=#e69138][size=85]Normalenform aufstellen[size=50][/size][/size][/color][color=#1155Cc][size=50][br]8 [size=85]En(x,y,z):=n*( (x,y,z) – Q ))[/size][/size][/color][/td][td][math]{En(x, y, z) \, := \, 3 \; x - 6 \; y + 6 \; z - 3}[/math][br][/td][/tr][tr][td][math]\frac{\vec{n}}{\surd\vec{n^2}}\left(\vec{x}-Q\right)=0[/math][br][/td][td][color=#e69138][size=85]Hesse'sche Normalenform[/size][/color][color=#1155Cc][size=50][br]9 [/size][size=85]Eh(x,y,z):=n/sqrt(n^2)*( (x,y,z) – Q )[br][br][/size][/color][/td][td][math]{Eh(x, y, z) \, := \, \frac{1}{3} \; x - \frac{2}{3} \; y + \frac{2}{3} \; z - \frac{1}{3}}[/math][br][/td][/tr][tr][td][math]\frac{\vec{n}}{\surd\vec{n^2}}\left(\vec{x}-Q\right)=0[/math][br][/td][td][color=#1155Cc][size=50][/size][/color][color=#e69138][size=85]Normalenform zum Einsetzen von [math]\vec{x}[/math] [/size][/color][color=#1155Cc][size=50][br]10 [/size][size=85]Nf(x,n,o):=n*( x – o ) [br][size=50]11[/size] E_1:=Nf( (x,y,z),(1,-2,2),(1,-1,-1) )=0 [/size][/color][br][/td][td][br][/td][/tr][/table]