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diff --git a/Master/texmf-dist/doc/latex/lapdf/rparams.tex b/Master/texmf-dist/doc/latex/lapdf/rparams.tex new file mode 100644 index 00000000000..210926d9425 --- /dev/null +++ b/Master/texmf-dist/doc/latex/lapdf/rparams.tex @@ -0,0 +1,68 @@ +\input preamble.tex + +\def\fr{\displaystyle\frac} + +% --------------------------------------------------------------------------- +\begin{document} +\unitlength1.125cm + +\begin{center} +{\Huge \bf{Ellipse Parameters}} +\bigskip + +\begin{lapdf}(16,16)(-8,-11) + \Lingrid(10)(1,1)(-8,8)(-11,5) + \Setwidth(0.01) + \Dash(1) + \Polygon(-7.2,-3.2)(0,4)(7.2,-3.2)(-7.2,-3.2)(0,-10.4)(7.2,-3.2) \Stroke + \Polygon(5.33,-1.33)(-5.33,-1.33)(0,-6.67)(5.33,-1.33) \Stroke + \Polygon(4.5,-0.5)(-4.5,-0.5)(0,-5)(4.5,-0.5) \Stroke + \Dash(0) + \Setwidth(0.02) + \Red + \Rcurve(128)(-4,0,3)(0,4,2)(4,0,3) \Stroke + \Rcurve(128)(-4,0,3)(0,4,-2)(4,0,3) \Stroke + \Green + \Rcurve(96)(-4,0,2)(0,4,1)(4,0,2) \Stroke + \Rcurve(96)(-4,0,2)(0,4,-1)(4,0,2) \Stroke + \Blue + \Rcurve(64)(-4,0,3)(0,4,1)(4,0,3) \Stroke + \Rcurve(64)(-4,0,3)(0,4,-1)(4,0,3) \Stroke + \Point(1)(-4,0) + \Point(1)(0,4) + \Point(1)(4,0) + \Point(1)(7.2,-3.2) + \Point(1)(4,-6.4) + \Point(1)(0,-10.4) + \Point(1)(-4,-6.4) + \Point(1)(-7.2,-3.2) + \Point(1)(-5.33,-1.33) + \Point(1)(-4,-2.67) + \Point(1)(0,-6.67) + \Point(1)(4,-2.67) + \Point(1)(5.33,-1.33) + \Point(1)(-4.5,-0.5) + \Point(1)(-4,-1) + \Point(1)(0,-5) + \Point(1)(4,-1) + \Point(1)(4.5,-0.5) + \Point(0)(0,-3.2) + \Point(0)(0,-1.33) + \Point(0)(0,-0.5) +\end{lapdf} +{\large $w=2/3$, $w=1/2$, $w=1/3$} +\end{center} +\parskip0.2cm +We know the center $M=(x_m,y_m)$ and the values of $a$ and $b$. We want +to calculate the curve points $P_0$, $P_1$ and $P_2$ and the weight +$w$ to draw the ellipse. With $r=\sqrt{a^2+b^2}$ we get: +\begin{equation} +P_0={{x_m-\fr{a^2}{r}}\choose{y_m+\fr{b^2}{r}}} \quad +P_1={{xm}\choose{ym+r}} \quad +P_2={{x_m+\fr{a^2}{r}}\choose{y_m+\fr{b^2}{r}}} \quad +w_0=1 \quad +w_1=\pm\fr{b}{r} \quad +\end{equation} +With these weights we can draw the ellipse with two segments. One segment +uses the positive and the other the negative weight $w_1$. +\end{document} |