From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001
From: Norbert Preining <norbert@preining.info>
Date: Mon, 2 Sep 2019 13:46:59 +0900
Subject: Initial commit

---
 macros/latex/contrib/lapdf/rational.tex | 58 +++++++++++++++++++++++++++++++++
 1 file changed, 58 insertions(+)
 create mode 100644 macros/latex/contrib/lapdf/rational.tex

(limited to 'macros/latex/contrib/lapdf/rational.tex')

diff --git a/macros/latex/contrib/lapdf/rational.tex b/macros/latex/contrib/lapdf/rational.tex
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+++ b/macros/latex/contrib/lapdf/rational.tex
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+\input preamble.tex
+
+% ---------------------------------------------------------------------------
+\begin{document}
+\begin{center}
+{\Huge \bf{Integral And Rational Bezier Curves}}
+\bigskip
+
+\begin{lapdf}(18,18)(-9,-9)
+ \Setwidth(0.01)
+ \Dash(1)
+ \Polygon(+0,+9)(+9,+9)
+  (+9,+3)(-9,-3)(+9,-9)
+  (+0,-9)(-9,-9)(+9,-3)
+  (-9,+3)(-9,+9)(+0,+9) \Stroke
+ \Setwidth(0.02)
+ \Dash(0)
+ \Red
+ \Curve(96)(+0,+9)(+9,+9)(+9,+3)(-9,-3)(+9,-9)(+0,-9)
+ \Curve(96)(+0,+9)(-9,+9)(-9,+3)(+9,-3)(-9,-9)(+0,-9) \Stroke
+ \Blue
+ \Rcurve(128)(+0,+9,1)(+9,+9,6)(+9,+3,1)(-9,-3,6)(+9,-9,6)(+0,-9,1)
+ \Rcurve(128)(+0,+9,1)(-9,+9,6)(-9,+3,1)(+9,-3,6)(-9,-9,6)(+0,-9,1) \Stroke
+ \Black
+ \Point(0)(+0,+9)
+ \Point(1)(+9,+9)
+ \Point(1)(+9,+3)
+ \Point(1)(-9,-3)
+ \Point(1)(+9,-9)
+ \Point(0)(+0,-9)
+ \Point(1)(-9,-9)
+ \Point(1)(+9,-3)
+ \Point(1)(-9,+3)
+ \Point(1)(-9,+9)
+ \Text(+0.0,+8.8,tc){$w=1$}
+ \Text(+8.8,+8.8,tr){$w=6$}
+ \Text(+8.8,+3.2,br){$w=1$}
+ \Text(-8.8,-3.0,lc){$w=6$}
+ \Text(+8.8,-8.8,br){$w=6$}
+ \Text(+0.0,-8.8,bc){$w=1$}
+ \Text(-8.8,-8.8,bl){$w=6$}
+ \Text(+8.8,-3.0,rc){$w=6$}
+ \Text(-8.8,+3.2,bl){$w=1$}
+ \Text(-8.8,+8.8,tl){$w=6$}
+\end{lapdf}
+\end{center}
+
+Both curves are degree five bezier curves and they share the same
+control points. The red one consists of two integral curves and the
+blue one consists of two rational curves with diffent weights, which
+are shown at their control points. Integral Bezier curves can be thought
+as rational curves with all weights set to one.
+
+As you can see, the curve is pulled towards the points, depending on
+their weights. Thus you will have much more control over the curve
+shape. Rational curves also allow to draw exact conics like ellipses,
+circles, parabolas and hyperbolas.
+\end{document}
-- 
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