From e0c6872cf40896c7be36b11dcc744620f10adf1d Mon Sep 17 00:00:00 2001 From: Norbert Preining 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 new file mode 100644 index 0000000000..eae95a1764 --- /dev/null +++ b/macros/latex/contrib/lapdf/rational.tex @@ -0,0 +1,58 @@ +\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} -- cgit v1.2.3