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author | Karl Berry <karl@freefriends.org> | 2011-09-04 16:35:48 +0000 |
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committer | Karl Berry <karl@freefriends.org> | 2011-09-04 16:35:48 +0000 |
commit | 60b4ec6f2bf1ba57aa206b2ac46c454d75f3bf93 (patch) | |
tree | cbf61d6f8bd4a2c6ff62d5e7940e22c352757cfa /Master/texmf-dist/doc/latex/lapdf/quartic.tex | |
parent | d422465c9efb44dd32ba6a50f6ef9879bce018be (diff) |
lapdf is back (2sep11)
git-svn-id: svn://tug.org/texlive/trunk@23806 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/latex/lapdf/quartic.tex')
-rw-r--r-- | Master/texmf-dist/doc/latex/lapdf/quartic.tex | 45 |
1 files changed, 45 insertions, 0 deletions
diff --git a/Master/texmf-dist/doc/latex/lapdf/quartic.tex b/Master/texmf-dist/doc/latex/lapdf/quartic.tex new file mode 100644 index 00000000000..b51af6c3e21 --- /dev/null +++ b/Master/texmf-dist/doc/latex/lapdf/quartic.tex @@ -0,0 +1,45 @@ +\input preamble.tex + +% --------------------------------------------------------------------------- +\begin{document} +\begin{center} +{\Huge \bf{Full Rational Quartic Bezier Curve}} +\bigskip + +\begin{lapdf}(18,17.5)(-9,-8) + \Setwidth(0.01) + \Dash(1) + \Polygon(-9,-6)(-8,+3)(+0,+8)(+8,+2)(+9,-6) \Stroke + \Setwidth(0.02) + \Dash(0) + \Red + \Rcurve(96)(-9,-6,+4)(-8,+3,+3)(+0,+8,+5)(8,+2,+3)(+9,-6,+4) \Stroke + \Blue + \Rcurve(96)(-9,-6,+4)(-8,+3,-3)(+0,+8,+5)(8,+2,-3)(+9,-6,+4) \Stroke + \Black + \Point(0)(-9,-6) + \Point(1)(-8,+3) + \Point(1)(+0,+8) + \Point(1)(+8,+2) + \Point(0)(+9,-6) + \Text(-9.2,-5.8,tr){$P_0$} + \Text(-8.2,+3.2,tr){$P_1$} + \Text(+0.0,+8.2,bc){$P_2$} + \Text(+8.2,+2.2,tl){$P_3$} + \Text(+9.2,-5.8,tl){$P_4$} +\end{lapdf} +\end{center} +\parskip0.2cm +$P_1$ and $P_3$ of the blue curve have negative weights, but both curves +share the same Bezier points and absolute weight values. Now we can see +the complete Bezier curve. The proof for this needs some insight in +projective geometry and it's rather involved, so I only give here the +general rule for drawing complete rational Bezier curves: Make every odd +weight negative and you'll get the complementary Bezier curve. + +You should notice that in this case the Bezier curve no longer lies in +the convex hull of it's control polygon, because his is only holds if all +weights are positive. It should also be mentioned that negative weights for +other points can cause numerical problems, because the denominator can +become zero. +\end{document} |