Des courbes (multi-foliums, etc), dont les équations sont du site de Robert Ferréol...

diff --git a/img/serie02/LISTE.txt b/img/serie02/LISTE.txt
index c4b196f..faa7c28 100644 (file)
--- a/img/serie02/LISTE.txt
+++ b/img/serie02/LISTE.txt
@@ -5,3 +5,4 @@ parapluie.eps
 sinus.png
 rayures.png
 damier.png
+foliums.png
\ No newline at end of file

diff --git a/img/serie02/foliums.pdf b/img/serie02/foliums.pdf
new file mode 100644 (file)
index 0000000..64e8f63
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diff --git a/img/serie02/foliums.png b/img/serie02/foliums.png
new file mode 100644 (file)
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Binary files /dev/null and b/img/serie02/foliums.png differ

diff --git a/img/serie02/foliums.tex b/img/serie02/foliums.tex
new file mode 100644 (file)
index 0000000..b89aeff
--- /dev/null
+++ b/img/serie02/foliums.tex
@@ -0,0 +1,194 @@
+\documentclass[12pt]{article}
+\usepackage{pst-anamorphosis-add,pst-plot,pst-grad}
+\usepackage[a4paper]{geometry}
+
+\makeatletter
+\def\psparametricplotA{\pst@object{parametricplotA}}%  hv 2008-11-22
+\def\parametricplotA{\pst@object{parametricplotA}}
+\def\parametricplotA@i#1#2{\@ifnextchar[{\parametricplotA@x{#1}{#2}}{\parametricplotA@x{#1}{#2}[]}}
+\def\parametricplotA@x#1#2[#3]{\@ifnextchar[{\parametricplotA@xi{#1}{#2}[#3]}{\parametricplotA@xi{#1}{#2}[#3][]}}
+\def\parametricplotA@xi#1#2[#3][#4]#5{%
+  \pst@killglue%
+  \begingroup%
+    \use@par%
+    \@nameuse{beginplot@\psplotstyle}%
+    \addto@pscode{%
+    \tx@optionsanamorphosis
+    \tx@optionsanamorphosisAdd
+      #3 %prefix PS code
+      \psplot@init
+      /t #1 def
+      /t1 #2 def
+      /dt t1 t sub \psk@plotpoints div def
+      /F@pstplot \ifPst@algebraic (#5)
+                    \ifx\psk@PlotDerivative\@none\else
+                      \psk@PlotDerivative\space { (t) tx@Derive begin Derive end } repeat
+                    \fi\space
+                    tx@AlgToPs begin AlgToPs end cvx
+                 \else { #5 } \fi  def
+      \ifPst@VarStep
+         /StillZero 0 def /LastNonZeroStep dt def
+         /F2@pstplot tx@Derive begin (#5) (t) Derive (t) Derive end
+                     \ifx\psk@PlotDerivative\@none\else
+                       \psk@PlotDerivative\space { (t) tx@Derive begin Derive end } repeat
+                     \fi\space
+                    tx@AlgToPs begin AlgToPs end cvx def
+         %% computation of the tolerance defined by plotpoints
+         /epsilon12 \ifx\psk@VarStepEpsilon\@default
+                       tx@Derive begin F2@pstplot end Pyth
+                       dt 3 exp abs mul
+                    \else\psk@VarStepEpsilon\space 12 mul \fi def
+         /ComputeStep {
+           dup 1e-4 lt
+           { pop StillZero 2 ge { LastNonZeroStep 2 mul } { LastNonZeroStep } ifelse /StillZero StillZero 1 add def }
+           { epsilon12 exch div 1 3 div exp /StillZero 0 def }
+           ifelse } bind def
+      \fi
+      /xy {
+        \ifPst@algebraic F@pstplot \else #5 \fi
+        \pst@number\psyunit mul exch
+        \pst@number\psxunit mul exch
+        tx@anamorphosisPathDict begin Anamorphose end
+      } def
+      }%
+    \gdef\psplot@init{}%
+    \@pstfalse
+    \@nameuse{testqp@\psplotstyle}%
+    \if@pst\parametricplotA@ii{#4}\else\parametricplotA@iii{#4}\fi
+  \endgroup%
+  \ignorespaces}
+%
+\def\parametricplotA@ii#1{% para is the post code
+  \ifPst@VarStep%
+    \addto@pscode{%
+      mark xy \@nameuse{beginqp@\psplotstyle}
+      { F2@pstplot Pyth ComputeStep
+        t 2 copy add dup t1 gt {pop t1} if /t exch def F2@pstplot Pyth ComputeStep
+        /t 3 -1 roll def 2 copy gt { exch } if pop
+        /t t 3 -1 roll add dup t1 gt {pop t1} if def
+        xy \@nameuse{doqp@\psplotstyle}
+        t t1 eq { exit } if } loop}%
+  \else\pst@killglue%
+    \addto@pscode{%
+      /ps@Exit false def
+      xy \@nameuse{beginqp@\psplotstyle}
+      \psk@plotpoints 1 sub {
+        /t t dt add def
+        xy \@nameuse{doqp@\psplotstyle}
+        ps@Exit { exit } if
+      } repeat
+      ps@Exit not {
+        /t t1 def
+        xy \@nameuse{doqp@\psplotstyle}
+      } if
+    }%
+  \fi%
+  \addto@pscode{ #1 }%
+  \@nameuse{endqp@\psplotstyle}}
+%
+\def\parametricplotA@iii#1{%
+  \ifPst@VarStep%
+    \addto@pscode{%
+      /n 2 def
+      mark
+      { xy n 2 roll F2@pstplot Pyth
+        ComputeStep t 2 copy add dup t1 gt {pop t1} if
+        /t exch def F2@pstplot Pyth ComputeStep
+        /t 3 -1 roll def 2 copy gt { exch } if pop
+        /t t 3 -1 roll dup /LastNonZeroStep exch def add dup t1 gt {pop t1} if def /n n 2 add def
+        t t1 eq { exit } if } loop
+      xy n 2 roll}%
+  \else\pst@killglue%
+    \addto@pscode{
+      mark
+      /n 2 def
+      \psk@plotpoints {
+        xy
+        n 2 roll
+        /n n 2 add def
+        /t t dt add def
+      } repeat
+      /t t1 def
+      xy
+      n 2 roll}%
+  \fi%
+  \addto@pscode{ #1 }%
+  \@nameuse{endplot@\psplotstyle}}
+%
+\makeatother
+\begin{document}
+\begin{center}
+\begin{pspicture}(-6,-6)(6,6)
+\pscircle[doubleline=true]{3}
+\psset{type=conical}
+\parametricplot[plotpoints=3600,linecolor=red,linewidth=0.5mm]{0}{360}{%
+  /Radius 0.75 t 4 mul cos mul def
+   Radius t cos mul 1 add
+  Radius t sin mul
+    }
+\parametricplotA[plotpoints=3600,linecolor=red,linewidth=0.5mm]{0}{360}{%
+  /Radius 0.75 t 4 mul cos mul def
+   Radius t cos mul 1 add
+  Radius t sin mul
+    }
+\parametricplot[plotpoints=3600,linecolor=blue,linewidth=0.5mm]{0}{360}{%
+  /Radius 1 t 5 mul cos mul def
+   Radius t cos mul -1.25 add
+  Radius t sin mul
+    }
+\parametricplotA[plotpoints=3600,linecolor=blue,linewidth=0.5mm]{0}{360}{%
+  /Radius 1 t 5 mul cos mul def
+   Radius t cos mul -1.25 add
+  Radius t sin mul
+    }
+\parametricplot[plotpoints=3600,fillstyle=solid,fillcolor=green!50]{0}{360}{%
+  /Radius 1 t 2 mul sin t 6 mul sin 4 div add mul def
+   Radius t cos mul
+  Radius t sin mul 1.5 add
+    }
+\parametricplotA[plotpoints=3600,fillstyle=solid,fillcolor=green!50]{0}{360}{%
+   /Radius 1 t 2 mul sin t 6 mul sin 4 div add mul def
+   Radius t cos mul
+  Radius t sin mul 1.5 add
+    }
+\parametricplot[plotpoints=3600,fillstyle=gradient,gradend=yellow,gradbegin=white]{0}{360}{%
+  /Radius 1 t cos 3 exp mul def
+    Radius t sin mul 0 add
+   Radius t cos mul 1 add neg
+    }
+\parametricplotA[plotpoints=3600,fillstyle=gradient,gradbegin=yellow,gradend=white]{0}{360}{%
+  /Radius 1 t cos 3 exp mul def
+    Radius t sin mul 0 add
+   Radius t cos mul 1 add neg
+    }
+{\psset{linewidth=0.5\pslinewidth,linecolor={[rgb]{1 0.75 0}}}
+\multido{\n=0.25+0.25,\N=0.25+0.25}{9}{%
+    \pnode(! \n\space -2.25){A}
+    \pnode(! \n\space 2.25){B}
+    \psline(A)(B)
+    \pslineA(A)(B)
+    \pnode(!-2.25 \N){A}
+    \pnode(!2.25 \N){B}
+    \pslineA(A)(B)
+    \psline(A)(B)
+    }
+\multido{\n=-2.25+0.25,\N=-2.25+0.25}{9}{%
+    \pnode(! \n\space -2.25){A}
+    \pnode(! \n\space 2.25){B}
+    \psline(A)(B)
+    \pslineA(A)(B)
+    \pnode(!-2.25 \N){A}
+    \pnode(!2.25 \N){B}
+    \pslineA(A)(B)
+    \psline(A)(B)
+    }
+\psline(-2.25,0)(2.25,0)
+\psline(0,-2.25)(0,2.25)
+\pslineA(0,-2.25)(0,-0.25)
+\pslineA(0,2.25)(0,0.25)
+\pslineA(-2.25,0)(-0.25,0)
+\pslineA(2.25,0)(0.25,0)}
+\psdot[dotstyle=x,dotsize=.2](0,0)
+\end{pspicture}
+\end{center}
+\end{document} 
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