pst-func 0.53

git-svn-id: svn://tug.org/texlive/trunk@7087 c570f23f-e606-0410-a88d-b1316a301751

4 files changed, 169 insertions, 18 deletions

diff --git a/Master/texmf-dist/doc/generic/pst-func/Changes b/Master/texmf-dist/doc/generic/pst-func/Changes
index 79457f263ef..d97578831f2 100644
--- a/Master/texmf-dist/doc/generic/pst-func/Changes
+++ b/Master/texmf-dist/doc/generic/pst-func/Changes
@@ -1,6 +1,8 @@
 ..... pst-func.tex
-0.52  2008-03-02  - changes macros from SpecialObj to OpenObj to allow
-                    using inside \pscustom
+0.53  2008-03-21  - added macro \psBezier# for Bezier curves of order
+		    #=1...9 with 2..10 pairs of coordinates
+0.52  2008-03-02  - changes macros from SpecialObj to OpenObj, which allows the use
+		    of the macros inside \pscustom
 0.51  2008-02-27  - enable filling support for \psIntegral  and \psCumIntegral
 		    (suggested by Rafal Bartczuk) 
 0.50  2007-08-30  - modified \psPoisson{m,N}{Lambda} (Gerry Coombes) 
@@ -52,6 +54,8 @@
 
 
 ..... pst-func.pro
+0.08  2008-03-21  added BezierCurve code for Bezier curves of up to
+		    order 9 
 0.07  2007-08-30  new subroutine LogGamma 
 0.06  2006-04-16  new subroutine MoverN (binomial coefficient)
 0.05  2005-12-19  new subroutine Si and si for the integral sin
diff --git a/Master/texmf-dist/doc/generic/pst-func/README b/Master/texmf-dist/doc/generic/pst-func/README
index c1b86678790..3dbe4b5fed4 100644
--- a/Master/texmf-dist/doc/generic/pst-func/README
+++ b/Master/texmf-dist/doc/generic/pst-func/README
@@ -1,4 +1,5 @@
 pst-func: plotting special mathematical functions:
+-- psBezier
 -- psPolynomial (with derivations)
 -- psFourier
 -- psBessel
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
index 74cc078a126..7b45c55c800 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.pdf
diff --git a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
index fb9e4d2a250..c8193b69342 100644
--- a/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
+++ b/Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
@@ -1,8 +1,9 @@
-\documentclass[dvips,a4paper,11pt,english]{article}
+\documentclass[dvips,a4paper,english]{article}
 \usepackage[T1]{fontenc}
-\usepackage[latin1]{inputenc}
-\usepackage{pamathx}%    use this if you have the palatino math font
-%\usepackage{mathpazo}%  use this if you do not have the palatino math font
+\usepackage[utf8]{inputenc}
+%\usepackage{pamathx}%    use this if you have the palatino math font
+\usepackage{arev}%  use this if you do not have the palatino math font
+%\usepackage[scaled=0.9]{luximono}%  use this if you do not have the palatino math font
 \usepackage{url}
 \usepackage{amsmath}
 \usepackage{tabularx}
@@ -25,6 +26,7 @@
 \def\PS{PostScript\xspace}
 \def\CMD#1{{\ttfamily\textbackslash #1}}
 \def\dt{\ensuremath{\,\mathrm{d}t}}
+\def\Index#1{\index{#1}#1}
 %
 \def\pshlabel#1{\footnotesize#1}
 \def\psvlabel#1{\footnotesize#1}
@@ -40,12 +42,13 @@ plotting special mathematical functions\\[5mm]
 %		  was build with VTeX/Free (\protect\url{http://www.micropress-inc.com/linux})}\\
 \author{Herbert Vo\ss\thanks{%
 Thanks to: 
-    \mbox{Martin Chicoine}, 
-    \mbox{Gerry Coombes}, 
-    \mbox{John Frampton}, 
-    \mbox{Attila Gati}, 
-    \mbox{Lars Kotthoff}, 
-    and \mbox{Jose-Emilio Vila-Forcen}.
+    Martin Chicoine, 
+    Gerry Coombes, 
+    John Frampton, 
+    Attila Gati, 
+    Horst Gierhardt,  
+    Lars Kotthoff, 
+    and Jose-Emilio Vila-Forcen.
 }}
 \date{\today}
 
@@ -65,6 +68,124 @@ of having older versions, go to \url{http://www.CTAN.org/} and load the newest v
 
 \clearpage
 
+\section{\CMD{psBezier\#}}
+This macro can plot a B\'ezier spline from order 1 up to 9 which needs
+(order+1) pairs of given coordinates.
+
+Given a set of $n+1$ control points $P_0$, $P_1$, \ldots, $P_n$, the corresponding \Index{B\'ezier} curve 
+(or \Index{Bernstein-B\'ezier} curve) is given by 
+
+\begin{align}
+C(t)=\sum_{i=0}^n P_i B_{i,n}(t)
+\end{align}
+
+Where $B_{i,n}(t)$ is a Bernstein polynomial $B_{i,n}(t)=\binom{n}{i}t^i(1-t)^{n-i}$, 
+ and $t \in [0,1]$. 
+The Bézier curve starts through the first and last given point and 
+lies within the convex hull of all control points. The curve is tangent 
+to $P_1-P_0$ and $P_n-P_{n-1}$ at the endpoint.
+Undesirable properties of Bézier curves are their numerical instability for 
+large numbers of control points, and the fact that moving a single control 
+point changes the global shape of the curve. The former is sometimes avoided 
+by smoothly patching together low-order Bézier curves. 
+
+The macro \CMD{psBezier} (note the upper case B) expects the number of the order 
+and $n=order+1$ pairs of coordinates:
+
+\begin{lstlisting}[style=syntax]
+\psBezier#[<options>](x0,y0)(x1,y1)...(xn,yn)
+\end{lstlisting}
+
+The number of steps between the first and last control points is given
+by the keyword \verb=plotpoints= and preset to 200. It can be
+changed in the usual way. 
+
+
+\begin{lstlisting}
+\psset{showpoints=true,linewidth=1.5pt}
+\begin{pspicture}(-2,-2)(2,2)% order 1 -- linear
+  \psBezier1{<->}(-2,0)(-2,2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 2 -- quadratric
+  \psBezier2{<->}(-2,0)(-2,2)(0,2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 3 -- cubic
+  \psBezier3{<->}(-2,0)(-2,2)(0,2)(2,2)
+\end{pspicture}\qquad
+
+\vspace{1cm}
+\begin{pspicture}(-2,-2)(2,2)% order 4 -- quartic
+  \psBezier4{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 5 -- quintic
+  \psBezier5{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 6
+  \psBezier6{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)
+\end{pspicture}\qquad
+
+\vspace{1cm}
+\begin{pspicture}(-2,-2)(2,2)% order 7
+  \psBezier7{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)(-2,-2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 8
+  \psBezier8{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)(-2,-2)(-2,0)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 9
+  \psBezier9{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)(-2,-2)(-2,0)(0,0)
+\end{pspicture}
+\end{lstlisting}
+
+
+\begingroup
+\psset{showpoints=true,linewidth=1.5pt}
+\begin{pspicture}(-2,-2)(2,2)% order 1 -- linear
+  \psBezier1{<->}(-2,0)(-2,2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 2 -- quadratric
+  \psBezier2{<->}(-2,0)(-2,2)(0,2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 3 -- cubic
+  \psBezier3{<->}(-2,0)(-2,2)(0,2)(2,2)
+\end{pspicture}\qquad
+
+\vspace{1cm}
+\begin{pspicture}(-2,-2)(2,2)% order 4 -- quartic
+  \psBezier4{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 5 -- quintic
+  \psBezier5{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 6
+  \psBezier6{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)
+\end{pspicture}\qquad
+
+\vspace{1cm}
+\begin{pspicture}(-2,-2)(2,2)% order 7
+  \psBezier7{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)(-2,-2)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 8
+  \psBezier8{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)(-2,-2)(-2,0)
+\end{pspicture}\qquad
+%
+\begin{pspicture}(-2,-2)(2,2)% order 9
+  \psBezier9{<->}(-2,0)(-2,2)(0,2)(2,2)(2,0)(2,-2)(0,-2)(-2,-2)(-2,0)(0,0)
+\end{pspicture}
+\endgroup
+
+
+
 \section{\CMD{psPolynomial}}
 The polynomial function is defined as
 \begin{align}
@@ -73,6 +194,7 @@ f^{\prime}(x) &= a_1 + 2a_2x + 3a_3x^2 + \ldots +(n-1)a_{n-1}x^{n-2} + na_nx^{n-
 f^{\prime\prime}(x) &= 2a_2 + 6a_3x + \ldots +(n-1)(n-2)a_{n-1}x^{n-3} + n(n-1)a_nx^{n-2}
 \end{align}
 
+
 \noindent so \verb+pst-func+ needs only the coefficients of the
 polynomial to calculate the function. The syntax is
 
@@ -260,7 +382,7 @@ syntax is similiar to \verb+psPolynomial+, except that there are
 two kinds of coefficients:
 
 \begin{lstlisting}[style=syntax]
-\psPolynomial[cosCoeff=a0 a1 a2 ..., sinCoeff=b1 b2 ...]{xStart}{xEnd}
+\psFourier[cosCoeff=a0 a1 a2 ..., sinCoeff=b1 b2 ...]{xStart}{xEnd}
 \end{lstlisting}
 The coefficients must have the orders $a_0\ a_1\ a_2\ \ldots$
 and $b_1\ b_2\ b_3\ \ldots$ and be separated by
@@ -385,6 +507,7 @@ way, at the cost of some reduction in graphics resolution.
 \end{LTXexample}
 
 
+
 \clearpage
 \section{\CMD{psSi}, \CMD{pssi} and \CMD{psCi}}
 The integral sin  and cosin are defined as
@@ -519,7 +642,7 @@ your system, otherwise install or update it from \textsc{CTAN}. It must the late
 
 
 
-
+\clearpage
 \subsection{Normal distribution (Gauss)}
 The Gauss function is defined as
 %
@@ -560,6 +683,8 @@ and is predefined with 5.
 \end{LTXexample}
 
 
+
+\clearpage
 \subsection{Binomial distribution}\label{sec:bindistri}
 
 These two macros plot binomial distribution, \CMD{psBinomialN} the normalized one. It is always 
@@ -661,6 +786,7 @@ P(k) &= P(k-1)\cdot\frac{N-k+1}{k}\cdot\frac{p}{1-p}
 \end{align}
 
 
+
 \begin{LTXexample}[pos=t,preset=\centering]
 \psset{xunit=1cm,yunit=5cm}%
 \begin{pspicture}(-3,-0.15)(4,0.55)%
@@ -671,6 +797,7 @@ P(k) &= P(k-1)\cdot\frac{N-k+1}{k}\cdot\frac{p}{1-p}
 \end{LTXexample}
 
 
+
 \begin{LTXexample}[pos=t,preset=\centering]
 \psset{yunit=10}
 \begin{pspicture*}(-8,-0.07)(8.1,0.55)
@@ -693,10 +820,13 @@ P(k) &= P(k-1)\cdot\frac{N-k+1}{k}\cdot\frac{p}{1-p}
 \end{pspicture*}
 \end{LTXexample}
 
+
+
 For the normalized distribution the plotstyle can be set to \verb+curve+ (\verb+plotstyle=curve+), 
 then the binomial distribution looks like a normal distribution. This option is only
 valid vor \CMD{psBinomialN}. The option \verb+showpoints+ is valid if \verb+curve+ was chosen.
 
+
 \begin{LTXexample}[pos=t,preset=\centering]
 \psset{xunit=1cm,yunit=10cm}%
 \begin{pspicture*}(-4,-0.06)(4.1,0.57)%
@@ -707,6 +837,7 @@ valid vor \CMD{psBinomialN}. The option \verb+showpoints+ is valid if \verb+curv
 \end{pspicture*}
 \end{LTXexample}
 
+
 \begin{LTXexample}[pos=t,preset=\centering]
 \psset{xunit=1cm,yunit=10cm}%
 \begin{pspicture*}(-4,-0.06)(4.2,0.57)%
@@ -718,6 +849,7 @@ valid vor \CMD{psBinomialN}. The option \verb+showpoints+ is valid if \verb+curv
 \end{LTXexample}
 
 
+\clearpage
 \subsection{Poisson distribution}
 Given a Poisson process\footnote{\url{http://mathworld.wolfram.com/PoissonProcess.html}}, 
 the probability of obtaining exactly $n$ successes in $N$ trials is given by the 
@@ -792,6 +924,7 @@ in which \texttt{M} is an optional argument with a default of 0.
 \end{LTXexample}
 
 
+
 \clearpage
 \subsection{Gamma distribution}
 A gamma distribution is a general type of statistical distribution that is related 
@@ -993,15 +1126,15 @@ and has the syntax (with a default setting of $s=1$ and $\mu=1$):
 
 
 \clearpage
-\section{\CMD{psLame} -- Lamé Curve, a superellipse}
+\section{\CMD{psLame} -- Lam\'e Curve, a superellipse}
 A superellipse is a curve with Cartesian equation
 %	
 \begin{align}
 \left|\frac{x}{a}\right|^r + \left|\frac{y}{b}\right|^r & =1
 \end{align}
 %
-first discussed in 1818 by Gabriel Lamé (1795--1870)%
-\footnote{Lamé worked on a wide variety of different topics. 
+first discussed in 1818 by Gabriel Lam\'e (1795--1870)%
+\footnote{Lam\'e worked on a wide variety of different topics. 
 His work on differential geometry and contributions to Fermat's Last Theorem 
 are important. He proved the theorem for $n = 7$ in 1839.}. 
 A superellipse may be described parametrically by
@@ -1011,7 +1144,7 @@ x = a\cdot\cos^{\frac{2}{r}} t\\
 y = b\cdot\sin^{\frac{2}{r}} t
 \end{align}
 %			
-Superellipses with $a=b$ are also known as Lamé curves or Lamé ovals and
+Superellipses with $a=b$ are also known as Lam\'e curves or Lam\'e ovals and
 the restriction to $r>2$ is sometimes also made. The following 
 table summarizes a few special cases. Piet Hein used $\frac{5}{2}$ with a number of different 
 $\frac{a}{b}$ ratios for various of his projects. For example, he used $\frac{a}{b}=\frac{6}{5}$ 
@@ -1331,10 +1464,23 @@ valuewidth & <number>     & 10     & the width of the string for the converted
 \end{lstlisting}
 
 
+\section{Examples}
+
+\begin{LTXexample}[preset=\centering]
+\psset{xunit=0.5cm,yunit=20cm,arrowscale=1.5}
+\begin{pspicture}(-1,-0.1)(21,0.2)
+\psChiIIDist[linewidth=1pt,nue=5]{0.01}{19.5}
+\psaxes[labels=none,ticks=none]{->}(20,0.2)
+\pscustom[fillstyle=solid,fillcolor=red!30]{%
+  \psChiIIDist[linewidth=1pt,nue=5]{8}{19.5}%
+  \psline(20,0)(8,0)}
+\end{pspicture}
+\end{LTXexample}
 
 
 \section{Credits}
 Rafal Bartczuk | Gerry Coombes | Denis Girou | Christophe Jorssen | Manuel Luque | Timothy Van Zandt 
+and \url{http://mathworld.wolfram.com}
 
 \bgroup
 \raggedright