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authorKarl Berry <karl@freefriends.org>2008-03-22 23:29:41 +0000
committerKarl Berry <karl@freefriends.org>2008-03-22 23:29:41 +0000
commit8328d8188fb85a8733a4f03c71b40f415ac51365 (patch)
tree7ad37fe6429fe77c892d6395d01700f1329ce34b /Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex
parentb552fc5adb5017e593f10eeed7bfd18e10e531ac (diff)
pst-func 0.53
git-svn-id: svn://tug.org/texlive/trunk@7087 c570f23f-e606-0410-a88d-b1316a301751
Diffstat (limited to 'Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex')
-rw-r--r--Master/texmf-dist/doc/generic/pst-func/pst-func-doc.tex178
1 files changed, 162 insertions, 16 deletions
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