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authordos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
committerdos-reis <gdr@axiomatics.org>2007-08-14 05:14:52 +0000
commitab8cc85adde879fb963c94d15675783f2cf4b183 (patch)
treec202482327f474583b750b2c45dedfc4e4312b1d /src/input/coordsys.input.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
Initial population.
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/input coordsys.input}
+\author{The Axiom Team}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{License}
+<<license>>=
+--Copyright The Numerical Algorithms Group Limited 1994.
+@
+<<*>>=
+<<license>>
+-- test input for CoordinateSystems package
+draw(sin(x),x=0.5..%pi,coordinates == bipolar(1$DFLOAT))
+m(u:DFLOAT,v:DFLOAT):DFLOAT == 1
+draw(m,0..2*%pi, 0..%pi,coordinates == bipolar(1$DFLOAT))
+
+draw(surface(u*cos(v),u*sin(v),u),u=1..4,v=1..2*%pi,coordinates == bipolarCylindrical(1$DFLOAT))
+
+--conical(a,b) maps a 3D point (lambda,mu,nu) to the rectangular coordinates:
+--x = lambda*mu*nu/(a*b)
+--y = lambda/a*sqrt((mu**2-a**2)*(nu**2-a**2)/(a**2-b**2))
+--z = lambda/b*sqrt((mu**2-b**2)*(nu**2-b**2)/(b**2-a**2))
+--NOTE: There will be a division by zero error if a*b = 0, or a**2-b**2 = 0,
+-- or if b**2-a**2 = 0. Also, the following relations must be true:
+-- (mu**2-a**2)*(nu**2-a**2)/(a**2-b**2) > 0 and
+-- (mu**2-b**2)*(nu**2-b**2)/(b**2-a**2) > 0.
+
+j1(t:DFLOAT):DFLOAT == 4
+j2(t:DFLOAT):DFLOAT == t
+draw(curve(j1,j2,j2),-9..9,coordinates == cylindrical)
+
+draw(sin(4*t/7),t=0..14*%pi,coordinates == elliptic(1$DFLOAT))
+m(u:DFLOAT,v:DFLOAT):DFLOAT == 1
+draw(m,0..2*%pi,0..%pi,coordinates == elliptic(1$DFLOAT))
+
+U2:Vector Expression Integer := vector [0,0,1]
+x(u,v) == beta(u) + v*delta(u)
+beta u == vector [cos u, sin u, 0]
+delta u == (cos(u/2)) * beta(u) + sin(u/2) * U2
+vec := x(u,v)
+draw(surface(vec.1,vec.2,vec.3),v=-0.5..0.5,u=0..2*%pi,coordinates == ellipticCylindrical(1$DFLOAT),var1Steps == 50,var2Steps == 50)
+
+m(u:DFLOAT,v:DFLOAT):DFLOAT == 1
+draw(m,-%pi/2..%pi/2,0..2*%pi,coordinates == oblateSpheroidal(1$DFLOAT))
+
+h1(t:DFLOAT):DFLOAT == t
+h2(t:DFLOAT):DFLOAT == 2
+draw(curve(h1,h2),-3..3,coordinates == parabolic)
+draw(surface(u*cos(v),u*sin(v),2*u),u=0..4,v=0..2*%pi,coordinates == parabolic)
+
+draw(surface(u*cos(v),u*sin(v),v*cos(u)),u=0..4,v=0..2*%pi,coordinates == parabolicCylindrical)
+
+draw(surface(u*cos(v),u*sin(v),u*v),u=0..4,v=0..2*%pi,coordinates==paraboloidal,var1Steps == 50, var2Steps == 50)
+
+draw(sin(4*t/7),t=0..14*%pi,coordinates == polar)
+m(u:DFLOAT,v:DFLOAT):DFLOAT == 1
+draw(m,0..2*%pi, 0..%pi,coordinates == polar)
+
+m(u:DFLOAT,v:DFLOAT):DFLOAT == 1
+draw(m,-%pi/2..%pi/2,0..2*%pi,coordinates == prolateSpheroidal(1$DFLOAT))
+
+m(u:DFLOAT,v:DFLOAT):DFLOAT == 1
+draw(m,0..2*%pi,0..%pi,coordinates == spherical)
+
+draw(surface(u*cos(v),u*sin(v),u),u=1..4,v=1..4*%pi,coordinates == toroidal(1$DFLOAT))
+
+
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}