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author | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
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committer | dos-reis <gdr@axiomatics.org> | 2007-08-14 05:14:52 +0000 |
commit | ab8cc85adde879fb963c94d15675783f2cf4b183 (patch) | |
tree | c202482327f474583b750b2c45dedfc4e4312b1d /src/input/coordsys.input.pamphlet | |
download | open-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz |
Initial population.
Diffstat (limited to 'src/input/coordsys.input.pamphlet')
-rw-r--r-- | src/input/coordsys.input.pamphlet | 79 |
1 files changed, 79 insertions, 0 deletions
diff --git a/src/input/coordsys.input.pamphlet b/src/input/coordsys.input.pamphlet new file mode 100644 index 00000000..af2f3129 --- /dev/null +++ b/src/input/coordsys.input.pamphlet @@ -0,0 +1,79 @@ +\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} |