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\documentclass{article}
\usepackage{open-axiom}
\begin{document}
\title{\$SPAD/src/algebra mesh.spad}
\author{James Wen, Jon Steinbach}
\maketitle
\begin{abstract}
\end{abstract}
\eject
\tableofcontents
\eject
\section{package MESH MeshCreationRoutinesForThreeDimensions}
<<package MESH MeshCreationRoutinesForThreeDimensions>>=
)abbrev package MESH MeshCreationRoutinesForThreeDimensions
++ <description of package>
++ Author: Jim Wen
++ Date Created: ??
++ Date Last Updated: October 1991 by Jon Steinbach
++ Keywords:
++ Examples:
++ References:
MeshCreationRoutinesForThreeDimensions():Exports == Implementation where
I ==> Integer
PI ==> PositiveInteger
SF ==> DoubleFloat
L ==> List
SEG ==> Segment
S ==> String
Fn1 ==> SF -> SF
Fn2 ==> (SF,SF) -> SF
Fn3 ==> (SF,SF,SF) -> SF
FnPt ==> (SF,SF) -> Point(SF)
FnU ==> Union(Fn3,"undefined")
EX ==> Expression
DROP ==> DrawOption
POINT ==> Point(SF)
SPACE3 ==> ThreeSpace(SF)
COMPPROP ==> SubSpaceComponentProperty
TUBE ==> TubePlot
Exports ==> with
meshPar2Var: (Fn2,Fn2,Fn2,FnU,SEG SF,SEG SF,L DROP) -> SPACE3
++ meshPar2Var(f,g,h,j,s1,s2,l) \undocumented
meshPar2Var: (FnPt,SEG SF,SEG SF,L DROP) -> SPACE3
++ meshPar2Var(f,s1,s2,l) \undocumented
meshPar2Var: (SPACE3,FnPt,SEG SF,SEG SF,L DROP) -> SPACE3
++ meshPar2Var(sp,f,s1,s2,l) \undocumented
meshFun2Var: (Fn2,FnU,SEG SF,SEG SF,L DROP) -> SPACE3
++ meshFun2Var(f,g,s1,s2,l) \undocumented
meshPar1Var: (EX I,EX I,EX I,Fn1,SEG SF,L DROP) -> SPACE3
++ meshPar1Var(s,t,u,f,s1,l) \undocumented
ptFunc: (Fn2,Fn2,Fn2,Fn3) -> ((SF,SF) -> POINT)
++ ptFunc(a,b,c,d) is an internal function exported in
++ order to compile packages.
Implementation ==> add
import ViewDefaultsPackage()
import SubSpaceComponentProperty()
import DrawOptionFunctions0
import SPACE3
--import TUBE()
-- local functions
numberCheck(nums:Point SF):Void ==
-- this function checks to see that the small floats are
-- actually just that - rather than complex numbers or
-- whatever (the whatever includes nothing presently
-- since NaN, Not a Number, is not necessarily supported
-- by common lisp). note that this function is dependent
-- upon the fact that Common Lisp supports complex numbers.
for i in minIndex(nums)..maxIndex(nums) repeat
COMPLEXP(nums.(i::PositiveInteger))$Lisp =>
error "An unexpected complex number was encountered in the calculations."
makePt:(SF,SF,SF,SF) -> POINT
makePt(x,y,z,c) == point(l : List SF := [x,y,z,c])
ptFunc(f,g,h,c) ==
x := f(#1,#2); y := g(#1,#2); z := h(#1,#2)
makePt(x,y,z,c(x,y,z))
-- parameterized equations of two variables
meshPar2Var(sp,ptFun,uSeg,vSeg,opts) ==
-- the issue of open and closed needs to be addressed, here, we are
-- defaulting to open (which is probably the correct default)
-- the user should be able to override that (optional argument?)
llp : L L POINT := nil()
uNum : PI := var1Steps(opts,var1StepsDefault())
vNum : PI := var2Steps(opts,var2StepsDefault())
ustep := (lo uSeg - hi uSeg)/uNum
vstep := (lo vSeg - hi vSeg)/vNum
someV := hi vSeg
for iv in vNum..0 by -1 repeat
if zero? iv then someV := lo vSeg
-- hack: get last number in segment within segment
lp : L POINT := nil()
someU := hi uSeg
for iu in uNum..0 by -1 repeat
if zero? iu then someU := lo uSeg
-- hack: get last number in segment within segment
pt := ptFun(someU,someV)
numberCheck pt
lp := concat(pt,lp)
someU := someU + ustep
llp := concat(lp,llp)
someV := someV + vstep
-- now llp contains a list of lists of points
-- for a surface that is a result of a function of 2 variables,
-- the main component is open and each sublist is open as well
lProp : L COMPPROP := [ new() for l in llp ]
for aProp in lProp repeat
close(aProp,false)
solid(aProp,false)
aProp : COMPPROP:= new()
close(aProp,false)
solid(aProp,false)
space := sp
-- space := create3Space()
mesh(space,llp,lProp,aProp)
space
meshPar2Var(ptFun,uSeg,vSeg,opts) ==
sp := create3Space()
meshPar2Var(sp,ptFun,uSeg,vSeg,opts)
zCoord: (SF,SF,SF) -> SF
zCoord(x,y,z) == z
meshPar2Var(xFun,yFun,zFun,colorFun,uSeg,vSeg,opts) ==
-- the color function should be parameterized by (u,v) as well,
-- not (x,y,z) but we also want some sort of consistency and so
-- changing this over would mean possibly changing the explicit
-- stuff over and there, we probably do want the color function
-- to be parameterized by (x,y,z) - not just (x,y) (this being
-- for convinience only since z is also defined in terms of (x,y)).
(colorFun case Fn3) =>
meshPar2Var(ptFunc(xFun,yFun,zFun,colorFun :: Fn3),uSeg,vSeg,opts)
meshPar2Var(ptFunc(xFun,yFun,zFun,zCoord),uSeg,vSeg,opts)
-- explicit equations of two variables
meshFun2Var(zFun,colorFun,xSeg,ySeg,opts) ==
-- here, we construct the data for a function of two variables
meshPar2Var(#1,#2,zFun,colorFun,xSeg,ySeg,opts)
@
\section{License}
<<license>>=
--Copyright (c) 1991-2002, The Numerical ALgorithms Group Ltd.
--All rights reserved.
--
--Redistribution and use in source and binary forms, with or without
--modification, are permitted provided that the following conditions are
--met:
--
-- - Redistributions of source code must retain the above copyright
-- notice, this list of conditions and the following disclaimer.
--
-- - Redistributions in binary form must reproduce the above copyright
-- notice, this list of conditions and the following disclaimer in
-- the documentation and/or other materials provided with the
-- distribution.
--
-- - Neither the name of The Numerical ALgorithms Group Ltd. nor the
-- names of its contributors may be used to endorse or promote products
-- derived from this software without specific prior written permission.
--
--THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS
--IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED
--TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A
--PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER
--OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL,
--EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO,
--PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR
--PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF
--LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING
--NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
--SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
@
<<*>>=
<<license>>
<<package MESH MeshCreationRoutinesForThreeDimensions>>
@
\eject
\begin{thebibliography}{99}
\bibitem{1} nothing
\end{thebibliography}
\end{document}
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