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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/algebra/paramete.spad.pamphlet
downloadopen-axiom-ab8cc85adde879fb963c94d15675783f2cf4b183.tar.gz
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+\documentclass{article}
+\usepackage{axiom}
+\begin{document}
+\title{\$SPAD/src/algebra paramete.spad}
+\author{Clifton J. Williamson}
+\maketitle
+\begin{abstract}
+\end{abstract}
+\eject
+\tableofcontents
+\eject
+\section{domain PARPCURV ParametricPlaneCurve}
+<<domain PARPCURV ParametricPlaneCurve>>=
+)abbrev domain PARPCURV ParametricPlaneCurve
+++ Author: Clifton J. Williamson
+++ Date Created: 24 May 1990
+++ Date Last Updated: 24 May 1990
+++ Basic Operations: curve, coordinate
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords: parametric curve, graphics
+++ References:
+++ Description: ParametricPlaneCurve is used for plotting parametric plane
+++ curves in the affine plane.
+
+ParametricPlaneCurve(ComponentFunction): Exports == Implementation where
+ ComponentFunction : Type
+ NNI ==> NonNegativeInteger
+
+ Exports ==> with
+ curve: (ComponentFunction,ComponentFunction) -> %
+ ++ curve(c1,c2) creates a plane curve from 2 component functions \spad{c1}
+ ++ and \spad{c2}.
+ coordinate: (%,NNI) -> ComponentFunction
+ ++ coordinate(c,i) returns a coordinate function for c using 1-based
+ ++ indexing according to i. This indicates what the function for the
+ ++ coordinate component i of the plane curve is.
+
+ Implementation ==> add
+
+ Rep := Record(xCoord:ComponentFunction,yCoord:ComponentFunction)
+
+ curve(x,y) == [x,y]
+ coordinate(c,n) ==
+ n = 1 => c.xCoord
+ n = 2 => c.yCoord
+ error "coordinate: index out of bounds"
+
+@
+\section{package PARPC2 ParametricPlaneCurveFunctions2}
+<<package PARPC2 ParametricPlaneCurveFunctions2>>=
+)abbrev package PARPC2 ParametricPlaneCurveFunctions2
+++ Description:
+++ This package \undocumented
+ParametricPlaneCurveFunctions2(CF1: Type, CF2:Type): with
+ map: (CF1 -> CF2, ParametricPlaneCurve(CF1)) -> ParametricPlaneCurve(CF2)
+ ++ map(f,x) \undocumented
+ == add
+ map(f, c) == curve(f coordinate(c,1), f coordinate(c, 2))
+
+@
+\section{domain PARSCURV ParametricSpaceCurve}
+<<domain PARSCURV ParametricSpaceCurve>>=
+)abbrev domain PARSCURV ParametricSpaceCurve
+++ Author: Clifton J. Williamson
+++ Date Created: 24 May 1990
+++ Date Last Updated: 24 May 1990
+++ Basic Operations: curve, coordinate
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords: parametric curve, graphics
+++ References:
+++ Description: ParametricSpaceCurve is used for plotting parametric space
+++ curves in affine 3-space.
+
+ParametricSpaceCurve(ComponentFunction): Exports == Implementation where
+ ComponentFunction : Type
+ NNI ==> NonNegativeInteger
+
+ Exports ==> with
+ curve: (ComponentFunction,ComponentFunction,ComponentFunction) -> %
+ ++ curve(c1,c2,c3) creates a space curve from 3 component functions
+ ++ \spad{c1}, \spad{c2}, and \spad{c3}.
+ coordinate: (%,NNI) -> ComponentFunction
+ ++ coordinate(c,i) returns a coordinate function of c using 1-based
+ ++ indexing according to i. This indicates what the function for the
+ ++ coordinate component, i, of the space curve is.
+
+ Implementation ==> add
+
+ Rep := Record(xCoord:ComponentFunction,_
+ yCoord:ComponentFunction,_
+ zCoord:ComponentFunction)
+
+ curve(x,y,z) == [x,y,z]
+ coordinate(c,n) ==
+ n = 1 => c.xCoord
+ n = 2 => c.yCoord
+ n = 3 => c.zCoord
+ error "coordinate: index out of bounds"
+
+@
+\section{package PARSC2 ParametricSpaceCurveFunctions2}
+<<package PARSC2 ParametricSpaceCurveFunctions2>>=
+)abbrev package PARSC2 ParametricSpaceCurveFunctions2
+++ Description:
+++ This package \undocumented
+ParametricSpaceCurveFunctions2(CF1: Type, CF2:Type): with
+ map: (CF1 -> CF2, ParametricSpaceCurve(CF1)) -> ParametricSpaceCurve(CF2)
+ ++ map(f,x) \undocumented
+ == add
+ map(f, c) == curve(f coordinate(c,1), f coordinate(c,2), f coordinate(c,3))
+
+@
+\section{domain PARSURF ParametricSurface}
+<<domain PARSURF ParametricSurface>>=
+)abbrev domain PARSURF ParametricSurface
+++ Author: Clifton J. Williamson
+++ Date Created: 24 May 1990
+++ Date Last Updated: 24 May 1990
+++ Basic Operations: surface, coordinate
+++ Related Constructors:
+++ Also See:
+++ AMS Classifications:
+++ Keywords: parametric surface, graphics
+++ References:
+++ Description: ParametricSurface is used for plotting parametric surfaces in
+++ affine 3-space.
+
+ParametricSurface(ComponentFunction): Exports == Implementation where
+ ComponentFunction : Type
+ NNI ==> NonNegativeInteger
+
+ Exports ==> with
+ surface: (ComponentFunction,ComponentFunction,ComponentFunction) -> %
+ ++ surface(c1,c2,c3) creates a surface from 3 parametric component
+ ++ functions \spad{c1}, \spad{c2}, and \spad{c3}.
+ coordinate: (%,NNI) -> ComponentFunction
+ ++ coordinate(s,i) returns a coordinate function of s using 1-based
+ ++ indexing according to i. This indicates what the function for the
+ ++ coordinate component, i, of the surface is.
+
+ Implementation ==> add
+
+ Rep := Record(xCoord:ComponentFunction,_
+ yCoord:ComponentFunction,_
+ zCoord:ComponentFunction)
+
+ surface(x,y,z) == [x,y,z]
+ coordinate(c,n) ==
+ n = 1 => c.xCoord
+ n = 2 => c.yCoord
+ n = 3 => c.zCoord
+ error "coordinate: index out of bounds"
+
+@
+\section{package PARSU2 ParametricSurfaceFunctions2}
+<<package PARSU2 ParametricSurfaceFunctions2>>=
+)abbrev package PARSU2 ParametricSurfaceFunctions2
+++ Description:
+++ This package \undocumented
+ParametricSurfaceFunctions2(CF1: Type, CF2:Type): with
+ map: (CF1 -> CF2, ParametricSurface(CF1)) -> ParametricSurface(CF2)
+ ++ map(f,x) \undocumented
+ == add
+ map(f, c) == surface(f coordinate(c,1), f coordinate(c,2), f coordinate(c,3))
+
+@
+\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>>
+
+<<domain PARPCURV ParametricPlaneCurve>>
+<<package PARPC2 ParametricPlaneCurveFunctions2>>
+<<domain PARSCURV ParametricSpaceCurve>>
+<<package PARSC2 ParametricSpaceCurveFunctions2>>
+<<domain PARSURF ParametricSurface>>
+<<package PARSU2 ParametricSurfaceFunctions2>>
+@
+\eject
+\begin{thebibliography}{99}
+\bibitem{1} nothing
+\end{thebibliography}
+\end{document}