/usr/share/axiom-20170501/src/algebra/DRAW.spad is in axiom-source 20170501-3.
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++ Author: Clifton J. Williamson
++ Date Created: 23 January 1990
++ Date Last Updated: October 1991 by Jon Steinbach
++ Description:
++ TopLevelDrawFunctions provides top level functions for
++ drawing graphics of expressions.
TopLevelDrawFunctions(Ex) : SIG == CODE where
Ex : Join(ConvertibleTo InputForm,SetCategory)
B ==> Boolean
BIND ==> SegmentBinding Float
L ==> List
SF ==> DoubleFloat
DROP ==> DrawOption
PPC ==> ParametricPlaneCurve Ex
PPCF ==> ParametricPlaneCurve(SF -> SF)
PSC ==> ParametricSpaceCurve Ex
PSCF ==> ParametricSpaceCurve(SF -> SF)
PSF ==> ParametricSurface Ex
PSFF ==> ParametricSurface((SF,SF) -> SF)
SPACE3 ==> ThreeSpace(SF)
VIEW2 ==> TwoDimensionalViewport
VIEW3 ==> ThreeDimensionalViewport
SIG ==> with
--% Two Dimensional Function Plots
draw : (Ex,BIND,L DROP) -> VIEW2
++ draw(f(x),x = a..b,l) draws the graph of \spad{y = f(x)} as x
++ ranges from \spad{min(a,b)} to \spad{max(a,b)}; \spad{f(x)} is the
++ default title, and the options contained in the list l of
++ the domain \spad{DrawOption} are applied.
draw : (Ex,BIND) -> VIEW2
++ draw(f(x),x = a..b) draws the graph of \spad{y = f(x)} as x
++ ranges from \spad{min(a,b)} to \spad{max(a,b)}; \spad{f(x)} appears
++ in the title bar.
--% Parametric Plane Curves
draw : (PPC,BIND,L DROP) -> VIEW2
++ draw(curve(f(t),g(t)),t = a..b,l) draws the graph of the parametric
++ curve \spad{x = f(t), y = g(t)} as t ranges from \spad{min(a,b)} to
++ \spad{max(a,b)}; \spad{(f(t),g(t))} is the default title, and the
++ options contained in the list l of the domain \spad{DrawOption}
++ are applied.
draw : (PPC,BIND) -> VIEW2
++ draw(curve(f(t),g(t)),t = a..b) draws the graph of the parametric
++ curve \spad{x = f(t), y = g(t)} as t ranges from \spad{min(a,b)} to
++ \spad{max(a,b)}; \spad{(f(t),g(t))} appears in the title bar.
--% Parametric Space Curves
draw : (PSC,BIND,L DROP) -> VIEW3
++ draw(curve(f(t),g(t),h(t)),t = a..b,l) draws the graph of the
++ parametric curve \spad{x = f(t)}, \spad{y = g(t)}, \spad{z = h(t)}
++ as t ranges from \spad{min(a,b)} to \spad{max(a,b)}; \spad{h(t)}
++ is the default title, and the options contained in the list l of
++ the domain \spad{DrawOption} are applied.
draw : (PSC,BIND) -> VIEW3
++ draw(curve(f(t),g(t),h(t)),t = a..b) draws the graph of the parametric
++ curve \spad{x = f(t)}, \spad{y = g(t)}, \spad{z = h(t)} as t ranges
++ from \spad{min(a,b)} to \spad{max(a,b)}; \spad{h(t)} is the default
++ title.
makeObject : (PSC,BIND,L DROP) -> SPACE3
++ makeObject(curve(f(t),g(t),h(t)),t = a..b,l) returns a space of
++ the domain \spadtype{ThreeSpace} which contains the graph of the
++ parametric curve \spad{x = f(t)}, \spad{y = g(t)}, \spad{z = h(t)}
++ as t ranges from \spad{min(a,b)} to \spad{max(a,b)}; \spad{h(t)}
++ is the default title, and the options contained in the list l of
++ the domain \spad{DrawOption} are applied.
makeObject : (PSC,BIND) -> SPACE3
++ makeObject(curve(f(t),g(t),h(t)),t = a..b) returns a space of the
++ domain \spadtype{ThreeSpace} which contains the graph of the
++ parametric curve \spad{x = f(t)}, \spad{y = g(t)}, \spad{z = h(t)}
++ as t ranges from \spad{min(a,b)} to \spad{max(a,b)}; \spad{h(t)} is
++ the default title.
--% Three Dimensional Function Plots
draw : (Ex,BIND,BIND,L DROP) -> VIEW3
++ draw(f(x,y),x = a..b,y = c..d,l) draws the graph of \spad{z = f(x,y)}
++ as x ranges from \spad{min(a,b)} to \spad{max(a,b)} and y ranges from
++ \spad{min(c,d)} to \spad{max(c,d)}; \spad{f(x,y)} is the default
++ title, and the options contained in the list l of the domain
++ \spad{DrawOption} are applied.
draw : (Ex,BIND,BIND) -> VIEW3
++ draw(f(x,y),x = a..b,y = c..d) draws the graph of \spad{z = f(x,y)}
++ as x ranges from \spad{min(a,b)} to \spad{max(a,b)} and y ranges from
++ \spad{min(c,d)} to \spad{max(c,d)}; \spad{f(x,y)} appears in the title bar.
makeObject : (Ex,BIND,BIND,L DROP) -> SPACE3
++ makeObject(f(x,y),x = a..b,y = c..d,l) returns a space of the
++ domain \spadtype{ThreeSpace} which contains the graph of
++ \spad{z = f(x,y)} as x ranges from \spad{min(a,b)} to \spad{max(a,b)}
++ and y ranges from \spad{min(c,d)} to \spad{max(c,d)}; \spad{f(x,y)}
++ is the default title, and the options contained in the list l of the
++ domain \spad{DrawOption} are applied.
makeObject : (Ex,BIND,BIND) -> SPACE3
++ makeObject(f(x,y),x = a..b,y = c..d) returns a space of the domain
++ \spadtype{ThreeSpace} which contains the graph of \spad{z = f(x,y)}
++ as x ranges from \spad{min(a,b)} to \spad{max(a,b)} and y ranges from
++ \spad{min(c,d)} to \spad{max(c,d)}; \spad{f(x,y)} appears as the
++ default title.
--% Parametric Surfaces
draw : (PSF,BIND,BIND,L DROP) -> VIEW3
++ draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l) draws the
++ graph of the parametric surface \spad{x = f(u,v)}, \spad{y = g(u,v)},
++ \spad{z = h(u,v)} as u ranges from \spad{min(a,b)} to \spad{max(a,b)}
++ and v ranges from \spad{min(c,d)} to \spad{max(c,d)}; \spad{h(t)}
++ is the default title, and the options contained in the list l of
++ the domain \spad{DrawOption} are applied.
draw : (PSF,BIND,BIND) -> VIEW3
++ draw(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d) draws the
++ graph of the parametric surface \spad{x = f(u,v)}, \spad{y = g(u,v)},
++ \spad{z = h(u,v)} as u ranges from \spad{min(a,b)} to \spad{max(a,b)}
++ and v ranges from \spad{min(c,d)} to \spad{max(c,d)}; \spad{h(t)} is
++ the default title.
makeObject : (PSF,BIND,BIND,L DROP) -> SPACE3
++ makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d,l) returns
++ a space of the domain \spadtype{ThreeSpace} which contains the graph
++ of the parametric surface \spad{x = f(u,v)}, \spad{y = g(u,v)},
++ \spad{z = h(u,v)} as u ranges from \spad{min(a,b)} to \spad{max(a,b)}
++ and v ranges from \spad{min(c,d)} to \spad{max(c,d)}; \spad{h(t)} is
++ the default title, and the options contained in the list l of
++ the domain \spad{DrawOption} are applied.
makeObject : (PSF,BIND,BIND) -> SPACE3
++ makeObject(surface(f(u,v),g(u,v),h(u,v)),u = a..b,v = c..d) returns
++ a space of the domain \spadtype{ThreeSpace} which contains the
++ graph of the parametric surface \spad{x = f(u,v)}, \spad{y = g(u,v)},
++ \spad{z = h(u,v)} as u ranges from \spad{min(a,b)} to \spad{max(a,b)}
++ and v ranges from \spad{min(c,d)} to \spad{max(c,d)}; \spad{h(t)} is
++ the default title.
CODE ==> add
import TopLevelDrawFunctionsForCompiledFunctions
import MakeFloatCompiledFunction(Ex)
import ParametricPlaneCurve(SF -> SF)
import ParametricSpaceCurve(SF -> SF)
import ParametricSurface((SF,SF) -> SF)
import ThreeSpace(SF)
------------------------------------------------------------------------
-- 2D - draw's (given by formulae)
------------------------------------------------------------------------
--% Two Dimensional Function Plots
draw(f:Ex,bind:BIND,l:L DROP) ==
-- create title if necessary
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM2D",l)
else l := concat(title s,l)
-- call 'draw'
draw(makeFloatFunction(f,variable bind),segment bind,l)
draw(f:Ex,bind:BIND) == draw(f,bind,nil())
--% Parametric Plane Curves
draw(ppc:PPC,bind:BIND,l:L DROP) ==
f := coordinate(ppc,1); g := coordinate(ppc,2)
-- create title if necessary
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM2D",l)
else l := concat(title s,l)
-- create curve with functions as coordinates
curve : PPCF := curve(makeFloatFunction(f,variable bind),_
makeFloatFunction(g,variable bind))$PPCF
-- call 'draw'
draw(curve,segment bind,l)
draw(ppc:PPC,bind:BIND) == draw(ppc,bind,nil())
------------------------------------------------------------------------
-- 3D - Curves (given by formulas)
------------------------------------------------------------------------
makeObject(psc:PSC,tBind:BIND,l:L DROP) ==
-- obtain dependent variable and coordinate functions
t := variable tBind; tSeg := segment tBind
f := coordinate(psc,1); g := coordinate(psc,2); h := coordinate(psc,3)
-- create title if necessary
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM3D",l)
else l := concat(title s,l)
-- indicate draw style if necessary
if not option?(l,"style" :: Symbol) then
l := concat(style unparse(convert(f)@InputForm),l)
-- create curve with functions as coordinates
curve : PSCF := curve(makeFloatFunction(f,t),_
makeFloatFunction(g,t),_
makeFloatFunction(h,t))
-- call 'draw'
makeObject(curve,tSeg,l)
makeObject(psc:PSC,tBind:BIND) ==
makeObject(psc,tBind,nil())
draw(psc:PSC,tBind:BIND,l:L DROP) ==
-- obtain dependent variable and coordinate functions
t := variable tBind; tSeg := segment tBind
f := coordinate(psc,1); g := coordinate(psc,2); h := coordinate(psc,3)
-- create title if necessary
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM3D",l)
else l := concat(title s,l)
-- indicate draw style if necessary
if not option?(l,"style" :: Symbol) then
l := concat(style unparse(convert(f)@InputForm),l)
-- create curve with functions as coordinates
curve : PSCF := curve(makeFloatFunction(f,t),_
makeFloatFunction(g,t),_
makeFloatFunction(h,t))
-- call 'draw'
draw(curve,tSeg,l)
draw(psc:PSC,tBind:BIND) ==
draw(psc,tBind,nil())
------------------------------------------------------------------------
-- 3D - Surfaces (given by formulas)
------------------------------------------------------------------------
--% Three Dimensional Function Plots
makeObject(f:Ex,xBind:BIND,yBind:BIND,l:L DROP) ==
-- create title if necessary
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM3D",l)
else l := concat(title s,l)
-- indicate draw style if necessary
if not option?(l,"style" :: Symbol) then
l := concat(style unparse(convert(f)@InputForm),l)
-- obtain dependent variables and their ranges
x := variable xBind; xSeg := segment xBind
y := variable yBind; ySeg := segment yBind
-- call 'draw'
makeObject(makeFloatFunction(f,x,y),xSeg,ySeg,l)
makeObject(f:Ex,xBind:BIND,yBind:BIND) ==
makeObject(f,xBind,yBind,nil())
draw(f:Ex,xBind:BIND,yBind:BIND,l:L DROP) ==
-- create title if necessary
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM3D",l)
else l := concat(title s,l)
-- indicate draw style if necessary
if not option?(l,"style" :: Symbol) then
l := concat(style unparse(convert(f)@InputForm),l)
-- obtain dependent variables and their ranges
x := variable xBind; xSeg := segment xBind
y := variable yBind; ySeg := segment yBind
-- call 'draw'
draw(makeFloatFunction(f,x,y),xSeg,ySeg,l)
draw(f:Ex,xBind:BIND,yBind:BIND) ==
draw(f,xBind,yBind,nil())
--% parametric surface
makeObject(s:PSF,uBind:BIND,vBind:BIND,l:L DROP) ==
f := coordinate(s,1); g := coordinate(s,2); h := coordinate(s,3)
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM3D",l)
else l := concat(title s,l)
if not option?(l,"style" :: Symbol) then
l := concat(style unparse(convert(f)@InputForm),l)
u := variable uBind; uSeg := segment uBind
v := variable vBind; vSeg := segment vBind
surf : PSFF := surface(makeFloatFunction(f,u,v),_
makeFloatFunction(g,u,v),_
makeFloatFunction(h,u,v))
makeObject(surf,uSeg,vSeg,l)
makeObject(s:PSF,uBind:BIND,vBind:BIND) ==
makeObject(s,uBind,vBind,nil())
draw(s:PSF,uBind:BIND,vBind:BIND,l:L DROP) ==
f := coordinate(s,1); g := coordinate(s,2); h := coordinate(s,3)
-- create title if necessary
if not option?(l,"title" :: Symbol) then
s:String := unparse(convert(f)@InputForm)
if sayLength(s)$DisplayPackage > 50 then
l := concat(title "AXIOM3D",l)
else l := concat(title s,l)
-- indicate draw style if necessary
if not option?(l,"style" :: Symbol) then
l := concat(style unparse(convert(f)@InputForm),l)
-- obtain dependent variables and their ranges
u := variable uBind; uSeg := segment uBind
v := variable vBind; vSeg := segment vBind
-- create surface with functions as coordinates
surf : PSFF := surface(makeFloatFunction(f,u,v),_
makeFloatFunction(g,u,v),_
makeFloatFunction(h,u,v))
-- call 'draw'
draw(surf,uSeg,vSeg,l)
draw(s:PSF,uBind:BIND,vBind:BIND) ==
draw(s,uBind,vBind,nil())
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