/usr/share/axiom-20170501/src/algebra/SPACE3.spad is in axiom-source 20170501-3.
This file is owned by root:root, with mode 0o644.
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++ Author: Mark Botch
++ Description:
++ The domain ThreeSpace is used for creating three dimensional
++ objects using functions for defining points, curves, polygons, constructs
++ and the subspaces containing them.
ThreeSpace(R) : SIG == CODE where
R : Ring
I ==> Integer
PI ==> PositiveInteger
NNI ==> NonNegativeInteger
L ==> List
B ==> Boolean
O ==> OutputForm
SUBSPACE ==> SubSpace(3,R)
POINT ==> Point(R)
PROP ==> SubSpaceComponentProperty()
REP3D ==> Record(lp:L POINT,llliPt:L L L NNI, llProp:L L PROP, lProp:L PROP)
OBJ3D ==> Record(points:NNI, curves:NNI, polygons:NNI, constructs:NNI)
SIG ==> ThreeSpaceCategory(R)
CODE ==> add
import COMPPROP
import POINT
import SUBSPACE
import ListFunctions2(List(R),POINT)
import Set(NNI)
Rep := Record( subspaceField:SUBSPACE, compositesField:L SUBSPACE, _
rep3DField:REP3D, objectsField:OBJ3D, _
converted:B)
--% Local Functions
convertSpace : % -> %
convertSpace space ==
space.converted => space
space.converted := true
lllipt : L L L NNI := []
llprop : L L PROP := []
lprop : L PROP := []
for component in children space.subspaceField repeat
lprop := cons(extractProperty component,lprop)
tmpllipt : L L NNI := []
tmplprop : L PROP := []
for curve in children component repeat
tmplprop := cons(extractProperty curve,tmplprop)
tmplipt : L NNI := []
for point in children curve repeat
tmplipt := cons(extractIndex point,tmplipt)
tmpllipt := cons(reverse_! tmplipt,tmpllipt)
llprop := cons(reverse_! tmplprop, llprop)
lllipt := cons(reverse_! tmpllipt, lllipt)
space.rep3DField := [pointData space.subspaceField,
reverse_! lllipt,reverse_! llprop,reverse_! lprop]
space
--% Exported Functions
polygon(space:%,points:L POINT) ==
#points < 3 =>
error "You need at least 3 points to define a polygon"
pt := addPoint2(space.subspaceField,first points)
points := rest points
addPointLast(space.subspaceField, pt, first points, 1)
for p in rest points repeat
addPointLast(space.subspaceField, pt, p, 2)
space.converted := false
space
create3Space() ==
[ new()$SUBSPACE, [], [ [], [], [], [] ], [0,0,0,0], false ]
create3Space(s) == [ s, [], [ [], [], [], [] ], [0,0,0,0], false ]
numberOfComponents(space) == #(children((space::Rep).subspaceField))
numberOfComposites(space) == #((space::Rep).compositesField)
merge(listOfThreeSpaces) ==
newspace := _
create3Space(merge([ts.subspaceField for ts in listOfThreeSpaces]))
for ts in listOfThreeSpaces repeat
newspace.compositesField := _
append(ts.compositesField,newspace.compositesField)
newspace
merge(s1,s2) == merge([s1,s2])
composite(listOfThreeSpaces) ==
space := create3Space()
space.subspaceField := merge [s.subspaceField for s in listOfThreeSpaces]
space.compositesField := [deepCopy space.subspaceField]
space
components(space) ==
[create3Space(s) for s in separate space.subspaceField]
composites(space) == [create3Space(s) for s in space.compositesField]
copy(space) ==
spc := create3Space(deepCopy(space.subspaceField))
spc.compositesField := [deepCopy s for s in space.compositesField]
spc
enterPointData(space,listOfPoints) ==
for p in listOfPoints repeat
addPoint(space.subspaceField,p)
#(pointData space.subspaceField)
modifyPointData(space,i,p) ==
modifyPoint(space.subspaceField,i,p)
space
-- 3D primitives, each grouped in the following order
-- xxx?(s) : query whether the threespace, s, holds an xxx
-- xxx(s) : extract xxx from threespace, s
-- xxx(p) : create a new three space with xxx, p
-- xxx(s,p) : add xxx, p, to a three space, s
-- xxx(s,q) : add an xxx, convertable from q, to a three space, s
-- xxx(s,i) : add an xxx, the data for xxx being indexed by reference
point?(space:%) ==
#(c:=children space.subspaceField) > 1$NNI =>
error "This ThreeSpace has more than one component"
-- our 3-space has one component, a list of list of points
-- the component has one subcomponent (a list of points)
#(kid:=children first c) = 1$NNI =>
-- this list of points only has one entry, so it's a point
#(children first kid) = 1$NNI
false
point(space:%) ==
point? space => _
extractPoint(traverse(space.subspaceField,[1,1,1]::L NNI))
error "This ThreeSpace is not a single point - try the objects() command"
point(aPoint:POINT) == point(create3Space(),aPoint)
point(space:%,aPoint:POINT) ==
addPoint(space.subspaceField,[],aPoint)
space.converted := false
space
point(space:%,l:L R) ==
pt := point(l)
point(space,pt)
point(space:%,i:NNI) ==
addPoint(space.subspaceField,[],i)
space.converted := false
space
curve?(space:%) ==
#(c:=children space.subspaceField) > 1$NNI =>
error "This ThreeSpace has more than one component"
-- our 3-space has one component, a list of list of points
-- there is only one subcomponent, so it's a list of points
#(children first c) = 1$NNI
curve(space:%) ==
curve? space =>
spc := first children first children space.subspaceField
[extractPoint(s) for s in children spc]
error "This ThreeSpace is not a curve - try the objects() command"
curve(points:L POINT) == curve(create3Space(),points)
curve(space:%,points:L POINT) ==
addPoint(space.subspaceField,[],first points)
path : L NNI := [#(children space.subspaceField),1]
for p in rest points repeat
addPoint(space.subspaceField,path,p)
space.converted := false
space
curve(space:%,points:L L R) ==
pts := map(point,points)
curve(space,pts)
closedCurve?(space:%) ==
#(c:=children space.subspaceField) > 1$NNI =>
error "This ThreeSpace has more than one component"
-- our 3-space has one component, a list of list of points
-- there is one subcomponent => it's a list of points
#(kid := children first c) = 1$NNI =>
extractClosed first kid -- is it a closed curve?
false
closedCurve(space:%) ==
closedCurve? space =>
spc := first children first children space.subspaceField
-- get the list of points
[extractPoint(s) for s in children spc]
-- for now, we are not repeating points...
error "This ThreeSpace is not a curve - try the objects() command"
closedCurve(points:L POINT) == closedCurve(create3Space(),points)
closedCurve(space:%,points:L POINT) ==
addPoint(space.subspaceField,[],first points)
path : L NNI := [#(children space.subspaceField),1]
closeComponent(space.subspaceField,path,true)
for p in rest points repeat
addPoint(space.subspaceField,path,p)
space.converted := false
space
closedCurve(space:%,points:L L R) ==
pts := map(point,points)
closedCurve(space,pts)
polygon?(space:%) ==
#(c:=children space.subspaceField) > 1$NNI =>
error "This ThreeSpace has more than one component"
-- our 3-space has one component, a list of list of points
#(kid:=children first c) = 2::NNI =>
-- there are two subcomponents
-- the convention is to have one point in the first child and to put
-- the remaining points (2 or more) in the second, and last, child
#(children first kid) = 1$NNI and #(children second kid) > 2::NNI
false -- => returns Void...?
polygon(space:%) ==
polygon? space =>
listOfPoints : L POINT :=
[extractPoint(first children first _
(cs := children first children space.subspaceField))]
[extractPoint(s) for s in children second cs]
error "This ThreeSpace is not a polygon - try the objects() command"
polygon(points:L POINT) == polygon(create3Space(),points)
polygon(space:%,points:L L R) ==
pts := map(point,points)
polygon(space,pts)
mesh?(space:%) ==
#(c:=children space.subspaceField) > 1$NNI =>
error "This ThreeSpace has more than one component"
-- our 3-space has one component, a list of list of points
#(kid:=children first c) > 1$NNI =>
-- there are two or more subcomponents (list of points)
-- so this may be a definition of a mesh; if the size
-- of each list of points is the same and they are all
-- greater than 1(?) then we have an acceptable mesh
-- use a set to hold the curve size info: if heterogenous
-- curve sizes exist, then the set would hold all the sizes;
-- otherwise it would just have the one element indicating
-- the sizes for all the curves
whatSizes := brace()$Set(NNI)
for eachCurve in kid repeat
insert_!(#children eachCurve,whatSizes)
#whatSizes > 1 => error "Mesh defined with curves of different sizes"
first parts whatSizes < 2 =>
error "Mesh defined with single point curves (use curve())"
true
false
mesh(space:%) ==
mesh? space =>
llp : L L POINT := []
for lpSpace in children first children space.subspaceField repeat
llp := cons([extractPoint(s) for s in children lpSpace],llp)
llp
error "This ThreeSpace is not a mesh - try the objects() command"
mesh(points:L L POINT) == mesh(create3Space(),points,false,false)
mesh(points:L L POINT,prop1:B,prop2:B) ==
mesh(create3Space(),points,prop1,prop2)
--+ old ones \/
mesh(space:%,llpoints:L L L R,lprops:L PROP,prop:PROP) ==
pts := [map(point,points) for points in llpoints]
mesh(space,pts,lprops,prop)
mesh(space:%,llp:L L POINT,lprops:L PROP,prop:PROP) ==
addPoint(space.subspaceField,[],first first llp)
defineProperty(space.subspaceField,path:L NNI:=_
[#children space.subspaceField],prop)
path := append(path,[1])
defineProperty(space.subspaceField,path,first lprops)
for p in rest (first llp) repeat
addPoint(space.subspaceField,path,p)
for lp in rest llp for aProp in rest lprops for count in 2.. repeat
addPoint(space.subspaceField,path := [first path],first lp)
path := append(path,[count])
defineProperty(space.subspaceField,path,aProp)
for p in rest lp repeat
addPoint(space.subspaceField,path,p)
space.converted := false
space
--+ old ones /\
mesh(space:%,llpoints:L L L R,prop1:B,prop2:B) ==
pts := [map(point,points) for points in llpoints]
mesh(space,pts,prop1,prop2)
mesh(space:%,llp:L L POINT,prop1:B,prop2:B) ==
-- prop2 refers to property of the ends of a surface
-- (list of lists of points)
-- while prop1 refers to the individual curves (list of points)
-- ** note we currently use Booleans for closed (rather than a pair
-- ** of booleans for closed and solid)
propA : PROP := new()
close(propA,prop1)
propB : PROP := new()
close(propB,prop2)
addPoint(space.subspaceField,[],first first llp)
defineProperty(space.subspaceField,path:L NNI:=_
[#children space.subspaceField],propB)
path := append(path,[1])
defineProperty(space.subspaceField,path,propA)
for p in rest (first llp) repeat
addPoint(space.subspaceField,path,p)
for lp in rest llp for count in 2.. repeat
addPoint(space.subspaceField,path := [first path],first lp)
path := append(path,[count])
defineProperty(space.subspaceField,path,propA)
for p in rest lp repeat
addPoint(space.subspaceField,path,p)
space.converted := false
space
lp space ==
if ^space.converted then space := convertSpace space
space.rep3DField.lp
lllip space ==
if ^space.converted then space := convertSpace space
space.rep3DField.llliPt
llprop space ==
if ^space.converted then space := convertSpace space
space.rep3DField.llProp
lprop space ==
if ^space.converted then space := convertSpace space
space.rep3DField.lProp
-- this function is just to see how this representation really
-- does work
objects space ==
if ^space.converted then space := convertSpace space
numPts := 0$NNI
numCurves := 0$NNI
numPolys := 0$NNI
numConstructs := 0$NNI
for component in children space.subspaceField repeat
#(kid:=children component) = 1 =>
#(children first kid) = 1 => numPts := numPts + 1
numCurves := numCurves + 1
(#kid = 2) and _
(#children first kid = 1) and _
(#children first rest kid ^= 1) =>
numPolys := numPolys + 1
numConstructs := numConstructs + 1
-- otherwise, a mathematical surface is assumed
-- there could also be garbage representation
-- since there are always more permutations that
-- we could ever want, so the user should not
-- fumble around too much with the structure
-- as other applications need to interpret it
[numPts,numCurves,numPolys,numConstructs]
check(s) ==
^s.converted => convertSpace s
s
subspace(s) == s.subspaceField
coerce(s) ==
if ^s.converted then s := convertSpace s
hconcat(["3-Space with "::O, _
(sizo:=#(s.rep3DField.llliPt))::O, _
(sizo=1=>" component"::O;" components"::O)])
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