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--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.
)abbrev category SPACEC ThreeSpaceCategory
++ Author:
++ Date Created:
++ Date Last Updated:
++ Basic Operations: create3Space, numberOfComponents, numberOfComposites,
++ merge, composite, components, copy, enterPointData, modifyPointData, point,
++ point?, curve, curve?, closedCurve, closedCurve?, polygon, polygon? mesh,
++ mesh?, lp, lllip, lllp, llprop, lprop, objects, check, subspace, coerce
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ Description: The category ThreeSpaceCategory is used for creating
++ three dimensional objects using functions for defining points, curves,
++ polygons, constructs and the subspaces containing them.
ThreeSpaceCategory(R:Ring): Exports == Implementation where
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)
Exports ==> Category
Implementation ==>
SetCategory with
create3Space : () -> %
++ create3Space() creates a \spadtype{ThreeSpace} object capable of
++ holding point, curve, mesh components and any combination.
create3Space : SUBSPACE -> %
++ create3Space(s) creates a \spadtype{ThreeSpace} object containing
++ objects pre-defined within some \spadtype{SubSpace} s.
numberOfComponents : % -> NNI
++ numberOfComponents(s) returns the number of distinct
++ object components in the indicated \spadtype{ThreeSpace}, s, such
++ as points, curves, polygons, and constructs.
numberOfComposites : % -> NNI
++ numberOfComposites(s) returns the number of supercomponents,
++ or composites, in the \spadtype{ThreeSpace}, s; Composites are
++ arbitrary groupings of otherwise distinct and unrelated components;
++ A \spadtype{ThreeSpace} need not have any composites defined at all
++ and, outside of the requirement that no component can belong
++ to more than one composite at a time, the definition and
++ interpretation of composites are unrestricted.
merge : L % -> %
++ merge([s1,s2,...,sn]) will create a new \spadtype{ThreeSpace} that has
++ the components of all the ones in the list; Groupings of components
++ into composites are maintained.
merge : (%,%) -> %
++ merge(s1,s2) will create a new \spadtype{ThreeSpace} that has the
++ components of \spad{s1} and \spad{s2}; Groupings of components
++ into composites are maintained.
composite : L % -> %
++ composite([s1,s2,...,sn]) will create a new \spadtype{ThreeSpace} that
++ is a union of all the components from each \spadtype{ThreeSpace} in
++ the parameter list, grouped as a composite.
components : % -> L %
++ components(s) takes the \spadtype{ThreeSpace} s, and creates a list
++ containing a unique \spadtype{ThreeSpace} for each single component
++ of s. If s has no components defined, the list returned is empty.
composites : % -> L %
++ composites(s) takes the \spadtype{ThreeSpace} s, and creates a list
++ containing a unique \spadtype{ThreeSpace} for each single composite
++ of s. If s has no composites defined (composites need to be explicitly
++ created), the list returned is empty. Note that not all the components
++ need to be part of a composite.
copy : % -> %
++ copy(s) returns a new \spadtype{ThreeSpace} that is an exact copy of s.
enterPointData : (%,L POINT) -> NNI
++ enterPointData(s,[p0,p1,...,pn]) adds a list of points from p0 through
++ pn to the \spadtype{ThreeSpace}, s, and returns the index, to the
++ starting point of the list;
modifyPointData : (%,NNI,POINT) -> %
++ modifyPointData(s,i,p) changes the point at the indexed
++ location i in the \spadtype{ThreeSpace}, s, to that of point p.
++ This is useful for making changes to a point which has been
++ transformed.
-- 3D primitives
point : (%,POINT) -> %
++ point(s,p) adds a point component defined by the point, p, specified as
++ a list from \spad{List(R)}, to the \spadtype{ThreeSpace}, s,
++ where R is the \spadtype{Ring} over which the point is defined.
point : (%,L R) -> %
++ point(s,[x,y,z]) adds a point component defined by a list of elements
++ which are from the \spad{PointDomain(R)} to the \spadtype{ThreeSpace},
++ s, where R is the \spadtype{Ring} over which the point elements are
++ defined.
point : (%,NNI) -> %
++ point(s,i) adds a point component which is placed into a component
++ list of the \spadtype{ThreeSpace}, s, at the index given by i.
point : POINT -> %
++ point(p) returns a \spadtype{ThreeSpace} object which is composed of
++ one component, the point p.
point : % -> POINT
++ point(s) checks to see if the \spadtype{ThreeSpace}, s, is composed of
++ only a single point and if so, returns the point. An error
++ is signaled otherwise.
point? : % -> B
++ point?(s) queries whether the \spadtype{ThreeSpace}, s, is composed of
++ a single component which is a point and returns the boolean result.
curve : (%,L POINT) -> %
++ curve(s,[p0,p1,...,pn]) adds a space curve component defined by a
++ list of points \spad{p0} through \spad{pn}, to the \spadtype{ThreeSpace} s.
curve : (%,L L R) -> %
++ curve(s,[[p0],[p1],...,[pn]]) adds a space curve which is a list of
++ points p0 through pn defined by lists of elements from the domain
++ \spad{PointDomain(m,R)}, where R is the \spadtype{Ring} over which the
++ point elements are defined and m is the dimension of the points, to
++ the \spadtype{ThreeSpace} s.
curve : L POINT -> %
++ curve([p0,p1,p2,...,pn]) creates a space curve defined
++ by the list of points \spad{p0} through \spad{pn}, and returns the
++ \spadtype{ThreeSpace} whose component is the curve.
curve : % -> L POINT
++ curve(s) checks to see if the \spadtype{ThreeSpace}, s, is composed of
++ a single curve defined by a list of points and if so, returns the
++ curve, i.e., list of points. An error is signaled otherwise.
curve? : % -> B
++ curve?(s) queries whether the \spadtype{ThreeSpace}, s, is a curve,
++ i.e., has one component, a list of list of points, and returns true if
++ it is, or false otherwise.
closedCurve : (%,L POINT) -> %
++ closedCurve(s,[p0,p1,...,pn,p0]) adds a closed curve component which is
++ a list of points defined by the first element p0 through the last
++ element pn and back to the first element p0 again, to the
++ \spadtype{ThreeSpace} s.
closedCurve : (%,L L R) -> %
++ closedCurve(s,[[lr0],[lr1],...,[lrn],[lr0]]) adds a closed curve
++ component defined by a list of points \spad{lr0} through \spad{lrn},
++ which are lists of elements from the domain \spad{PointDomain(m,R)},
++ where R is the \spadtype{Ring} over which the point elements are
++ defined and m is the dimension of the points, in which the last element
++ of the list of points contains a copy of the first element list, lr0.
++ The closed curve is added to the \spadtype{ThreeSpace}, s.
closedCurve : L POINT -> %
++ closedCurve(lp) sets a list of points defined by the first element
++ of lp through the last element of lp and back to the first elelment
++ again and returns a \spadtype{ThreeSpace} whose component is the
++ closed curve defined by lp.
closedCurve : % -> L POINT
++ closedCurve(s) checks to see if the \spadtype{ThreeSpace}, s, is
++ composed of a single closed curve component defined by a list of
++ points in which the first point is also the last point, all of which
++ are from the domain \spad{PointDomain(m,R)} and if so, returns the
++ list of points. An error is signaled otherwise.
closedCurve? : % -> B
++ closedCurve?(s) returns true if the \spadtype{ThreeSpace} s contains
++ a single closed curve component, i.e., the first element of the curve
++ is also the last element, or false otherwise.
polygon : (%,L POINT) -> %
++ polygon(s,[p0,p1,...,pn]) adds a polygon component defined by a list of
++ points, p0 throught pn, to the \spadtype{ThreeSpace} s.
polygon : (%,L L R) -> %
++ polygon(s,[[r0],[r1],...,[rn]]) adds a polygon component defined
++ by a list of points \spad{r0} through \spad{rn}, which are lists of
++ elements from the domain \spad{PointDomain(m,R)} to the
++ \spadtype{ThreeSpace} s, where m is the dimension of the points
++ and R is the \spadtype{Ring} over which the points are defined.
polygon : L POINT -> %
++ polygon([p0,p1,...,pn]) creates a polygon defined by a list of points,
++ p0 through pn, and returns a \spadtype{ThreeSpace} whose component
++ is the polygon.
polygon : % -> L POINT
++ polygon(s) checks to see if the \spadtype{ThreeSpace}, s, is
++ composed of a single polygon component defined by a list of
++ points, and if so, returns the list of points; An error is signaled
++ otherwise.
polygon? : % -> B
++ polygon?(s) returns true if the \spadtype{ThreeSpace} s contains
++ a single polygon component, or false otherwise.
mesh : (%,L L POINT,L PROP,PROP) -> %
++ mesh(s,[[p0],[p1],...,[pn]],[props],prop) adds a surface component,
++ defined over a list curves which contains lists of points, to the
++ \spadtype{ThreeSpace} s; props is a list which contains the subspace
++ component properties for each surface parameter, and prop is the
++ subspace component property by which the points are defined.
mesh : (%,L L L R,L PROP,PROP) -> %
++ mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], [props], prop)
++ adds a surface component to the \spadtype{ThreeSpace} s, which is
++ defined over a rectangular domain of size WxH where W is the number
++ of lists of points from the domain \spad{PointDomain(R)} and H is the
++ number of elements in each of those lists; lprops is the list of the
++ subspace component properties for each curve list, and prop is
++ the subspace component property by which the points are defined.
mesh : (%,L L POINT,B,B) -> %
++ mesh(s,[[p0],[p1],...,[pn]], close1, close2) adds a surface component to
++ the \spadtype{ThreeSpace}, which is defined over a list of curves,
++ in which each of these curves is a list of points.
++ The boolean arguments close1 and close2 indicate how the surface
++ is to be closed. Argument close1 equal true
++ means that each individual list (a curve) is to be closed, i.e. the
++ last point of the list is to be connected to the first point.
++ Argument close2 equal true
++ means that the boundary at one end of the surface is to be
++ connected to the boundary at the other end, i.e. the boundaries
++ are defined as the first list of points (curve) and
++ the last list of points (curve).
mesh : (%,L L L R,B,B) -> %
++ mesh(s,[ [[r10]...,[r1m]], [[r20]...,[r2m]],..., [[rn0]...,[rnm]] ], close1, close2)
++ adds a surface component to the \spadtype{ThreeSpace} s, which is
++ defined over a rectangular domain of size WxH where W is the number
++ of lists of points from the domain \spad{PointDomain(R)} and H is the
++ number of elements in each of those lists; the booleans close1 and
++ close2 indicate how the surface is to be closed: if close1 is true
++ this means that each individual list (a curve) is to be closed (i.e.,
++ the last point of the list is to be connected to the first point);
++ if close2 is true, this means that the boundary at one end of the
++ surface is to be connected to the boundary at the other end
++ (the boundaries are defined as the first list of points (curve)
++ and the last list of points (curve)).
mesh : L L POINT -> %
++ mesh([[p0],[p1],...,[pn]]) creates a surface defined by a list of
++ curves which are lists, p0 through pn, of points, and returns a
++ \spadtype{ThreeSpace} whose component is the surface.
mesh : (L L POINT,B,B) -> %
++ mesh([[p0],[p1],...,[pn]], close1, close2) creates a surface defined
++ over a list of curves, p0 through pn, which are lists of points;
++ the booleans close1 and close2 indicate how the surface is to be
++ closed: close1 set to true means that each individual list (a curve)
++ is to be closed (that is, the last point of the list is to be
++ connected to the first point); close2 set to true means that the
++ boundary at one end of the surface is to be connected to the boundary
++ at the other end (the boundaries are defined as the first list of
++ points (curve) and the last list of points (curve)); the
++ \spadtype{ThreeSpace} containing this surface is returned.
mesh : % -> L L POINT
++ mesh(s) checks to see if the \spadtype{ThreeSpace}, s, is
++ composed of a single surface component defined by a list curves which
++ contain lists of points, and if so, returns the list of lists of
++ points; An error is signaled otherwise.
mesh? : % -> B
++ mesh?(s) returns true if the \spadtype{ThreeSpace} s is composed of one
++ component, a mesh comprising a list of curves which are lists
++ of points, or returns false if otherwise
lp : % -> L POINT
++ lp(s) returns the list of points component which the
++ \spadtype{ThreeSpace}, s, contains; these points are used by reference,
++ i.e., the component holds indices referring to the points rather
++ than the points themselves. This allows for sharing of the points.
lllip : % -> L L L NNI
++ lllip(s) checks to see if the \spadtype{ThreeSpace}, s, is
++ composed of a list of components, which are lists of curves,
++ which are lists of indices to points, and if so, returns the list of
++ lists of lists; An error is signaled otherwise.
lllp : % -> L L L POINT -- used by view3D
++ lllp(s) checks to see if the \spadtype{ThreeSpace}, s, is
++ composed of a list of components, which are lists of curves,
++ which are lists of points, and if so, returns the list of
++ lists of lists; An error is signaled otherwise.
llprop : % -> L L PROP -- used by view3D
++ llprop(s) checks to see if the \spadtype{ThreeSpace}, s, is
++ composed of a list of curves which are lists of the
++ subspace component properties of the curves, and if so, returns the
++ list of lists; An error is signaled otherwise.
lprop : % -> L PROP -- used by view3D
++ lprop(s) checks to see if the \spadtype{ThreeSpace}, s, is
++ composed of a list of subspace component properties, and if so,
++ returns the list; An error is signaled otherwise.
objects : % -> OBJ3D
++ objects(s) returns the \spadtype{ThreeSpace}, s, in the form of a
++ 3D object record containing information on the number of points,
++ curves, polygons and constructs comprising the \spadtype{ThreeSpace}..
check : % -> % -- used by mesh
++ check(s) returns lllpt, list of lists of lists of point information
++ about the \spadtype{ThreeSpace} s.
subspace : % -> SUBSPACE
++ subspace(s) returns the \spadtype{SubSpace} which holds all the point
++ information in the \spadtype{ThreeSpace}, s.
coerce : % -> O
++ coerce(s) returns the \spadtype{ThreeSpace} s to Output format.
)abbrev domain SPACE3 ThreeSpace
++ Author:
++ Date Created:
++ Date Last Updated:
++ Basic Operations: create3Space, numberOfComponents, numberOfComposites,
++ merge, composite, components, copy, enterPointData, modifyPointData, point,
++ point?, curve, curve?, closedCurve, closedCurve?, polygon, polygon? mesh,
++ mesh?, lp, lllip, lllp, llprop, lprop, objects, check, subspace, coerce
++ Related Constructors:
++ Also See:
++ AMS Classifications:
++ Keywords:
++ References:
++ 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:Ring):Exports == Implementation where
-- m is the dimension of the point
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)
Exports ==> ThreeSpaceCategory(R)
Implementation ==> 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) ==
-- * -- we may want to remove duplicate components when that functionality exists in List
newspace := create3Space(merge([ts.subspaceField for ts in listOfThreeSpaces]))
-- newspace.compositesField := [for cs in ts.compositesField 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]
-- for aSpace in listOfThreeSpaces repeat
-- create a composite (which are supercomponents that group
-- separate components together) out of all possible components
-- space.compositesField := append(children aSpace.subspaceField,space.compositesField)
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 *** complete this
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
#(kid:=children first c) = 1$NNI => -- the component has one subcomponent (a list of points)
#(children first kid) = 1$NNI -- this list of points only has one entry, so it's a point
false
point(space:%) ==
point? space => extractPoint(traverse(space.subspaceField,[1,1,1]::L NNI))
error "This ThreeSpace holds something other than 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$NNI =>
error "This ThreeSpace has more than one component"
-- our 3-space has one component, a list of list of points
#(children first c) = 1$NNI -- there is only one subcomponent, so it's a list of points
curve(space:%) ==
curve? space =>
spc := first children first children space.subspaceField
[extractPoint(s) for s in children spc]
error "This ThreeSpace holds something other than 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$NNI =>
error "This ThreeSpace has more than one component"
-- our 3-space has one component, a list of list of points
#(kid := children first c) = 1$NNI => -- there is one subcomponent => it's a list of points
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 holds something other than 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 holds something other than 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 holds something other than 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 not space.converted then space := convertSpace space
space.rep3DField.lp
lllip space ==
if not space.converted then space := convertSpace space
space.rep3DField.llliPt
-- lllp space ==
-- if not space.converted then space := convertSpace space
-- space.rep3DField.lllPt
llprop space ==
if not space.converted then space := convertSpace space
space.rep3DField.llProp
lprop space ==
if not space.converted then space := convertSpace space
space.rep3DField.lProp
-- this function is just to see how this representation really
-- does work
objects space ==
if not space.converted then space := convertSpace space
numPts := 0$NNI
numCurves := 0$NNI
numPolys := 0$NNI
numConstructs := 0$NNI
for component in children space.subspaceField repeat
#(kid:=children component) = 1 =>
#(children first kid) = 1 => numPts := numPts + 1
numCurves := numCurves + 1
(#kid = 2) and _
(#children first kid = 1) and _
not one?(#children first rest kid) =>
numPolys := numPolys + 1
numConstructs := numConstructs + 1
-- otherwise, a mathematical surface is assumed
-- there could also be garbage representation
-- since there are always more permutations that
-- we could ever want, so the user should not
-- fumble around too much with the structure
-- as other applications need to interpret it
[numPts,numCurves,numPolys,numConstructs]
check(s) ==
not s.converted => convertSpace s
s
subspace(s) == s.subspaceField
coerce(s) ==
if not s.converted then s := convertSpace s
hconcat(["3-Space with "::O, _
(sizo:=#(s.rep3DField.llliPt))::O, _
(sizo=1=>" component"::O;" components"::O)])
)abbrev package TOPSP TopLevelThreeSpace
++ Description:
++ This package exports a function for making a \spadtype{ThreeSpace}
TopLevelThreeSpace(): with
createThreeSpace: () -> ThreeSpace DoubleFloat
++ createThreeSpace() creates a \spadtype{ThreeSpace(DoubleFloat)} object
++ capable of holding point, curve, mesh components and any combination.
== add
createThreeSpace() == create3Space()$ThreeSpace(DoubleFloat)
|