DIRECTORY G2dBasic, G3dBasic, G3dOctree, G3dPolygon, G3dVector, ImplicitAdapt, ImplicitDefs, ImplicitPoints, ImplicitPolygons, IO, MessageWindow, RealFns, Rope;

ImplicitAdaptImpl: CEDAR MONITOR
IMPORTS G2dBasic, G3dOctree, G3dPolygon, G3dVector, ImplicitPoints, ImplicitPolygons, IO, MessageWindow, RealFns
EXPORTS ImplicitAdapt

~ BEGIN

Triple:					TYPE ~ G3dBasic.Triple;
TripleSequence:		TYPE ~ G3dBasic.TripleSequence;
TripleSequenceRep:	TYPE ~ G3dBasic.TripleSequenceRep;
ActiveFaces:			TYPE ~ G3dOctree.ActiveFaces;
Cross:					TYPE ~ G3dOctree.Cross;
CrossedEdges:			TYPE ~ G3dOctree.CrossedEdges;
CrossPolygonProc:	TYPE ~ G3dOctree.CrossPolygonProc;
Cube:					TYPE ~ G3dOctree.Cube;
Corner:					TYPE ~ G3dOctree.Corner;
Corners:					TYPE ~ G3dOctree.Corners;
CubeProc:				TYPE ~ G3dOctree.CubeProc;
CubeStack:				TYPE ~ G3dOctree.CubeStack;
DirectionCorners:		TYPE ~ G3dOctree.DirectionCorners;
Edge:						TYPE ~ G3dOctree.Edge;
Face:						TYPE ~ G3dOctree.Face;
FourCorners:			TYPE ~ G3dOctree.FourCorners;
FourOctants:			TYPE ~ G3dOctree.FourOctants;
Octant:					TYPE ~ G3dOctree.Octant;
Octree:					TYPE ~ G3dOctree.Octree;
OctreeRep:				TYPE ~ G3dOctree.OctreeRep;
TwoCorners:			TYPE ~ G3dOctree.TwoCorners;
ThreeCubes:			TYPE ~ G3dOctree.ThreeCubes;
FourDirections:		TYPE ~ G3dOctree.FourDirections;
Direction:				TYPE ~ G3dOctree.Direction;
Neighborhood:			TYPE ~ G3dOctree.Neighborhood;
TwoFaces:				TYPE ~ G3dOctree.TwoFaces;
TwoOctants:			TYPE ~ G3dOctree.TwoOctants;
CrossSequence:		TYPE ~ ImplicitDefs.CrossSequence;
MacroPolygons:		TYPE ~ ImplicitDefs.MacroPolygons;
NormalProc:			TYPE ~ ImplicitDefs.NormalProc;
StatusProc:				TYPE ~ ImplicitDefs.StatusProc;
ValueProc:				TYPE ~ ImplicitDefs.ValueProc;
ROPE:					TYPE ~ Rope.ROPE;
SubdivideAbort: ERROR = CODE;

Subdivide: PUBLIC PROC [
root: Cube,
adaptLimit: NAT,
flatLimit: REAL,
valueProc: ValueProc,
threshold: REAL � 1.0,
normalProc: NormalProc � NIL,
statusProc: StatusProc � NIL,
clientData: REF ANY � NIL]
RETURNS [msg: ROPE]
~ {
SubdivideAndMore: PROC [parent: Cube] ~ {
MaybeInheritSurfacePoint: PROC [edge: Edge] ~ {
kid: Corner ~ directionCorners[G3dOctree.DirectionFromEdge[edge]];
par: Corner ~ G3dOctree.EdgeCorners[parent, edge].c1;
IF par.inside = kid.inside
THEN SELECT G3dOctree.AxisFromEdge[edge] FROM
x => kid.lCross � par.lCross;
y => kid.bCross � par.bCross;
z => kid.nCross � par.nCross;
ENDCASE;
};
MaybeSubdivideEdgeNeighbors: PROC [edge: Edge] ~ {
twoCorners: TwoCorners ~ G3dOctree.EdgeCorners[parent, edge];
IF twoCorners.c0.inside = twoCorners.c1.inside THEN {
kidCorner: Corner ~ directionCorners[G3dOctree.DirectionFromEdge[edge]];
IF twoCorners.c0.inside # kidCorner.inside THEN {
cs: ThreeCubes � G3dOctree.EdgeNeighbors[parent, edge];
IF cs.c0 # NIL AND cs.c0.terminal THEN AddToBottomOfStack[cs.c0];
IF cs.c1 # NIL AND cs.c1.terminal THEN AddToBottomOfStack[cs.c1];
IF cs.c2 # NIL AND cs.c2.terminal THEN AddToBottomOfStack[cs.c2];
};
};
};
MaybeSubdivideFaceNeighbor: PROC [face: Face] ~ {
d: FourDirections ~ SELECT face FROM
l			=> [lb, lt, ln, lf],
r			=> [rb, rt, rn, rf],
b			=> [lb, rb, bn, bf],
t			=> [lt, rt, tn, tf],
n			=> [ln, rn, bn, tn],
ENDCASE	=> [lf, rf, bf, tf];
bool: BOOL ~ directionCorners[d.d0].inside;
IF bool = directionCorners[d.d1].inside AND
bool = directionCorners[d.d2].inside AND
bool = directionCorners[d.g3d].inside AND
bool # directionCorners[G3dOctree.DirectionFromFace[face]].inside THEN {
nbor: Cube ~ neighbors[G3dOctree.DirectionFromFace[face]];
IF nbor # NIL AND nbor.terminal THEN AddToBottomOfStack[nbor];
};
};
RestrictOctree: PROC [parent: Cube] ~ {
FOR direction: Direction IN Direction DO
IF direction # c AND direction # none AND
grandNeighbors[direction] # NIL AND grandNeighbors[direction].terminal
THEN AddToBottomOfStack[grandNeighbors[direction]];
ENDLOOP;
};
directionCorners: DirectionCorners;
neighbors, grandNeighbors: Neighborhood;
neighbors � G3dOctree.Neighbors[parent];
grandNeighbors � G3dOctree.Neighbors[parent.parent];
G3dOctree.Subdivide[parent];
ImplicitPoints.SetKidValues[parent, valueProc, threshold, clientData];
directionCorners � G3dOctree.GetDirectionCorners[parent];
FOR edge: Edge IN Edge DO
MaybeInheritSurfacePoint[edge];
ENDLOOP;
IF parent.parent # NIL THEN RestrictOctree[parent];			-- restricted octree
FOR edge: Edge IN Edge DO										-- edge anomaly
MaybeSubdivideEdgeNeighbors[edge];
ENDLOOP;
FOR face: Face IN Face DO											-- face anomaly
MaybeSubdivideFaceNeighbor[face];
ENDLOOP;
FOR octant: Octant IN Octant DO
IF ShouldSubdivide[parent.kids[octant]] THEN AddToBottomOfStack[parent.kids[octant]];
ENDLOOP;
};
ShouldSubdivide: PROC [cube: Cube] RETURNS [should: BOOL] ~ {
IF cube = NIL OR NOT cube.terminal OR cube.level >= levelLimit
THEN RETURN[FALSE]
ELSE {
mp: MacroPolygons � MacroPolygonize[cube, valueProc, threshold, clientData];
polygon: CrossSequence � mp.polygon;
should � SELECT mp.nPolygons FROM
none => FALSE,
one => TooRound[polygon, cosFlatLimit, cosPerpFlatLimit, valueProc, threshold, normalProc, cube, clientData],
ENDCASE => TRUE;
};
};
CheckStatusProc: PROC [cube: Cube, atom: ATOM] ~ {
IF statusProc = NIL THEN RETURN;
cube.refAny � atom;
IF statusProc[cube] = $Abort THEN ERROR SubdivideAbort;
};
TerminalProc: CubeProc ~ {
terminalLevel � cube.level;
levelLimit � terminalLevel+adaptLimit;
RETURN[FALSE];
};
MaybeSubdivide: CubeProc ~ {
nTerminal � nTerminal+1;
CheckStatusProc[cube, $Dot];
IF ShouldSubdivide[cube] THEN AddToBottomOfStack[cube];
};
AddToBottomOfStack: PROC [cube: Cube] ~ {
IF cube = NIL OR NOT cube.terminal OR cube.level >= levelLimit THEN RETURN;
G3dOctree.WriteBottomOfCubeStack[cube, cubeStack];
CheckStatusProc[cube, $Cross];
};
ProcessTopOfStack: PROC ~ {
cube: Cube � G3dOctree.ReadTopOfCubeStack[cubeStack];
IF cube = NIL OR NOT cube.terminal OR cube.level >= levelLimit THEN RETURN;
counts[cube.level] � counts[cube.level]+1;
SubdivideAndMore[cube];
CheckStatusProc[cube, $X];
};
terminalLevel, levelLimit, nTerminal: NAT � 0;
counts: ARRAY [0..100) OF NAT � ALL[0];
cosPerpFlatLimit: REAL � RealFns.CosDeg[90.0-flatLimit];
cosFlatLimit: REAL � RealFns.CosDeg[flatLimit];
cubeStack: CubeStack � G3dOctree.NewCubeStack[20000];
ImplicitPoints.SetTerminalCubeValues[root, valueProc, threshold, clientData];
G3dOctree.ApplyToTerminal[root, TerminalProc];
G3dOctree.ApplyToLevel[root, MaybeSubdivide, terminalLevel];
WHILE NOT G3dOctree.CubeStackEmpty[cubeStack] DO
ProcessTopOfStack[! SubdivideAbort => EXIT];
ENDLOOP;
msg � IO.PutFR["%g/%g", IO.int[counts[terminalLevel]], IO.int[nTerminal]];
FOR n: NAT IN (terminalLevel..100) WHILE counts[n] # 0 DO
msg � IO.PutFR["%g,%g/%g", IO.rope[msg], IO.int[counts[n]], IO.int[8*counts[n-1]]];
ENDLOOP;
msg � IO.PutFR1["%g adapted", IO.rope[msg]];
};
TrackAbort: ERROR = CODE;

Track: PUBLIC PROC [
seedSize: REAL,
surfacePoint: Triple,
valueProc: ValueProc,
threshold: REAL � 1.0,
normalProc: NormalProc � NIL,
statusProc: StatusProc � NIL,
clientData: REF ANY � NIL,
adaptLimit: NAT � 0,
flatLimit: REAL � 30.0,
tolerance: REAL � 0.0001]
RETURNS [octree: Octree]
~ {
GetActiveFaces: PROC [cube: Cube] RETURNS [activeFaces: ActiveFaces] ~ {
FOR e: Edge IN Edge DO
corners: TwoCorners � G3dOctree.EdgeCorners[cube, e];
IF corners.c0.inside # corners.c1.inside AND
NOT corners.c0.outOfRange AND
NOT corners.c1.outOfRange THEN {
twoFaces: TwoFaces ~ G3dOctree.EdgeFaces[e];
activeFaces[twoFaces.f0] � activeFaces[twoFaces.f1] � TRUE;
};
ENDLOOP;
};
ShouldSubdivideTest: PROC [cube: Cube] RETURNS [should: BOOL � FALSE] ~ {
crossPolygonProc: CrossPolygonProc ~ {
InnerTest: PROC RETURNS [shouldSubdivide: BOOL � FALSE] ~ {
SELECT TRUE FROM
nPolygon # 0 => RETURN[TRUE];	-- more than one polygon in cube
polygon.length >= 3 => {
center, normal, p1: Triple;
FOR n: NAT IN [0..polygon.length) DO
points[n] � polygon[n].point;
ENDLOOP;
points.length � polygon.length;
center � G3dPolygon.PolygonCenter[points];
normal � ImplicitPoints.GetPointNormal[
center, valueProc, valueProc[center, clientData], delta, clientData];
FOR n: NAT IN [0..polygon.length) DO
IF G3dVector.Dot[polygon[n].normal, normal] < cosFlatLimit
THEN RETURN[TRUE];
ENDLOOP;
p1 � polygon[polygon.length-1].point;
FOR n: NAT IN [0..polygon.length) DO
p0: Triple � p1;
v: Triple � G3dVector.Sub[p1 � polygon[n].point, p0];
v � G3dVector.Unit[v];
IF G3dVector.Dot[normal, v] > cosPerpFlatLimit THEN RETURN[TRUE];
ENDLOOP;
};
ENDCASE;
};
IF (should � InnerTest[]) THEN RETURN[FALSE];
};
IF TRUE THEN RETURN[FALSE];
IF 0.5*cube.size < sizeLimit THEN RETURN[FALSE];
IF cube.size # cubeSize THEN delta � 0.001*(cubeSize � cube.size);
[] � ImplicitPoints.CheckAndGetCrossedEdges[
cube, valueProc, threshold, NProc, tolerance, clientData];
[] � ImplicitPolygons.CrossPolygonizeCube[cube, crossPolygonProc, crossSequence, FALSE];
};
ShouldCoalesce: PROC [parent: Cube] RETURNS [should: BOOL] ~ {
IF parent = NIL OR parent.terminal THEN RETURN[FALSE];
IF (should � NOT ShouldSubdivideTest[parent]) THEN {
FOR edge: Edge IN Edge DO
twoOctants: TwoOctants ~ G3dOctree.EdgeOctants[edge];
state: BOOL � parent.corners[twoOctants.o0].inside;
IF parent.corners[twoOctants.o1].inside = state THEN {
o: Octant � twoOctants.o1;
k: Cube � parent.kids[twoOctants.o0];
IF k = NIL THEN {k � parent.kids[twoOctants.o1]; o � twoOctants.o0};
IF k # NIL AND k.corners[o].inside # state THEN RETURN[FALSE];
};
ENDLOOP;
FOR face: Face IN Face DO
fourOctants: FourOctants � G3dOctree.FaceOctants[face];
state: BOOL � parent.corners[fourOctants.o0].inside;
IF parent.corners[fourOctants.o1].inside = state AND
parent.corners[fourOctants.o2].inside = state AND
parent.corners[fourOctants.o3].inside = state THEN {
o: Octant � fourOctants.o2;
k: Cube � parent.kids[fourOctants.o0];
IF k = NIL THEN {k � parent.kids[fourOctants.o1]; o � fourOctants.o3};
IF k = NIL THEN {k � parent.kids[fourOctants.o2]; o � fourOctants.o0};
IF k = NIL THEN {k � parent.kids[fourOctants.o3]; o � fourOctants.o1};
IF k # NIL AND k.corners[o].inside # state THEN RETURN[FALSE];
};
ENDLOOP;
};
};
DefaultNormalProc: NormalProc ~ {
RETURN[ImplicitPoints.GetPointNormal[point, valueProc, value, delta, clientData]];
};
AddToBottomOfStack: PROC [cube: Cube] ~ {
IF (counter � counter+1) > 10 THEN {
counter � 0;
MessageWindow.Append[IO.PutFR1["\tstack size: %g", IO.int[cubeStack.size]], TRUE];
};
IF cube = NIL OR NOT cube.terminal OR cube.size < sizeLimit THEN RETURN;
ImplicitPoints.SetCornerValues[cube, valueProc, threshold, clientData];
IF NOT ImplicitPoints.IsCrossed[cube] THEN RETURN;
G3dOctree.WriteBottomOfCubeStack[cube, cubeStack];
cube.refAny � $AddedToStack;
IF statusProc # NIL AND statusProc[cube] = $Abort THEN ERROR TrackAbort;
IF NOT G3dOctree.FullyPointed[G3dOctree.Root[cube]] THEN ERROR;
};
InnerSubdivide: PROC [parent: Cube] ~ {
MaybeInheritCross: PROC [edge: Edge] ~ {
kid: Corner ~ directionCorners[G3dOctree.DirectionFromEdge[edge]];
par: Corner ~ G3dOctree.EdgeCorners[parent, edge].c1;
IF par.inside = kid.inside THEN SELECT G3dOctree.AxisFromEdge[edge] FROM
x => kid.lCross � par.lCross;
y => kid.bCross � par.bCross;
z => kid.nCross � par.nCross;
ENDCASE;
};
MaybeSubdivideEdgeNeighbors: PROC [edge: Edge] ~ {
twoCorners: TwoCorners ~ G3dOctree.EdgeCorners[parent, edge];
IF twoCorners.c0.inside = twoCorners.c1.inside THEN {
kidCorner: Corner ~ directionCorners[G3dOctree.DirectionFromEdge[edge]];
IF twoCorners.c0.inside # kidCorner.inside THEN {
ds: G3dOctree.ThreeDirections � G3dOctree.EdgeDirections[edge];
c0: Cube � neighbors[ds.d0];
c1: Cube � neighbors[ds.d1];
c2: Cube � neighbors[ds.d2];
IF c0 # NIL AND c0.terminal THEN InnerSubdivide[c0];
IF c1 # NIL AND c1.terminal THEN InnerSubdivide[c1];
IF c2 # NIL AND c2.terminal THEN InnerSubdivide[c2];
};
};
};
MaybeSubdivideFaceNeighbor: PROC [face: Face] ~ {
d: FourDirections � G3dOctree.FaceDirections[face];
bool: BOOL ~ directionCorners[d.d0].inside;
IF bool = directionCorners[d.d1].inside AND
bool = directionCorners[d.d2].inside AND
bool = directionCorners[d.g3d].inside AND
bool # directionCorners[G3dOctree.DirectionFromFace[face]].inside
THEN {
neighbor: Cube ~ neighbors[G3dOctree.DirectionFromFace[face]];
IF neighbor # NIL AND neighbor.terminal THEN InnerSubdivide[neighbor];
};
};
directionCorners: DirectionCorners;
neighbors: Neighborhood � G3dOctree.Neighbors[parent];
G3dOctree.Subdivide[parent];
ImplicitPoints.SetKidValues[parent, valueProc, threshold, clientData];
FOR o: Octant IN Octant DO
k: Cube � parent.kids[o];
IF ShouldSubdivideTest[k]
THEN InnerSubdivide[k]
ELSE AddToBottomOfStack[k];
ENDLOOP;
directionCorners � G3dOctree.GetDirectionCorners[parent];
FOR edge: Edge IN Edge DO
MaybeInheritCross[edge];
ENDLOOP;
FOR edge: Edge IN Edge DO										-- test for edge anomaly
MaybeSubdivideEdgeNeighbors[edge];
ENDLOOP;
FOR face: Face IN Face DO											-- test for face anomaly
MaybeSubdivideFaceNeighbor[face];
ENDLOOP;
};
ProcessTopOfStack: PROC [cubeStack: CubeStack] ~ {
cube: Cube � G3dOctree.ReadTopOfCubeStack[cubeStack];
IF (counter � counter+1) > 10 THEN {
counter � 0;
MessageWindow.Append[IO.PutFR1["\tstack size: %g", IO.int[cubeStack.size]], TRUE];
};
IF cube.terminal AND cube.refAny # $Coalesced THEN {
activeFaces: ActiveFaces � GetActiveFaces[cube];
FOR face: Face IN Face DO
IF cube.refAny = $Coalesced THEN RETURN;
IF activeFaces[face] THEN {
neighbor: Cube � G3dOctree.FaceNeighbor[cube, face];
IF neighbor = NIL THEN {
new: Cube;
octree.root � G3dOctree.AddCube[cube, face];
new � G3dOctree.FaceNeighbor[cube, face];
IF NOT new.terminal THEN ERROR;
FOR p: Cube � new.parent, p.parent WHILE p # NIL DO
IF p.refAny = $Coalesced THEN {
Coalesce[p];
RETURN;
};
ENDLOOP;
ConsiderCube[new];
}
ELSE IF neighbor.refAny = NIL THEN ConsiderCube[neighbor];
};
ENDLOOP;
};
};
Coalesce: PROC [parent: Cube] ~ {
Inner: CubeProc ~ {cube.refAny � $Coalesced};
G3dOctree.ApplyToKids[parent, Inner];
};
ConsiderCube: PROC [new: Cube] ~ {
IF new.refAny = $Coalesced THEN ERROR;
new.refAny � $Considered;
IF ShouldSubdivideTest[new]
THEN InnerSubdivide[new]
ELSE IF ShouldCoalesce[new.parent] THEN {
Coalesce[new.parent];
new.parent.terminal � TRUE;
AddToBottomOfStack[new.parent];
}
ELSE AddToBottomOfStack[new];
};
RemoveCoalescedCubes: PROC [root: Cube] ~ {
IsCoalesced: PROC [cube: Cube] RETURNS [b: BOOL � TRUE] ~ {
Test: CubeProc ~ {IF cube.refAny # $Coalesced THEN ERROR};
IF (b � cube.refAny = $Coalesced) THEN G3dOctree.ApplyToKids[cube, Test];
};
Inner: PROC [cube: Cube] ~ {
cube.terminal � TRUE;
FOR o: Octant IN Octant DO
k: Cube � cube.kids[o];
IF k = NIL THEN LOOP;
IF IsCoalesced[k]
THEN cube.kids[o] � NIL
ELSE {
cube.terminal � FALSE;
Inner[k];
};
ENDLOOP;
};
Inner[root];
};
CheckForNeededSubdivisions: PROC [root: Cube] ~ {
Inner: CubeProc ~ {
state: BOOL;
neighbors: Neighborhood � G3dOctree.Neighbors[cube];
TestNeighborIfDivide: PROC [d: Direction] RETURNS [b: BOOL] ~ {
n: Cube � neighbors[d];
b � n # NIL AND NOT n.terminal AND n.refAny # $Coalesced;
IF b THEN {
c: Corner � G3dOctree.GetDirectionCorner[n, G3dOctree.OppositeDirection[d]];
b � c # NIL AND state # c.inside;
};
};
TestEdgeNeighborIfDivide: PROC [d0, d1: Direction] RETURNS [b: BOOL] ~ {
n: Cube � neighbors[d0];
b � n # NIL AND NOT n.terminal AND n.refAny # $Coalesced;
IF b THEN {
d: Direction � G3dOctree.AddDirection[d1, G3dOctree.OppositeDirection[d0]];
c: Corner � G3dOctree.GetDirectionCorner[n, d];
b � c # NIL AND state # c.inside;
};
};
FOR edge: Edge IN Edge DO
twoCorners: TwoCorners ~ G3dOctree.EdgeCorners[cube, edge];
state � twoCorners.c0.inside;
IF state = twoCorners.c1.inside THEN {
ds: G3dOctree.ThreeDirections � G3dOctree.EdgeDirections[edge];
IF TestEdgeNeighborIfDivide[ds.d0, ds.d1] THEN GOTO subdiv;
IF TestEdgeNeighborIfDivide[ds.d1, ds.d0] THEN GOTO subdiv;
IF TestNeighborIfDivide[ds.d2] THEN GOTO subdiv;
};
ENDLOOP;
FOR face: Face IN Face DO
fourCorners: FourCorners � G3dOctree.FaceCorners[cube, face];
state � fourCorners.c0.inside;
IF state = fourCorners.c1.inside AND
state = fourCorners.c2.inside AND
state = fourCorners.c3.inside AND
TestNeighborIfDivide[G3dOctree.DirectionFromFace[face]] THEN GOTO subdiv;
ENDLOOP;
EXITS
subdiv => {
InnerSubdivide[cube];
FOR o: Octant IN Octant DO [] � Inner[cube.kids[o]]; ENDLOOP;
};
};
G3dOctree.ApplyToTerminal[root, Inner];
};
NProc: NormalProc � IF normalProc # NIL THEN normalProc ELSE DefaultNormalProc;
counter, nRecursiveTrackFaces, nRecurseFailures: NAT � 0;
cubeStack: CubeStack � G3dOctree.NewCubeStack[20000];
cosFlatLimit: REAL � RealFns.CosDeg[flatLimit];
cosPerpFlatLimit: REAL � RealFns.CosDeg[90.0-flatLimit];
delta, cubeSize: REAL � 0.0;
crossSequence: CrossSequence � G3dOctree.ObtainCrossSequence[];
points: TripleSequence � NEW[TripleSequenceRep[12]];
sizeLimit: REAL � seedSize;
FOR n: NAT IN [0..adaptLimit) DO sizeLimit � 0.5*sizeLimit; ENDLOOP;
octree � NEW[OctreeRep];
octree.root � G3dOctree.NewCube[seedSize, surfacePoint];
ConsiderCube[octree.root];
WHILE NOT G3dOctree.CubeStackEmpty[cubeStack] DO
ProcessTopOfStack[cubeStack ! TrackAbort => EXIT];
ENDLOOP;
CheckForNeededSubdivisions[octree.root];
RemoveCoalescedCubes[octree.root];
IF NOT G3dOctree.FullyPointed[octree.root] THEN ERROR;
IF NOT G3dOctree.CubeOk[octree.root] THEN ERROR;
G3dOctree.ReleaseCrossSequence[crossSequence];
G3dOctree.SetOctreeFields[octree];
};

Roundness: PUBLIC PROC [
cube: Cube,
valueProc: ValueProc,
threshold: REAL � 1.0,
normalProc: NormalProc,
clientData: REF ANY � NIL]
RETURNS [max: REAL � 0.0]
~ {
v, normal: Triple � [];
polygon: CrossSequence � MacroPolygonize[cube, valueProc, threshold, clientData].polygon;
IF polygon = NIL OR polygon.length = 0 THEN RETURN;
normal � G3dVector.Unit[NormalFromCrossSequence[polygon]];
IF polygon.length > 3 THEN {
p1: Triple � polygon[polygon.length-1].point;
FOR i: NAT IN [0..polygon.length) DO
p0: Triple � p1;
v � G3dVector.Unit[G3dVector.Sub[p1 � polygon[i].point, p0]];
max � MAX[max, 90.0-G2dBasic.ArcCos[G3dVector.Dot[normal, v]]];
ENDLOOP;
};
FOR n: NAT IN [0..polygon.length) DO
cross: Cross � polygon[n];
IF cross.normal = [] THEN {
cross.normal � IF normalProc # NIL
THEN normalProc[cross.point, cross.value, clientData]
ELSE ImplicitPoints.GetPointNormal[
cross.point, valueProc, cross.value, 0.01*cube.size, clientData];
};
max � MAX[max, G2dBasic.ArcCos[G3dVector.Dot[normal, cross.normal]]];
ENDLOOP;
G3dOctree.ReleaseCrossSequence[polygon];
};

NormalFromCrossSequence: PUBLIC PROC [polygon: CrossSequence]
RETURNS [n: Triple � []]
~ {
p1: Triple � polygon[polygon.length-1].point;
FOR i: NAT IN[0..polygon.length) DO				-- Newells' method
p0: Triple � p1;
p1 � polygon[i].point;
n.x � n.x+(p0.y-p1.y)*(p0.z+p1.z);
n.y � n.y+(p0.z-p1.z)*(p0.x+p1.x);
n.z � n.z+(p0.x-p1.x)*(p0.y+p1.y);
ENDLOOP;
};

LinearDeviation: PUBLIC PROC [cube: Cube] RETURNS [error: REAL � 0.0] ~ {
corners: Corners ~ cube.corners;
F: PROC [i, j, k: NAT] RETURNS [REAL] ~ {
o: Octant;
d: Direction � c;
d � G3dOctree.AddDirection[d, IF i = 0 THEN l ELSE r];
d � G3dOctree.AddDirection[d, IF j = 0 THEN b ELSE t];
d � G3dOctree.AddDirection[d, IF k = 0 THEN n ELSE f];
o � G3dOctree.OctantFromDirection[d];
IF NOT corners[o].valueSet THEN ERROR;
RETURN[corners[o].value];
};
f000: REAL ~ corners[lbn].value;
f001: REAL ~ corners[lbf].value;
f010: REAL ~ corners[ltn].value;
f011: REAL ~ corners[ltf].value;
f100: REAL ~ corners[rbn].value;
f101: REAL ~ corners[rbf].value;
f110: REAL ~ corners[rtn].value;
f111: REAL ~ corners[rtf].value;
a: REAL � 0.25*((f100+f101+f110+f111)-(f000+f001+f010+f011));
b: REAL ~ 0.25*((f010+f011+f110+f111)-(f000+f001+f100+f101));
c: REAL ~ 0.25*((f001+f011+f101+f111)-(f000+f100+f010+f110));
d: REAL ~ 0.5*f000+0.25*(f100+f010+f001-f111);
FOR i: NAT IN [0..1] DO
FOR j: NAT IN [0..1] DO
FOR k: NAT IN [0..1] DO
dif: REAL ~ a*i+b*j+c*k+d-F[i, j, k];
error � error+dif*dif;
ENDLOOP;
ENDLOOP;
ENDLOOP;
error � error/cube.size;
};

TooRound: PUBLIC PROC [
polygon: CrossSequence,
cosFlatLimit: REAL,
cosPerpFlatLimit: REAL,
valueProc: ValueProc,
threshold: REAL � 1.0,
normalProc: NormalProc,
cube: Cube,
clientData: REF ANY]
RETURNS [tooRound: BOOL � FALSE]
   ~ {
p0, p1, v, normal: Triple � [];
p1 � polygon[polygon.length-1].point;
FOR i: NAT IN[0..polygon.length) DO								-- Newells' method
p0 � p1;
p1 � polygon[i].point;
normal � [
normal.x+(p0.y-p1.y)*(p0.z+p1.z),
normal.y+(p0.z-p1.z)*(p0.x+p1.x),
normal.z+(p0.x-p1.x)*(p0.y+p1.y)];
ENDLOOP;
normal � G3dVector.Unit[normal];
IF polygon.length > 3 THEN {
p1 � polygon[polygon.length-1].point;
FOR i: NAT IN [0..polygon.length) DO
p0 � p1;
v � G3dVector.Unit[G3dVector.Sub[p1 � polygon[i].point, p0]];
IF G3dVector.Dot[normal, v] > cosPerpFlatLimit THEN {tooRound � TRUE; EXIT};
ENDLOOP;
};
IF tooRound = FALSE THEN
FOR n: NAT IN [0..polygon.length) DO
cross: Cross � polygon[n];
IF cross.normal = [] THEN {
cross.normal � IF normalProc # NIL
THEN normalProc[cross.point, cross.value, clientData]
ELSE ImplicitPoints.GetPointNormal[
cross.point, valueProc, cross.value+threshold, 0.01*cube.size, clientData];
};
IF G3dVector.Dot[normal, cross.normal] < cosFlatLimit THEN {tooRound � TRUE; EXIT};
ENDLOOP;
};

MacroPolygonize: PUBLIC PROC [
cube: Cube,
valueProc: ValueProc,
threshold: REAL � 1.0,
clientData: REF ANY]
RETURNS [macro: MacroPolygons]
~ {
crossedEdges: CrossedEdges �
ImplicitPoints.CheckAndGetCrossedEdges[cube, valueProc, threshold,,, clientData];
FOR e: Edge IN Edge DO
IF crossedEdges[e].cIn # NIL THEN GOTO found;
REPEAT
found => {
edge, start: Edge � e;
done: ARRAY Edge OF BOOL � ALL[FALSE];
crosses: CrossSequence � G3dOctree.ObtainCrossSequence[];
DO
edge � ImplicitPoints.NextCWEdgeCrossed[edge, crossedEdges];
crosses[crosses.length] � ImplicitPoints.CrossedPoint[crossedEdges[edge], valueProc, threshold,,,, clientData];
crosses.length � crosses.length+1;
done[edge] � TRUE;
IF edge = start THEN {
macro.polygon � crosses;
macro.nPolygons � one;
EXIT;
};
ENDLOOP;
FOR e: Edge IN Edge DO
IF crossedEdges[e].cIn # NIL AND NOT done[e] THEN {
G3dOctree.ReleaseCrossSequence[crosses];
macro.nPolygons � many;
RETURN;
};
ENDLOOP;
};
FINISHED => {
macro.nPolygons � none;
RETURN;
};
ENDLOOP;
};

END.

@
ImplicitAdaptImpl.mesa
Copyright � 1985, 1990 by Xerox Corporation.  All rights reserved.
Bloomenthal, February 27, 1993 9:48 pm PST
Part 1: Adaptive Subdivision of an Existing Octree
 The Algorithm
Adaptively subdivide the terminal cubes of the octree.
For each terminal cube, if the maximum limit of subdivision is not yet reached
If one polygon results from polygonization of the cube
If the polygon is insufficiently flat, or
The surface curvature too great, or
The tangeny of the surface disagrees with the tangency of the polygon
Subdivide the cube
If more than one polygon results from the polygonization of the cube
Subdivide the cube and all its neighbors
Subdivision of the cube
Call the cube "parent;" set its terminal field to false.
Subdivide parent into eight "children."
Set each child's terminal field to true.

Each child shares 1 of parent's 8 corners; compute locations and implicit values of 19
new corners (1 center of parent, 12 midpoints of parent's edges, 6 face centers).

Each parent corner has 3 points associated with the 3 edges leaving the corner in
the leftward, downward, and near directions.  Each of these points, if set, must be
properly copied to those child corners that are midpoints of the parent's edges.  This
is done by finding in which half-edge the point lies.
For each of parent's twelve edges
If the corners disagree in sign
If the edge is left to right, consider right corner's value, lSet and lPoint fields.
If edge is bottom to top, consider the top corner's value, bSet and bPoint fields.
If the edge is near to far, consider the far corner's value, nSet and nPoint fields.
If value disagrees in sign from the child's corner that's midway along the edge
Set child corner's appropriate Set field and copy the appropriate Point field.
If the corners agree in sign:
If child's corner disagrees in sign, subdivide the three edge neighbors of parent.
For each of parent's six faces:
If the 4 child corners that are midpoints of 4 edges of the face all agree in sign
but disagree with the center of the face, subdivide the face neighbor.

Subdivide parent; compute location and implicit value for all new child corners.
Appropriately set child corners' Set and Point fields.
Cause subdivision of neighbors to insure restricted octree.
Subdivide edge neighbors if child midpoint introduces a new surface edge.
Subdivide face neighbor if child face center introduces a new surface region.
Part 2: Adaptively Sized Surface Tracking
 The Algorithm
Begin with a point on the surface
Create a cube centered on this point
add it to the stack
make it the root octree node
For each cube on the stack:
Remove cube from stack.
If cube is not terminal (ie, has been subdivided) or cube.parent is terminal (ie, children were coalesced), do nothing
Else test cubes in direction of those faces intersected by the surface
if no previous cube exists there:
add it to octree
test it against subdivision criteria:
if the maximum limit of subdivision is not yet reached
if the polygon is insufficiently flat
the surface curvature too great
the tangeny of the surface disagrees with the tangency of the polygon
if more than one polygon results from the polygonization of the cube
in previous method, > 1 polygons => subdivision of cube and its neighbors, why?
subdivide any neighbor adjacent to a "holed" edge or a "holed" face
if subdivide, then Subdivide cube
else test its parent for coalescence
is there a need to subdivide parent
test as above, but also, test if there are child-edge or child-face problems (see below)
if coalesce, nilify children, set parent.terminal TRUE, add parent to stack
else add cube to stack
Subdivision of the cube
Call the cube "parent;" set its terminal field to FALSE.
Subdivide parent into eight "children."
Set each child's terminal field to TRUE.

Each child shares 1 of parent's 8 corners; compute locations and implicit values of the
19 new corners (1 center of parent, 12 midpoints of edges, and 6 face centers).

Each parent corner has 3 points associated with the three edges leaving the corner in
the leftward, downward, and nearward directions.  Each of these points, if set, must
be properly copied to those child corners that are midpoints of the parent's edges. 
This is done by finding in which half-edge the point lies.
Add the eight children to the stack.
For each of parent's twelve edges
If the corners disagree in sign (child-edge problem)
If the edge is from left to right, consider right corner's value, lSet and lPoint fields.
If the edge is from bottom to top, consider top corner's value, bSet and bPoint fields.
If the edge is from near to far, consider far corner's value, nSet and nPoint fields.
If the value disagrees in sign from the child's corner that is midpoint along the edge
Set the child corner's appropriate Set field and copy the appropriate Point field.
If the corners agree in sign:
If child's corner disagrees in sign, subdivide the 3 edge neighbors of parent.
For each of parent's six faces (child-face problem):
If the 4 child corners that are midpoints of the 4 edges of the face all agree in sign
but disagree with the center of the face, subdivide the face neighbor.

Test polygon normal for collinearity with vertex normals:
Test polygon edges for perpendicularity to plane normal:
parent may've been coalesced by testing one of its kids, so first verify it's not terminal:
Check for edge-surface anomaly:
Check for face-surface anomaly:
Subdivide parent; compute location, implicit value, and valueSet for all new child corners.
Subdivide edge neighbors if child midpoint introduces a new surface edge.
Subdivide face neighbor if child face center introduces a new surface region.
A cube may have been subdivided or coalesced since going on stack, so test:
In a prior pass through this loop, cube may get coalesced, so test each time:
New cube's parent must be fully pointed since RemoveCoalescedCubes and
ImplicitPolygons.RecursiveTrackFace presume nonterminal cubes have all kids
If new attached to coalesced part of octree, ensure all branch is coalesced;
leave new in octree (reduce future neighbor testing), don't add to stack:
If neighbor was created as artifact of prior AddCube, it needs to be considered:
ELSE cube.refAny � $RejectedFromStack;
Coalesce parent.kids but keep .kids so kids' neighbors needn't re-investigate their space:
Parent is now effectively terminal, so, in order to be processed from stack:
UnCoalesceAnyCoalescedParents: PROC [cube: Cube] ~ {
Inner: PROC [parent: Cube] ~ {
parent.terminal � FALSE;
FOR o: Octant IN Octant DO
k: Cube � parent.kids[o];
IF k.refAny = $RejectedFromStack THEN AddToBottomOfStack[k];
IF k.refAny # $AddedToStack THEN k.refAny � NIL;
ENDLOOP;
parent.refAny � $KidsUnCoalesced;
IF parent.parent # NIL THEN Inner[parent.parent];
};
Inner[cube.parent];
};
Part 3: Miscellaneous Procedures
Test polygon edges for perpendicularity to plane normal:
Test vertex normal for collinearity with plane normal:
Test polygon edges for perpendicularity to plane normal:
Test vertex normal for collinearity with plane normal:
TooCurving: PROC [cube: Cube, valueProc: ValueProc] RETURNS [BOOL] ~ {
compute gradient at corners, scale by cube.size; do face by face compare?
};

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