DIRECTORY
CADIO,
CADTypes USING [CellRec, CellSequence, CompoundOperator, QuantifierFreeFormula, QuantifierFreeFormulaSequence, Scad, SimpleOperator, TriangleSequence, VariableRec, VertexSequence, VisibleMask],
Convert,
FormulaOperators,
Formulas,
FS USING [StreamOpen],
Interminal USING [MousePosition],
IO USING [BreakProc, Close, CR, GetTokenRope, IDProc, int, NUL, PutF, PutFR, real, rope, SP, STREAM],
MultiPolynomial USING [EvaluationBindings, RefFromRope, RopeFromRef, TotallyEvaluate],
AlgebraClasses,
Ints,
Polynomials,
PopUpMenu USING [RequestSelection],
Points,
Sequences,
CoveringSets,
Triangles,
Cells,
Cads,
Reals,
Rope USING [Compare, Concat, ROPE],
Vector3d USING [Triple];


CADIOImpl: CEDAR PROGRAM
IMPORTS Convert, FS, IO, MultiPolynomial, Polynomials, PopUpMenu, Triangles, Cads, Rope
EXPORTS CADIO
~ BEGIN

Error: PUBLIC ERROR[why: ATOM] = CODE;

ReadVAXCadFiles: PUBLIC PROC [cadFile, csFile: Rope.ROPE] RETURNS [info: CADTypes.Scad] ~ BEGIN

cadStream, csStream: IO.STREAM;
qeCad: Cads.Cad;
qeCadData: Cads.CadData;
oldCellsData: Sequences.SequenceData;
polySeqData: Sequences.SequenceData;
cellData: Cells.CellData;
pointData: Points.PointData;
inputPoly: Polynomials.Polynomial;
cadStructure: AlgebraClasses.Structure _ Cads. MakeCadStructure[];
surfaceRope: Rope.ROPE;
oldCells: Sequences.Sequence;
numberOfOldCells: NAT;
newCells: REF CADTypes.CellSequence;
newCellIndex: NAT;
compressedNewCells: REF CADTypes.CellSequence;


TranslateQFF: PROC [old: Formulas.Formula] RETURNS [new: CADTypes.QuantifierFreeFormula] ~ BEGIN

oldData: Formulas.FormulaData _ NARROW[old.data];
mainOp: FormulaOperators.Op _ NARROW[oldData.mainOperator.data, FormulaOperators.OperatorData]^;

IF oldData.atomicMatrix THEN BEGIN
newOperator: CADTypes.SimpleOperator;
SELECT mainOp FROM
lt	=> newOperator _ isNegative;
gt 	=> newOperator _ isPositive;
eq	=> newOperator _ isZero;
le, ge, ne	=> ERROR Error[$UnimplementedOperator];
ENDCASE	=> ERROR Error[$BadOperator];
RETURN [[
isCompound: FALSE,
compoundOperator: none,
compoundArguments: NIL,
simpleOperator: newOperator,
simpleArgument: MultiPolynomial.RefFromRope[Polynomials.ToRope[oldData.polynomial]]
]];
END

ELSE BEGIN
newOperator: CADTypes.CompoundOperator;
newOperands: REF CADTypes.QuantifierFreeFormulaSequence;
oldOperands: LIST OF Formulas.Formula;
nOperands: NAT;
SELECT mainOp FROM
and	=> newOperator _ and;
or	=> newOperator _ or;
not	=> ERROR Error[$UnimplementedOperator];
ENDCASE	=> ERROR Error[$BadOperator];
nOperands _ 0;
oldOperands _ oldData.operands; 
UNTIL oldOperands = NIL DO
nOperands _ nOperands + 1;
oldOperands _ oldOperands.rest;
ENDLOOP;
newOperands _ NEW[CADTypes.QuantifierFreeFormulaSequence[nOperands]];
oldOperands _ oldData.operands;
FOR i: NAT IN [0..nOperands) DO
newOperands[i] _ TranslateQFF[oldOperands.first];
oldOperands _ oldOperands.rest;
ENDLOOP;
RETURN [[
isCompound: TRUE,
compoundOperator: newOperator,
compoundArguments: newOperands,
simpleOperator: none,
simpleArgument: NIL
]];
END;

END;

cadStream _ FS.StreamOpen[cadFile];
qeCad _ cadStructure.class.read[cadStream, cadStructure];
csStream _ FS.StreamOpen[csFile];
qeCad _ Cads.ReadCSets[csStream, qeCad];
qeCadData _ NARROW[qeCad.data];
polySeqData _ NARROW[qeCadData.inputPolynomials.data];
inputPoly _ polySeqData[1];
surfaceRope _ inputPoly.structure.class.toRope[inputPoly];

oldCells _ qeCadData.cells;
oldCellsData _ NARROW[oldCells.data];
numberOfOldCells _ oldCellsData.lengthPlus1 - 1;
newCells _ NEW[CADTypes.CellSequence[numberOfOldCells]];
newCellIndex _ 0;

FOR oldCellIndex: NAT IN [1..numberOfOldCells] DO

cellData _ NARROW[oldCellsData[oldCellIndex].data];
pointData _ NARROW[cellData.index.data];
IF NARROW[pointData[3].data, Ints.IntData]^ MOD 2 = 0 THEN BEGIN

newCells[newCellIndex].indexX _ NARROW[pointData[1].data, Ints.IntData]^;
newCells[newCellIndex].indexY _ NARROW[pointData[2].data, Ints.IntData]^;
newCells[newCellIndex].indexZ _ NARROW[pointData[3].data, Ints.IntData]^;
newCells[newCellIndex].dimension _ cellData.dimension;

newCells[newCellIndex].definingFormula _ TranslateQFF[cellData.definingFormula];

SELECT newCells[newCellIndex].dimension FROM

0 => BEGIN
xReal, yReal, zReal: REAL;
coveringSetData: CoveringSets.CoveringSetData _ NARROW[cellData.coveringSet.data];
setData: Sequences.SequenceData _ NARROW[coveringSetData.dataPoints.data];
columnData: Sequences.SequenceData _ NARROW[setData[1].data];
pointData: Points.PointData _ NARROW[columnData[1].data ];
newCells[newCellIndex].vertices _ NEW[CADTypes.VertexSequence[1]];
xReal _ NARROW[pointData[1].data, Reals.RealData]^;
yReal _ NARROW[pointData[2].data, Reals.RealData]^;
zReal _ NARROW[pointData[3].data, Reals.RealData]^;
newCells[newCellIndex].vertices[0] _ [
x: xReal,
y: yReal,
z: zReal
];
newCells[newCellIndex].polygons _ NEW[CADTypes.TriangleSequence[0]];
END;

1 => BEGIN
coveringSetData: CoveringSets.CoveringSetData _ NARROW[cellData.coveringSet.data];
setData: Sequences.SequenceData _ NARROW[coveringSetData.dataPoints.data];
columnData: Sequences.SequenceData _ NARROW[setData[1].data];
numberOfPoints: NAT _ columnData.lengthPlus1 - 1;
newCells[newCellIndex].vertices _ NEW[CADTypes.VertexSequence[numberOfPoints]];
FOR j: NAT IN [0..numberOfPoints) DO
xReal, yReal, zReal: REAL;
pointData: Points.PointData _ NARROW[columnData[j + 1].data ];
xReal _ NARROW[pointData[1].data, Reals.RealData]^;
yReal _ NARROW[pointData[2].data, Reals.RealData]^;
zReal _ NARROW[pointData[3].data, Reals.RealData]^;
newCells[newCellIndex].vertices[j] _ [
x: xReal,
y: yReal,
z: zReal
];
ENDLOOP;
newCells[newCellIndex].polygons _ NEW[CADTypes.TriangleSequence[0]];
END;

2 => BEGIN
numberOfPoints, pointIndex: NAT;
triangulation: Triangles.TriangleSeq;
coveringSetData: CoveringSets.CoveringSetData _ NARROW[cellData.coveringSet.data];
setData: Sequences.SequenceData _ NARROW[coveringSetData.dataPoints.data];

numberOfPoints _ 0;
FOR i: NAT IN [1..setData.lengthPlus1) DO
columnData: Sequences.SequenceData _ NARROW[setData[i].data];
numberOfPoints _ numberOfPoints + columnData.lengthPlus1 - 1;
ENDLOOP;
newCells[newCellIndex].vertices _ NEW[CADTypes.VertexSequence[numberOfPoints]];

pointIndex _ 0;
FOR i: NAT IN [1..setData.lengthPlus1) DO
columnData: Sequences.SequenceData _ NARROW[setData[i].data];
FOR j: NAT IN [1..columnData.lengthPlus1) DO
xReal, yReal, zReal: REAL;
pointData: Points.PointData _ NARROW[columnData[j].data ];
xReal _ NARROW[pointData[1].data, Reals.RealData]^;
yReal _ NARROW[pointData[2].data, Reals.RealData]^;
zReal _ NARROW[pointData[3].data, Reals.RealData]^;
newCells[newCellIndex].vertices[pointIndex] _ [
x: xReal,
y: yReal,
z: zReal
];
pointIndex _ pointIndex + 1;
ENDLOOP;
ENDLOOP;

triangulation _ Triangles.GenerateTriangles[cellData.coveringSet];

IF triangulation = NIL THEN
newCells[newCellIndex].polygons _ NEW[CADTypes.TriangleSequence[0]]
ELSE {
newCells[newCellIndex].polygons _ NEW[CADTypes.TriangleSequence [triangulation.trianglesPlusOne - 1]];
FOR i: NAT IN [1..triangulation.trianglesPlusOne) DO
newCells[newCellIndex].polygons[i - 1] _ [
firstVertex: triangulation[i].firstVertex,
secondVertex: triangulation[i].secondVertex,
thirdVertex: triangulation[i].thirdVertex
];
ENDLOOP;
};

END;

ENDCASE => BEGIN
ERROR Error[$DegreeOutOfRange];
END;

newCellIndex _ newCellIndex + 1;
END;

ENDLOOP;

compressedNewCells _ NEW[CADTypes.CellSequence[newCellIndex]];
FOR i: NAT IN [0..newCellIndex) DO
compressedNewCells[i] _ newCells[i];
ENDLOOP;

info _ [
surface: MultiPolynomial.RefFromRope[surfaceRope],
named: FALSE,
name: "(none)",
color: [1, 1, 1],
cells: compressedNewCells];

END;

ReadInfoFile: PUBLIC PROC [filename: Rope.ROPE] RETURNS [info: CADTypes.Scad] ~ BEGIN


infoStream: IO.STREAM _ FS.StreamOpen[filename];
token: Rope.ROPE _ "";
InfoFileError: ERROR = CODE;
TestError: ERROR = CODE;
Break: SIGNAL = CODE;
BreakProc: IO.BreakProc ~ IO.IDProc;
numberOfCells: NAT;

TokenBreakProc: IO.BreakProc ~ BEGIN
RETURN [SELECT char FROM
IN [IO.NUL .. IO.SP], '$	=> sepr,
ENDCASE		=> other
];
END;

PolynomialBreakProc: IO.BreakProc ~ BEGIN
RETURN [SELECT char FROM
'$, IO.CR		=> break,
ENDCASE		=> other
];
END;

NextToken: PROC [proc: IO.BreakProc _ TokenBreakProc] RETURNS [Rope.ROPE] ~ BEGIN
token: Rope.ROPE;
[token: token] _ IO.GetTokenRope[infoStream, proc];
RETURN [token];
END;

GetDefiningFormula: PROC RETURNS [CADTypes.QuantifierFreeFormula] ~ BEGIN
operatorRope: Rope.ROPE;
simpleOperator: CADTypes.SimpleOperator;
compoundOperator: CADTypes.CompoundOperator;
isCompound: BOOLEAN;
operatorRope _ NextToken[];
IF Rope.Compare[operatorRope, "IsPositive"] = equal THEN
{simpleOperator _ isPositive; isCompound _ FALSE}
ELSE IF Rope.Compare[operatorRope, "IsZero"] = equal THEN
{simpleOperator _ isZero; isCompound _ FALSE}
ELSE IF Rope.Compare[operatorRope, "IsNegative"] = equal THEN
{simpleOperator _ isNegative; isCompound _ FALSE}
ELSE IF Rope.Compare[operatorRope, "And"] = equal THEN
{compoundOperator _ and; isCompound _ TRUE}
ELSE IF Rope.Compare[operatorRope, "Or"] = equal THEN
{compoundOperator _ or; isCompound _ TRUE}
ELSE ERROR InfoFileError;
IF ~isCompound THEN BEGIN
polyRope: Rope.ROPE _ NextToken[PolynomialBreakProc];
RETURN [[
isCompound: FALSE,
compoundOperator: none,
compoundArguments: NIL,
simpleOperator: simpleOperator,
simpleArgument: MultiPolynomial.RefFromRope[polyRope]
]];
END
ELSE BEGIN
numberOfArguments: NAT _ Convert.IntFromRope[NextToken[]];
qff: CADTypes.QuantifierFreeFormula _ [
isCompound: TRUE,
compoundOperator: compoundOperator,
compoundArguments: NEW[CADTypes.QuantifierFreeFormulaSequence[numberOfArguments]],
simpleOperator: none,
simpleArgument: NIL];
FOR argument: NAT IN [0..numberOfArguments) DO
qff.compoundArguments[argument] _ GetDefiningFormula[];
ENDLOOP;
RETURN [qff];
END;
END;


UNTIL Rope.Compare[token, "BEGIN"] = equal DO
token _ NextToken[];
ENDLOOP;

IF Rope.Compare[NextToken[], "CAD"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "DESCRIPTION"] # equal THEN ERROR InfoFileError;

IF Rope.Compare[NextToken[], "Surface"] # equal THEN ERROR InfoFileError;
token _ NextToken[PolynomialBreakProc];
info.surface _ MultiPolynomial.RefFromRope[token];

IF Rope.Compare[NextToken[], "Name"] # equal THEN ERROR InfoFileError;
token _ NextToken[];
IF Rope.Compare[token, "UNNAMED"] = equal THEN BEGIN
info.named _ FALSE;
info.name _ "(unnamed)";
END
ELSE BEGIN
info.named _ TRUE;
info.name _ token;
END;
IF Rope.Compare[NextToken[], "Color"] # equal THEN ERROR InfoFileError;
info.color.R _ Convert.RealFromRope[NextToken[]];
info.color.G _ Convert.RealFromRope[NextToken[]];
info.color.B _ Convert.RealFromRope[NextToken[]];
IF Rope.Compare[NextToken[], "Cells"] # equal THEN ERROR InfoFileError;
numberOfCells _ Convert.IntFromRope[NextToken[]];
info.cells _ NEW[CADTypes.CellSequence[numberOfCells]];

IF Rope.Compare[NextToken[], "BEGIN"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "CELL"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "DEFINITIONS"] # equal THEN ERROR InfoFileError;
FOR cell: NAT IN [0..numberOfCells) DO

dimension: CARDINAL;

IF Rope.Compare[NextToken[], "CellIndices"] # equal THEN ERROR InfoFileError;
info.cells[cell].indexX _ Convert.IntFromRope[NextToken[]];
info.cells[cell].indexY _ Convert.IntFromRope[NextToken[]];
info.cells[cell].indexZ _ Convert.IntFromRope[NextToken[]];
IF Rope.Compare[NextToken[], "CellDegree"] # equal THEN ERROR InfoFileError;
dimension _ Convert.CardFromRope[NextToken[]];
IF dimension > 2 THEN ERROR InfoFileError;
info.cells[cell].dimension _ dimension;

IF Rope.Compare[NextToken[], "DefiningFormula"] # equal THEN ERROR InfoFileError;
info.cells[cell].definingFormula _ GetDefiningFormula[];

ENDLOOP;

IF Rope.Compare[NextToken[], "END"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "CELL"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "DEFINITIONS"] # equal THEN ERROR InfoFileError;

IF Rope.Compare[NextToken[], "BEGIN"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "CELL"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "DISPLAY"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "INFORMATION"] # equal THEN ERROR InfoFileError;

FOR cell: NAT IN [0..numberOfCells) DO

dimension: CARDINAL;
nVertices, nTriangles: NAT;

IF Rope.Compare[NextToken[], "Indices"] # equal THEN ERROR InfoFileError;
IF Convert.IntFromRope[NextToken[]] # info.cells[cell].indexX THEN ERROR InfoFileError;
IF Convert.IntFromRope[NextToken[]] # info.cells[cell].indexY THEN ERROR InfoFileError;
IF Convert.IntFromRope[NextToken[]] # info.cells[cell].indexZ THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "Degree"] # equal THEN ERROR InfoFileError;
dimension _ Convert.CardFromRope[NextToken[]];
IF dimension # info.cells[cell].dimension THEN ERROR InfoFileError;

IF dimension = 0 THEN BEGIN
IF Rope.Compare[NextToken[], "Position"] # equal THEN ERROR InfoFileError;
info.cells[cell].vertices _ NEW[CADTypes.VertexSequence[1]];
info.cells[cell].vertices[0].x _ Convert.RealFromRope[NextToken[]];
info.cells[cell].vertices[0].y _ Convert.RealFromRope[NextToken[]];
info.cells[cell].vertices[0].z _ Convert.RealFromRope[NextToken[]];
END
ELSE IF dimension = 1 OR dimension = 2 THEN BEGIN
IF Rope.Compare[NextToken[], "Vertices"] # equal THEN ERROR InfoFileError;
nVertices _ Convert.IntFromRope[NextToken[]];
info.cells[cell].vertices _ NEW[CADTypes.VertexSequence[nVertices]];
FOR i: NAT IN [0..nVertices) DO
info.cells[cell].vertices[i].x _ Convert.RealFromRope[NextToken[]];
info.cells[cell].vertices[i].y _ Convert.RealFromRope[NextToken[]];
info.cells[cell].vertices[i].z _ Convert.RealFromRope[NextToken[]];
ENDLOOP;
END
ELSE ERROR InfoFileError;

IF dimension = 2 THEN BEGIN
IF Rope.Compare[NextToken[], "Triangles"] # equal THEN ERROR InfoFileError;
nTriangles _ Convert.IntFromRope[NextToken[]];
info.cells[cell].polygons _ NEW[CADTypes.TriangleSequence[nTriangles]];
FOR i: NAT IN [0..nTriangles) DO
info.cells[cell].polygons[i].firstVertex _ Convert.IntFromRope[NextToken[]];
info.cells[cell].polygons[i].secondVertex _ Convert.IntFromRope[NextToken[]];
info.cells[cell].polygons[i].thirdVertex _ Convert.IntFromRope[NextToken[]];
ENDLOOP;
END
ELSE BEGIN
info.cells[cell].polygons _ NEW[CADTypes.TriangleSequence[0]];
END;

ENDLOOP;

IF Rope.Compare[NextToken[], "END"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "CELL"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "DISPLAY"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "INFORMATION"] # equal THEN ERROR InfoFileError;

IF Rope.Compare[NextToken[], "END"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "CAD"] # equal THEN ERROR InfoFileError;
IF Rope.Compare[NextToken[], "DESCRIPTION"] # equal THEN ERROR InfoFileError;

END;

WriteInfoFile: PUBLIC PROC [filename: Rope.ROPE, info: CADTypes.Scad] ~ BEGIN

infoStream: IO.STREAM _ FS.StreamOpen[filename, $create];
InternalError: ERROR = CODE;

WriteDefiningFormula: PROC[df: CADTypes.QuantifierFreeFormula, nesting: NAT _ 2] ~ BEGIN
operatorRope: Rope.ROPE _
IF df.isCompound THEN SELECT df.compoundOperator FROM
and 	=> "And",
or	=> "Or",
ENDCASE	=> ERROR InternalError
ELSE SELECT df.simpleOperator FROM
isPositive	=> "IsPositive",
isZero	=> "IsZero",
isNegative	=> "IsNegative"
ENDCASE	=> ERROR InternalError;

IF nesting # 2 THEN FOR i: NAT IN [1..nesting] DO
IO.PutF[infoStream, "\t"];
ENDLOOP;

IF df.isCompound THEN BEGIN
IO.PutF[
infoStream,
"%g %g\n",
IO.rope[operatorRope],
IO.int[df.compoundArguments.length]];
FOR formula: NAT IN [0..df.compoundArguments.length) DO
WriteDefiningFormula[df.compoundArguments[formula], nesting + 1];
ENDLOOP;
END
ELSE BEGIN
IO.PutF[
infoStream,
"%g %g\n",
IO.rope[operatorRope],
IO.rope[MultiPolynomial.RopeFromRef[df.simpleArgument]]];
END;

END;

IO.PutF[infoStream, "BEGIN CAD DESCRIPTION\n\n"];
IO.PutF[
infoStream,
"\tSurface %g\n",
IO.rope[MultiPolynomial.RopeFromRef[info.surface]]];
IF info.named THEN IO.PutF[infoStream, "\tName %g\n", IO.rope[info.name]]
ELSE IO.PutF[infoStream, "\tName UNNAMED\n"];
IO.PutF[
infoStream,
"\tColor %g %g %g\n",
IO.real[info.color.R],
IO.real[info.color.G],
IO.real[info.color.B]];
IO.PutF[infoStream, "\tCells %g\n", IO.int[info.cells.nCells]];
IO.PutF[infoStream, "\n\tBEGIN CELL DEFINITIONS\n"];

FOR cell: NAT IN [0..info.cells.nCells) DO
IO.PutF[
infoStream,
"\n\t\tCellIndices %g %g %g\n",
IO.int[info.cells[cell].indexX],
IO.int[info.cells[cell].indexY],
IO.int[info.cells[cell].indexZ]];
IO.PutF[infoStream, "\t\tCellDegree %g\n", IO.int[info.cells[cell].dimension]];
IO.PutF[infoStream, "\t\tDefiningFormula "];
WriteDefiningFormula[info.cells[cell].definingFormula, 2];
ENDLOOP;
IO.PutF[infoStream, "\n\tEND CELL DEFINITIONS\n"];
IO.PutF[infoStream, "\n\tBEGIN CELL DISPLAY INFORMATION\n"];

FOR cell: NAT IN [0..info.cells.nCells) DO

dimension: CARDINAL _ info.cells[cell].dimension;
nVertices: NAT _ info.cells[cell].vertices.nVertices;
nTriangles: NAT _ info.cells[cell].polygons.nTriangles;

IO.PutF[
infoStream,
"\n\t\tIndices %g %g %g\n",
IO.int[info.cells[cell].indexX],
IO.int[info.cells[cell].indexY],
IO.int[info.cells[cell].indexZ]];
IO.PutF[infoStream, "\t\tDegree %g\n", IO.int[dimension]];

IF dimension = 0 THEN IO.PutF[
infoStream,
"\t\tPosition %g %g %g\n",
IO.real[info.cells[cell].vertices[0].x],
IO.real[info.cells[cell].vertices[0].y],
IO.real[info.cells[cell].vertices[0].z]]
ELSE BEGIN
IO.PutF[infoStream, "\t\tVertices %g\n", IO.int[nVertices]];
FOR i: NAT IN [0..nVertices) DO
IO.PutF[
infoStream,
"\t\t\t%g %g %g\n",
IO.real[info.cells[cell].vertices[i].x],
IO.real[info.cells[cell].vertices[i].y],
IO.real[info.cells[cell].vertices[i].z]];
ENDLOOP;
END;

IF dimension = 2 THEN BEGIN
IO.PutF[infoStream, "\t\tTriangles %g\n", IO.int[nTriangles]];
FOR i: NAT IN [0..nTriangles) DO
IO.PutF[
infoStream,
"\t\t\t%g %g %g\n",
IO.int[info.cells[cell].polygons[i].firstVertex],
IO.int[info.cells[cell].polygons[i].secondVertex],
IO.int[info.cells[cell].polygons[i].thirdVertex]];
ENDLOOP;
END;

ENDLOOP;
IO.PutF[infoStream, "\n\tEND CELL DISPLAY INFORMATION\n"];
IO.PutF[infoStream, "\nEND CAD DESCRIPTION\n"];
IO.Close[infoStream];

END;

SelectCell: PUBLIC PROC [scad: CADTypes.Scad, mask: REF CADTypes.VisibleMask, title: Rope.ROPE] RETURNS [index: INT] ~ BEGIN

menuRopes: LIST OF Rope.ROPE _ NIL;
mousePosition: REF Interminal.MousePosition;
selection: INT;

IF scad.cells.nCells # mask.length THEN ERROR Error[$WrongNumberOfCells];

FOR i: INT IN [0..scad.cells.nCells) DO
j: NAT _ scad.cells.nCells - i - 1;
cell: CADTypes.CellRec _ scad.cells[j];
cellRope: Rope.ROPE _ IO.PutFR["(%g, %g, %g)", IO.int[cell.indexX], IO.int[cell.indexY], IO.int[cell.indexZ]];
IF mask[j] THEN cellRope _ Rope.Concat[cellRope, " V"];
menuRopes _ CONS[cellRope, menuRopes];
ENDLOOP;

mousePosition _ NEW[Interminal.MousePosition _ [mouseX: 0, color: FALSE, mouseY: 0]];
selection _ PopUpMenu.RequestSelection[
label: title,
choice: menuRopes,
timeOut: 0,
mouse: mousePosition];

IF (selection = 0) OR (selection = -1) THEN RETURN[-1]
ELSE RETURN[selection - 1];
END;

WhatCellIsItOn: PUBLIC PROC[point: Vector3d.Triple, variables: CADTypes.VariableRec, scad: CADTypes.Scad] RETURNS [cell: NAT] ~ BEGIN
FOR i: NAT IN [0..scad.cells.nCells) DO
IF SatisfiesQFF[point, variables, scad.cells[i].definingFormula] THEN RETURN[i];
ENDLOOP;
ERROR Error[$NotOnAnyCell];
END;
SatisfiesQFF: PROC[point: Vector3d.Triple, variables: CADTypes.VariableRec, qff: CADTypes.QuantifierFreeFormula] RETURNS [satisfiesQFF: BOOLEAN] ~ BEGIN

whoops: ERROR = CODE;
epsilon: REAL ~ 0.0001;
IF qff.isCompound THEN
SELECT qff.compoundOperator FROM
and => BEGIN
FOR i: NAT IN [0..qff.compoundArguments.length) DO
IF ~SatisfiesQFF[point, variables, qff.compoundArguments[i]] THEN RETURN[FALSE];
ENDLOOP;
RETURN[TRUE];
END;
or => BEGIN
FOR i: NAT IN [0..qff.compoundArguments.length) DO
IF SatisfiesQFF[point, variables, qff.compoundArguments[i]] THEN RETURN[TRUE];
ENDLOOP;
RETURN[FALSE];
END;
ENDCASE => ERROR whoops

ELSE BEGIN
bindings: MultiPolynomial.EvaluationBindings _ LIST [
[variable: variables.x, value: point.x],
[variable: variables.y, value: point.y],
[variable: variables.z, value: point.z]
];
evaluatedPol: REAL _ MultiPolynomial.TotallyEvaluate[qff.simpleArgument, bindings];
SELECT qff.simpleOperator FROM
isPositive	=> RETURN[evaluatedPol > 0];
isZero	=> RETURN[ABS[evaluatedPol] < epsilon];
isNegative	=> RETURN[evaluatedPol < 0];
ENDCASE	=> ERROR whoops;
END;
END;





END.
šCADIOImpl.mesa
James Rauen, August 21, 1986 6:18:48 pm PDT

Declarations
Here is a procedure that translates quantifier-free-formulas between representations.
Translate an atomic formula.
Or translate a compound formula.
Read the CAD and covering set files.

Get the surface equation.
Get the old cells and instantiate the new ones.
Iterate over the old cells.
Only do the cell if it is part of the surface.

IF QEIO.CellDimension[oldCells[oldCellIndex].index ] < 3 THEN BEGIN
9/11/86 Do the cell if it has dimension less than 3; clearly wrong;  the intent here was just to pick up nasty vertical lines.

Translate its indices and dimension.
pointData: Points.PointData _ NARROW[oldCells[oldCellIndex].index.data];
Interim calculation of dimension; replace when ReadCad computes it.
newCells[newCellIndex].dimension _
(NARROW[oldCells[oldCellIndex].index.data, Points.PointData][1] MOD 2) +
(NARROW[oldCells[oldCellIndex].index.data, Points.PointData][2] MOD 2) + 
(NARROW[oldCells[oldCellIndex].index.data, Points.PointData][3] MOD 2);

Translate its defining formula.
Translate the vertex and polygon sequences.
Count the number of points.  
numberOfPoints _ 1;
newCells[newCellIndex].vertices[0] _ [6, 1, 70];
Translate the points.
Generate a triangulation of the points.
Translate the triangles.
Note!  These "triangulations" number the vertices from 1, 2, ..., while the vertices are indexed from 0, 1, ....  For example, triangle [firstVertex: 2, secondVertex: 3, thirdVertex: 4] refers to vertices[1], vertices[2], and vertices[3].  The discrepancy is remedied when the 2-cells are written
to a temporary file by ThreeDHacks.
Increment the index into the new cells.
Do the next cell.
Compress the new cells.
Construct and return the Scad.
No guarantees for incorrectly formatted files.  Will raise syntax errors.  It won't make some checks, such as if vertices listed in the Triangles section actually exist.
Declarations
Define a break procedure that gets a token.
Define a break procedure that gets a polynomial.
Define a procedure to get the next token or polynomial.
Recursive procedure to get a defining formula.
Get the BEGIN token
Get the CAD DESCRIPTION tokens.
Get the surface polynomial.
Get the name of the surface.

Get the color of the surface.

Get the number of cells and create the cell sequence in the Scad.
Get the BEGIN CELL DEFINITIONS tokens.

Iterate over the cells.
Declarations
Get the indices.

Get the dimension.
Get the defining formula.
Do the next cell.
Get the END CELL DEFINITIONS tokens.
Get the BEGIN CELL DISPLAY INFORMATION tokens.
Iterate over the cells.
Declarations
Get the indices for comparison.

Get the dimension for comparison.
Get the vertex sequence.  For zero-cells, there is only one vertex, the Position; for one- and two-cells, the number of vertices is specified in the file.
Get the triangle sequence.  For two-cells, the number of vertices is specified in the file; for zero- and one-cells, there are none.
Do the next cell.
Get the END CELL DISPLAY INFORMATION tokens.
Get the END CAD DESCRIPTION tokens.
Declarations
Procedure to write a defining formula.
Get the operator
Indent unless the nesting level is 2.
Write the defining formula.
Write the header.
Iterate over the cells, writing the indices, dimension, and defining formula.

Write the end of the cell definitions block and the start of the display information block.
Iterate over the cells, writing the display information.
Extract some useful quantities.

Write the indices and dimension.
Write the vertex sequence.
Write the triangle sequence if the cell has dimension 2.
Do the next cell.

Write the "END"s and close the file.
Declarations.
Ensure that the scad and mask have the same number of elements.
Build the list of ropes, backwards (of course), for the menu.
Get a selection from the pop-up menu.
Return the selection (minus 1 so the counts start at zero), or return -1 on timeout/abort.

Returns a boolean value indicating if point satisfies the qff.


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