Cells.mesa
Last Edited by: Arnon, May 3, 1986 3:53:47 pm PDT
DIRECTORY
Rope,
IO,
AlgebraClasses,
Ints,
BigRats,
RatIntervals,
Variables,
Polynomials,
AlgebraicNumbers,
Points,
Sequences,
Formulas,
SamplePoints,
Colors,
CoveringSets;
Cells: CEDAR DEFINITIONS
~ BEGIN OPEN AC: AlgebraClasses, BR: BigRats, RI: RatIntervals, VARS: Variables, AN: AlgebraicNumbers, PTS: Points, SEQ: Sequences, POL: Polynomials, QFF: Formulas, SP: SamplePoints, CS: CoveringSets;
Cell Representation
Cell: TYPE = AC.Object;
CellIndex: TYPE = PTS.Point; -- of Ints
Signature: TYPE = PTS.Point; -- of FormulaOperators.Operators
CellData: TYPE = REF CellDataRec;
CellDataRec: TYPE = RECORD [
cad: AC.Object ← NIL, -- access to the cad to which this cell belongs
dimension: CARDINAL ← 0, -- = sum of parities of index components
index: CellIndex, -- length of index (= cad.dimension) is dimension r of ambient space
abstractVertex: Graphs.Vertex ← Graphs.nullVertex,
adjacentCells: SEQ.Sequence ← NIL, -- of cells, in lexicographic order (for binary searching).
basisSignature: Signature ← NIL, -- signature with respect to cad.basis
inputSignature: Signature ← NIL, -- signature with respect to cad.inputPolynomials
primarySignature: Signature ← NIL, -- with respect to cad.primaryPolynomials
primaryRegion: NAT ← 0, -- which signed component wrt primarySignature
secondarySignature: Signature ← NIL, -- with respect to cad.secondaryPolynomials
secondaryRegion: NAT ← 0, -- which signed component wrt secondarySignature
samplePoint: SP.SamplePoint ← NIL,
definingFormula: QFF.Formula ← NIL,
extensionData: ExtensionData ← NIL, -- needed by current E^3 adjacency algorithm
identicallyZeroBasisElements: SEQ.Sequence ← NIL, -- of polynomials, elements of cad.basis which are identically zero on this cell; currently used only for degenerate 0-cells in E^2.
sectionDefiningPolynomial: POL.Polynomial ← NIL, -- possibly nonNIL for sections only; r-variate integral polynomial whose variety contains it (used by display)
sectionDefiningPolynomialRoot: NAT ← 0, -- which real root of sectionDefiningPolynomial is this section (over base of this stack) (used by display)
coveringSet: CS.CoveringSet ← NIL,
color: Colors.Color ← NIL -- paint this color in display
];
Class for Cell Structures
cellStructureClass: AC.StructureClass;
Instance Data for Cell Structures
CellStructureData: TYPE = REF CellStructureDataRec;
CellStructureDataRec: TYPE = RECORD [
inputPolynomialRing: AC.Structure,
minPolyRing: AC.Structure,
basisSignatureStructure: AC.Structure
];
Operations Unique to Cell Structures
CellOps: TYPE = REF CellOpsRec; -- prop key is $CellStructure.
CellOpsRec: TYPE = RECORD [
cad: AC.UnaryOp,
adjacentCells: AC.UnaryOp,
basisSignature: AC.UnaryOp,
samplePoint: AC.UnaryOp,
definingFormula: AC.UnaryOp,
coveringSet: AC.UnaryOp,
color: AC.UnaryOp,
setColor: AC.BinaryInPlaceOp,
boundingBox: AC.UnaryOp,
display2D: AC.Display2DOp
];
Cell Structure Constructor
MakeCellStructure: PROC [inputPolynomialRing, minPolyRing: AC.Structure, numBasisElements: CARDINAL] RETURNS [cellStructure: AC.Structure];
Extract Cell Operations from Class Property Lists
IsCellStructure: PROC [structure: AC.Structure] RETURNS [BOOL];
Cad: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
AdjacentCells: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
BasisSignature: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
SamplePoint: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
DefiningFormula: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
CoveringSet: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
Color: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
SetColor: PROC [structure: AC.Structure] RETURNS [AC.BinaryInPlaceOp];
BoundingBox: PROC [structure: AC.Structure] RETURNS [AC.UnaryOp];
Format is [minX, maxX, minY, maxY, ...], each element is a Reals.Real
Display2D: PROC [structure: AC.Structure] RETURNS [AC.Display2DOp];
Conversion and IO
Read: AC.ReadOp;
FromRope: AC.FromRopeOp;
ToRope: AC.ToRopeOp;
Write: AC.WriteOp;
Operations
SetCad: PROC [cell, cad: AC.Object];
GetCad: AC.UnaryOp;
CellDim: AC.ElementRankOp;
AdjCells: AC.UnaryOp;
BasisSig: AC.UnaryOp;
SamplePt: AC.UnaryOp;
DefiningForm: AC.UnaryOp;
CoverSet: AC.UnaryOp;
Col: AC.UnaryOp;
SetCol: AC.BinaryInPlaceOp;
BoundBox: AC.UnaryOp;
Disp2D: AC.Display2DOp;
END.