Cad2D.mesa
Last Edited by: Arnon, March 7, 1986 2:40:12 pm PST
DIRECTORY
Imager,
ImagerPath,
IO,
Rope,
Points,
QETypes;
=
BEGIN
OPEN
QET: QETypes;
ImagerVecFromRealPoint:
PROC [point: Points.Point]
RETURNS [v: Imager.
VEC];
DisplayCad:
PROC [cad:
QET.Cad, context: Imager.Context, dotWidth, segmentWidth:
REAL];
Display0Cell:
PROC [cell:
QET.Cell, context: Imager.Context, dotWidth:
REAL];
Display1Cell:
PROC [cell:
QET.Cell, context: Imager.Context, segmentWidth:
REAL];
Frame: PROC [twoDCad: QET.Cad, ratApproxBound: RN.RatNum] RETURNS [frameLeftX, frameRightX, frameLowerY, frameUpperY: RN.RatNum];
Bounding box is defined by min and max of x- and y-coordinates of 0-cells. Frame is widening of bounding box by averageStripWidth, and heightening by averageStripWidth * bounding box aspect ratio. ratApproxBound specifies how accurately we want the vertices of bounding box.
DisplayCad: PROC [cad: QET.Cad, stepSize, ratApproxMultiplier: RN.RatNum, context: Imager.Context, segmentWidth: INT ← 2, dotWidth: INT ← 10];
stepSize * ratApproxMultiplier is tolerance for rational approximations of algebraic numbers
RightAdjacentZeroCell: PROC [oneSection: QET.Cell] RETURNS [zeroCell: QET.Cell ← NIL];
oneSection is a 1-section in a cad D of the plane. zeroCell is the unique 0-cell of D to the right of, and adjacent to, oneSection, if such a cell exists, otherwise zeroCell = NIL.
LeftAdjacentZeroCell: PROC [oneSection: QET.Cell] RETURNS [zeroCell: QET.Cell ← NIL];
oneSection is a 1-section in a cad D of the plane. zeroCell is the unique 0-cell of D to the left of, and adjacent to, oneSection, if such a cell exists, otherwise zeroCell = NIL.
RatApproxIntervalLength: PUBLIC PROC [oneDCad: QET.Cad, leftZeroCell: CARDINAL, ratApproxBound: RN.RatNum] RETURNS [approxWidth: RN.RatNum];
Rational approximation to the width of a 1-sector in a cad of the line. The 1-sector is assumed finite, i.e. it has both a left bounding 0-cell (with index leftZeroCellIndex) and a right bounding 0-cell.
RatApproxSectionYCood: PROC [sectionDefiningPolynomial: RP.RatPolynomial, ratX: RN.RatNum, section: CARDINAL, ratApproxBound: RN.RatNum] RETURNS [approxYCood: RN.RatNum];
ImagerVecFromRats: PROC [x, y: RN.RatNum] RETURNS [v: Imager.VEC];
DisplaySemiAlgebraicSet: PROC [cad: QET.Cad, definingFormula: QFF.QFFormula];
Display a 0, 1, or 2-dimensional semi-algebraic set in 2-space whose df is definingFormula.
Displays a 2-cell by walking around boundary creating a single trajectory, then MaskFills it (need a way to knit together two trajectories that are segments of this boundary). Use colors for boundary cells to indicate whether they are in the sas, e.g. to distinguish display of a closed 2-cell from that of an open 2-cell.
So algorithms for displaying a sas is to build region outlines in the graph with IsAProc of "element of the sas?", MaskFill them or MaskStroke them as appropriate.
The idea of doing "incremental" cad's by "combining", i.e. "merge" a new curve into the cad by doing point location, intersection computation, etc.
END.