
DIRECTORY
Imager USING [Rectangle, VEC, Transformation],
ImagerPath USING [MoveToProc, CurveToProc],
CubicSplines USING [CoeffsSequence],
Cubic2 USING [Bezier];

CubicPaths: CEDAR DEFINITIONS ~ BEGIN

VEC: TYPE = Imager.VEC;
Bezier: TYPE = Cubic2.Bezier;
Path: TYPE = REF PathRec; 
PathRec: TYPE = RECORD[bounds: Imager.Rectangle, cubics: REF PathSequence]; 
PathSequence: TYPE = RECORD[bezier: SEQUENCE length: NAT OF Bezier]; 

PathFromCubic: PROC [coeffs: CubicSplines.CoeffsSequence, newBounds: BOOL ¬ TRUE] 
RETURNS [Path];
EnumeratePath: PROC [path: Path, 
moveTo: ImagerPath.MoveToProc, curveTo: ImagerPath.CurveToProc];
PointProc: TYPE = PROC [p: VEC] RETURNS [stop: BOOLEAN ¬ FALSE];
WalkPath: PROC [path: Path, tol: REAL, proc: PointProc]; 
PointOnPath: PROC [pt: VEC, path: Path, tol: REAL] RETURNS [BOOLEAN]; 
TranslatePath: PROC [path: Path, offset: VEC];
TransformPath: PROC [path: Path, tranformation: Imager.Transformation, 
newBounds: BOOL ¬ TRUE]; 
UpdateBounds: PROC [path: Path];
ClosestPoint: PROC [pt: VEC, path: Path] RETURNS[VEC];
CopyPath: PROC [path: Path] RETURNS[Path];
ReversePath: PROC [path: Path];
ClosestPointAnalytic: PROC[pt: VEC, path: Path, tolerance: REAL ¬ 9999.0] 
RETURNS [closest: VEC, success: BOOL];
GetParam: PROC [bezier: Bezier, pt: VEC] RETURNS [u: REAL];
CubicMeetsLine: PROC [bezier: Bezier, a, b, c: REAL] 
RETURNS [points: ARRAY [0..2] OF VEC, hitCount: [0..3], tangency: ARRAY [0..2] OF BOOL];
END.
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CubicPaths.mesa
Copyright س 1985, 1986, 1987, 1992 by Xerox Corporation.  All rights reserved.
Written by:  Maureen Stone August 5, 1985 8:39:13 pm PDT
Last edited by Bier on December 1, 1986 4:42:55 pm PST
Russ Atkinson (RRA) February 2, 1987 10:43:11 pm PST
Pier, August 5, 1987 3:50:29 pm PDT
Doug Wyatt, April 8, 1992 5:49 pm PDT

Call this inside of an Imager.PathProc to display the path.
ie: pathProc: ImagerPath.PathProc = {EnumeratePath[path, moveTo, curveTo]};


Enumerates all the points on the curve.  Uses subdivision.  tol is for the flatness test


updates the bounding rectangle


reverses it in place

Faster than ClosestPointSubdivide, more accurate, and almost as robust.  If success = TRUE, the point returned is guaranteed to be quite close to the Bezier path.  The point is quite close because it results from plugging in a value of the parameter.  The point returned is also quite close to the actual closest point, since the parameter chosen is within a floating point round-off error of being a root of the "closest point" polynomials.  IF success = FALSE, no point on path is within tolerance of pt.  In this case, closest is not valid data.

Given a bezier curve, and a point on the curve, find the parameter value u that generates pt.

Find the intersection points of the Bezier cubic piece bezier and the line: ax + by + c = 0.

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