DIRECTORY Cubic2, CubicPaths, GGSegmentTypes, Polynomial, Vector2; GGCubic2: CEDAR DEFINITIONS = BEGIN Bezier: TYPE = Cubic2.Bezier; BezierRef: TYPE = REF Bezier; Path: TYPE = CubicPaths.Path; ShortRealRootRec: TYPE = Polynomial.ShortRealRootRec; VEC: TYPE = Vector2.VEC; ClosestPointSubdivide: PROC[pt: VEC, path: Path, epsilon: REAL, tolerance: REAL _ 9999.0] RETURNS [closest: VEC, success: BOOL]; CheapRealRootsInInterval: PROC [poly: Polynomial.Ref, lo, hi: REAL] RETURNS [roots: ShortRealRootRec]; PairSequence: TYPE ~ GGSegmentTypes.PairSequence; AsPolyline: PROC [bezier: Bezier, tolerance: REAL] RETURNS [polyline: PairSequence]; END. ŽGGCubic2.mesa Copyright c 1986 by Xerox Corporation. All rights reserved. Last edited by Bier on December 1, 1986 4:42:55 pm PST Contents: The routines in Cubic2 and CubicPaths are inadequate for Gargoyle purposes. The Closest Point routine is too slow and doesn't properly document its accuracy. There is also a need for routines that are slow but very accurate so we can test how good our fast routines are (maybe using rational arithmetic?). Hopefully, these routines will eventually find their way back into Cubic2, and CubicPaths. Finds the closest point on bezier to pt. If success = TRUE, the point returned is guaranteed to be no farther than epsilon from bezier, and no farther than epsilon from the actual closest point. If no point on the curve is within tolerance then ClosestPoint has the option of returning success = FALSE, leaving closest uninitialized. This can save time, since we can throw away all parts of the curve that are outside tolerance, right from the beginning. Like CheapRealRoots, but it only finds those roots that are in the closed interval [lo..hi]. As a result, it runs 2 or 3 times faster for many cases. It is also more robust since it only evaluates poly in the range [lo..hi], whereas CheapRealRoots may evaluate poly at very large numbers, resulting in floating point errors. Approximate bezier with a polyline that deviates by no more than tolerance from bezier. ÊW˜J˜Icodešœ ™ Kšœ Ïmœ1™