DIRECTORY Complex USING [VEC], Cubic USING [Bezier], Seq USING [ComplexSequence, RealSequence]; LSPiece: CEDAR DEFINITIONS = BEGIN OPEN Seq; Metrics: TYPE = REF MetricsRec; MetricsRec: TYPE = RECORD [ maxItr: INT _ 500, -- limit on number of iterations maxDev: REAL _ .00001, --stop iterating if the maximum deviation gets below this amount sumErr: REAL _ .00001, -- stop iterating if the sum of squares gets below this amount deltaT: REAL _ 0.000005 -- stop when the t values each change by less than this ]; FitPiece: PROCEDURE [ z: ComplexSequence, t: RealSequence _ NIL, metrics: Metrics, from, thru: NAT, -- fit points in range [from..thru] modulo z.length initFree, finalFree: BOOLEAN _ FALSE, initTangent, finalTangent: Complex.VEC _ [0,0], useOldTValues: BOOLEAN _ FALSE] RETURNS [b: Cubic.Bezier, err: REAL, iterations: INT, maxDev: REAL]; END. *LSPiece.mesa Copyright c 1985 by Xerox Corporation. All rights reserved. Maureen Stone August 29, 1984 5:33:42 pm PDT Michael Plass 28-Jan-82 12:14:59 Doug Wyatt, September 5, 1985 1:13:09 pm PDT For fitting a single cubic piece with specified endpoints, and possibly specified tangents. FitPiece will fit a cubic patch to the points z[from], z[(from+1) MOD l],..., z[thru], where l=z.length. The curve will pass through the points z[from] (if initFree) and z[thru] (if finalFree), and the tangents at the endpoints will be parallel to initTangent and finalTangent, if these are specified to be non-zero. The sum of the squares of the distances from the points to the curve are returned in err, and the largest deviation is returned in maxDev. The values of t[from] thru t[thru] will be set to the parameters of these closest points, with t[from]=0 and t[thru]=1. The iteration is stopped when either (1) err <= eps, (2) err has increased over the previous iteration, (3) the largest change in a t value is less than deltat, or (4) iterations >= maxit. ʃ˜codešœ ™ Kšœ Ïmœ1™˜UKšœžœ  7˜OK˜—K˜šÏnœž œ˜Kšœ&žœ˜*Kšœ˜Kšœ žœ 3˜DKšœžœžœ˜%Kšœ#žœ ˜/Kšœžœžœ˜Kšžœžœžœ žœ˜DK™šœÿ™ÿK˜——Kšžœ˜—…—\