Complex,

Cubic,

Seq;

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

];

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];

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.