-- LSPiece.mesa
-- For fitting a single cubic piece with specified endpoints, and possibly specified tangents.
-- Maureen Stone July 17, 1982 4:07 pm
-- Michael Plass 28-Jan-82 12:14:59

DIRECTORY
  Complex,
  Cubic,
  Seq;

LSPiece: DEFINITIONS =
BEGIN OPEN Seq;

FitPiece: PROCEDURE
	[z: ComplexSequence, t: RealSequence _ NIL,
	from, thru: NAT, -- fit points in range [from..thru] modulo z.length
	eps: REAL _ .00001, -- stop iterating if the sum of squares gets below this amount
    maxd: REAL _ .00001,  --stop iterating if the maximum deviation gets below this amount
	maxit: NAT _ 500, -- limit on number of iterations
	deltat: REAL _ 0.000005, -- stop when the t values each change by less than this
	initFree, finalFree: BOOLEAN _ FALSE,
	initTangent, finalTangent: Complex.Vec _ [0,0],
	useOldTValues: BOOLEAN _ FALSE]
	RETURNS [b: Cubic.Bezier, err: REAL, iterations: NAT, 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.

END.