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: CEDAR 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.