[_CDMiwok_01_]<cedarcommon2.0>PiecewiseFit>LSCurve.mesa!1

LSCurve.mesa

Michael Plass November 29, 1982 9:52 am

Doug Wyatt, September 5, 1985 1:16:58 pm PDT

DIRECTORY

Complex USING [VEC],

Cubic USING [Bezier],

LSFit USING [Patch, PatchSequence, PatchSequenceRec],

PiecewiseCubic USING [Handle],

Seq USING [BooleanSequence, ComplexSequence, RealSequence];

LSCurve: CEDAR DEFINITIONS =

BEGIN OPEN Seq;

Patch: TYPE = LSFit.Patch;

PatchSequence: TYPE = LSFit.PatchSequence;

PatchSequenceRec: TYPE = LSFit.PatchSequenceRec;

Handle: TYPE = REF StateRec;

StateRec: TYPE = RECORD

[z: ComplexSequence, -- the points to fit

weight: RealSequence, -- weights for each point

t: RealSequence, -- the current best guess of parameter values. Always between 0 and 1.

oldt,oldoldt: RealSequence, -- for convergence acceleration

l,n: NAT, -- use just the points in the range [l..n]

splineBasis: SplineBasis, -- the current basis functions

a: RealSequence, -- the coefficients on the basis funtions for the current fit

free: BooleanSequence, -- tells which coefficients may be varied

closedCurve: BOOLEAN,

initialEndFree, finalEndFree: BOOLEAN, -- tells how to rescale

implementor private stuff follows

patchCacheValid: BOOLEAN ← FALSE,

patchCache: SplineFunction

];

SplineBasis: TYPE = REF SplineBasisRec;

SplineBasisRec: TYPE =

RECORD[SEQUENCE nBasis: NAT OF SplineFunction];

SplineFunction: TYPE = RECORD [x, y: PiecewiseCubic.Handle];

Create: PROCEDURE [sa: Seq.ComplexSequence] RETURNS [Handle];

XYat: PROCEDURE [h: Handle, t: REAL] RETURNS [Complex.VEC];

PatchesOf: PROCEDURE [h: Handle] RETURNS [x, y: PatchSequence, knots: RealSequence];

ArcLengthInitialTValues: PUBLIC PROCEDURE [h: Handle]; -- sets t values on the basis of arc length

UnitInitialTValues: PUBLIC PROCEDURE [h: Handle]; -- sets t values on equal steps

AngleInitialTValues: PUBLIC PROCEDURE [h: Handle];

AdjustTValues: PUBLIC PROCEDURE [h: Handle] RETURNS [maxChange: REAL]; -- uses 1 step of Newton's method

AccelTValues: PUBLIC PROCEDURE [h: Handle] RETURNS [r, maxChange: REAL]; -- applies convergence acceleration - assume SolveCurve has just been done

SolveTValues: PUBLIC PROCEDURE [h: Handle]; -- really sets the t values, assuming no old ones are known, but that the curve is known

SolveCurve: PUBLIC PROCEDURE [h: Handle]; -- finds the best fit, assuming the t values are known. Only the free coefficients are altered.

PointSlopeBasis: PUBLIC PROCEDURE [h: Handle, b: Cubic.Bezier];

SmoothBasis: PUBLIC PROCEDURE [h: Handle, nKnots: NAT];

BSplineBasis: PUBLIC PROCEDURE [h: Handle, nKnots: NAT];

CubicBasis: PUBLIC PROCEDURE [h: Handle];

CubicPieceBasis: PUBLIC PROCEDURE [h: Handle];

ParabolaBasis: PUBLIC PROCEDURE [h: Handle];

CircleBasis: PUBLIC PROCEDURE [h: Handle];

EllipseBasis: PUBLIC PROCEDURE [h: Handle];

END.