/*
* FitCubic :
* Fit a Bezier curve to a (sub)set of digitized points
*/
static void FitCubic(Point2 *d, int first, int last, Vector2 tHat1, Vector2 tHat2,
double error, BezierContour &bezContour)
{
BezierCurve bezCurve; /*Control points of fitted Bezier curve*/
double *u; /* Parameter values for point */
double *uPrime; /* Improved parameter values */
double maxError; /* Maximum fitting error */
int splitPoint; /* Point to split point set at */
int nPts; /* Number of points in subset */
double iterationError; /*Error below which you try iterating */
int maxIterations = 4; /* Max times to try iterating */
Vector2 tHatCenter; /* Unit tangent vector at splitPoint */
int i;
iterationError = error * error;
nPts = last - first + 1;
/* Use heuristic if region only has two points in it */
if (nPts == 2) {
double dist = V2DistanceBetween2Points(&d[last], &d[first]) / 3.0;
bezCurve = (Point2 *)malloc(4 * sizeof(Point2));
bezCurve[0] = d[first];
bezCurve[3] = d[last];
V2Add(&bezCurve[0], V2Scale(&tHat1, dist), &bezCurve[1]);
V2Add(&bezCurve[3], V2Scale(&tHat2, dist), &bezCurve[2]);
DrawBezierCurve(3, bezCurve, bezContour);
free((void *)bezCurve);
return;
}
/* Parameterize points, and attempt to fit curve */
u = ChordLengthParameterize(d, first, last);
bezCurve = GenerateBezier(d, first, last, u, tHat1, tHat2);
/* Find max deviation of points to fitted curve */
maxError = ComputeMaxError(d, first, last, bezCurve, u, &splitPoint);
if (maxError < error) {
DrawBezierCurve(3, bezCurve, bezContour);
free((void *)u);
free((void *)bezCurve);
return;
}
/* If error not too large, try some reparameterization */
/* and iteration */
if (maxError < iterationError) {
for (i = 0; i < maxIterations; i++) {
uPrime = Reparameterize(d, first, last, u, bezCurve);
free((void *)bezCurve);
bezCurve = GenerateBezier(d, first, last, uPrime, tHat1, tHat2);
maxError = ComputeMaxError(d, first, last,
bezCurve, uPrime, &splitPoint);
if (maxError < error) {
DrawBezierCurve(3, bezCurve, bezContour);
free((void *)u);
free((void *)bezCurve);
free((void *)uPrime);
return;
}
free((void *)u);
u = uPrime;
}
}
/* Fitting failed -- split at max error point and fit recursively */
free((void *)u);
free((void *)bezCurve);
tHatCenter = ComputeCenterTangent(d, splitPoint);
FitCubic(d, first, splitPoint, tHat1, tHatCenter, error, bezContour);
V2Negate(&tHatCenter);
FitCubic(d, splitPoint, last, tHatCenter, tHat2, error, bezContour);
}
QPointF *FitCubic(const QList<QPointF> &points, int first, int last, FitVector tHat1, FitVector tHat2, float error, int &width)
{
qreal *u;
qreal *uPrime;
qreal maxError;
int splitPoint;
int nPts;
qreal iterationError;
int maxIterations = 4;
FitVector tHatCenter;
QPointF *curve;
int i;
width = 0;
iterationError = error * error;
nPts = last - first + 1;
if (nPts == 2) {
qreal dist = distance(points.at(last), points.at(first)) / 3.0;
curve = new QPointF[4];
curve[0] = points.at(first);
curve[3] = points.at(last);
tHat1.scale(dist);
tHat2.scale(dist);
curve[1] = tHat1 + curve[0];
curve[2] = tHat2 + curve[3];
width = 4;
return curve;
}
/* Parameterize points, and attempt to fit curve */
u = ChordLengthParameterize(points, first, last);
curve = GenerateBezier(points, first, last, u, tHat1, tHat2);
/* Find max deviation of points to fitted curve */
maxError = ComputeMaxError(points, first, last, curve, u, &splitPoint);
if (maxError < error) {
delete[] u;
width = 4;
return curve;
}
/* If error not too large, try some reparameterization */
/* and iteration */
if (maxError < iterationError) {
for (i = 0; i < maxIterations; ++i) {
uPrime = Reparameterize(points, first, last, u, curve);
delete[] curve;
curve = GenerateBezier(points, first, last, uPrime, tHat1, tHat2);
maxError = ComputeMaxError(points, first, last,
curve, uPrime, &splitPoint);
if (maxError < error) {
delete[] u;
delete[] uPrime;
width = 4;
return curve;
}
delete[] u;
u = uPrime;
}
}
/* Fitting failed -- split at max error point and fit recursively */
delete[] u;
delete[] curve;
tHatCenter = ComputeCenterTangent(points, splitPoint);
int w1, w2;
QPointF *cu1 = NULL, *cu2 = NULL;
cu1 = FitCubic(points, first, splitPoint, tHat1, tHatCenter, error, w1);
tHatCenter.negate();
cu2 = FitCubic(points, splitPoint, last, tHatCenter, tHat2, error, w2);
QPointF *newcurve = new QPointF[w1+w2];
for (int i = 0; i < w1; ++i) {
newcurve[i] = cu1[i];
}
for (int i = 0; i < w2; ++i) {
newcurve[i+w1] = cu2[i];
}
delete[] cu1;
delete[] cu2;
width = w1 + w2;
return newcurve;
}