/*
* ComputeMaxError :
* Find the maximum squared distance of digitized points
* to fitted curve.
*/
static double ComputeMaxError(
Point2 *d, /* Array of digitized points */
int first, int last, /* Indices defining region */
BezierCurve bezCurve, /* Fitted Bezier curve */
double *u, /* Parameterization of points */
int *splitPoint) /* Point of maximum error */
{
int i;
double maxDist; /* Maximum error */
double dist; /* Current error */
Point2 P; /* Point on curve */
Vector2 v; /* Vector from point to curve */
*splitPoint = (last - first + 1)/2;
maxDist = 0.0;
for (i = first + 1; i < last; i++) {
P = BezierII(3, bezCurve, u[i-first]);
v = V2SubII(P, d[i]);
dist = V2SquaredLength(&v);
if (dist >= maxDist) {
maxDist = dist;
*splitPoint = i;
}
}
return (maxDist);
}
/*
* NewtonRaphsonRootFind :
* Use Newton-Raphson iteration to find better root.
*/
static qreal NewtonRaphsonRootFind(QPointF *Q, QPointF P, qreal u)
{
qreal numerator, denominator;
QPointF Q1[3], Q2[2]; /* Q' and Q'' */
QPointF Q_u, Q1_u, Q2_u; /*u evaluated at Q, Q', & Q'' */
qreal uPrime; /* Improved u */
int i;
/* Compute Q(u) */
Q_u = BezierII(3, Q, u);
/* Generate control vertices for Q' */
for (i = 0; i <= 2; ++i) {
Q1[i].setX((Q[i+1].x() - Q[i].x()) * 3.0);
Q1[i].setY((Q[i+1].y() - Q[i].y()) * 3.0);
}
/* Generate control vertices for Q'' */
for (i = 0; i <= 1; ++i) {
Q2[i].setX((Q1[i+1].x() - Q1[i].x()) * 2.0);
Q2[i].setY((Q1[i+1].y() - Q1[i].y()) * 2.0);
}
/* Compute Q'(u) and Q''(u) */
Q1_u = BezierII(2, Q1, u);
Q2_u = BezierII(1, Q2, u);
/* Compute f(u)/f'(u) */
numerator = (Q_u.x() - P.x()) * (Q1_u.x()) + (Q_u.y() - P.y()) * (Q1_u.y());
denominator = (Q1_u.x()) * (Q1_u.x()) + (Q1_u.y()) * (Q1_u.y()) +
(Q_u.x() - P.x()) * (Q2_u.x()) + (Q_u.y() - P.y()) * (Q2_u.y());
if (qFuzzyCompare(denominator, qreal(0.0))) {
denominator = Zero;
}
/* u = u - f(u)/f'(u) */
uPrime = u - (numerator / denominator);
return (uPrime);
}
/*
* NewtonRaphsonRootFind :
* Use Newton-Raphson iteration to find better root.
*/
static double NewtonRaphsonRootFind(
BezierCurve Q, /* Current fitted curve */
Point2 P, /* Digitized point */
double u) /* Parameter value for "P" */
{
double numerator, denominator;
Point2 Q1[3], Q2[2]; /* Q' and Q'' */
Point2 Q_u, Q1_u, Q2_u; /*u evaluated at Q, Q', & Q'' */
double uPrime; /* Improved u */
int i;
/* Compute Q(u) */
Q_u = BezierII(3, Q, u);
/* Generate control vertices for Q' */
for (i = 0; i <= 2; i++) {
Q1[i].x = (Q[i+1].x - Q[i].x) * 3.0;
Q1[i].y = (Q[i+1].y - Q[i].y) * 3.0;
}
/* Generate control vertices for Q'' */
for (i = 0; i <= 1; i++) {
Q2[i].x = (Q1[i+1].x - Q1[i].x) * 2.0;
Q2[i].y = (Q1[i+1].y - Q1[i].y) * 2.0;
}
/* Compute Q'(u) and Q''(u) */
Q1_u = BezierII(2, Q1, u);
Q2_u = BezierII(1, Q2, u);
/* Compute f(u)/f'(u) */
numerator = (Q_u.x - P.x) * (Q1_u.x) + (Q_u.y - P.y) * (Q1_u.y);
denominator = (Q1_u.x) * (Q1_u.x) + (Q1_u.y) * (Q1_u.y) +
(Q_u.x - P.x) * (Q2_u.x) + (Q_u.y - P.y) * (Q2_u.y);
/* u = u - f(u)/f'(u) */
uPrime = u - (numerator/denominator);
return (uPrime);
}
/*
* ComputeMaxError :
* Find the maximum squared distance of digitized points
* to fitted curve.
*/
static qreal ComputeMaxError(const QList<QPointF> &points, int first, int last, QPointF *curve, qreal *u, int *splitPoint)
{
int i;
qreal maxDist; /* Maximum error */
qreal dist; /* Current error */
QPointF P; /* Point on curve */
FitVector v; /* Vector from point to curve */
*splitPoint = (last - first + 1) / 2;
maxDist = 0.0;
for (i = first + 1; i < last; ++i) {
P = BezierII(3, curve, u[i-first]);
v = VectorSub(P, points.at(i));
dist = v.length();
if (dist >= maxDist) {
maxDist = dist;
*splitPoint = i;
}
}
return (maxDist);
}
/*
* ComputeMaxError :
* Find the maximum squared distance of digitized points
* to fitted curve.
*/
static double ComputeMaxError(Point2 *d, int first, int last, BezierCurve bezCurve,
double *u, int *splitPoint)
{
int i;
double maxDist; /* Maximum error */
double dist; /* Current error */
Point2 P; /* Point on curve */
Vector2 v; /* Vector from point to curve */
*splitPoint = (last - first + 1)/2;
maxDist = 0.0;
for (i = first + 1; i < last; i++) {
P = BezierII(3, bezCurve, u[i-first]);
v = V2SubII(P, d[i]);
dist = V2SquaredLength(&v);
if (dist >= maxDist) {
maxDist = dist;
*splitPoint = i;
}
}
return (maxDist);
}