double Measurement::NearestPointOnCurve(QPointF P, vector<QPointF> V)
{
QPointF *w; /* Ctl pts for 5th-degree eqn */
double t_candidate[W_DEGREE]; /* Possible roots */
int n_solutions; /* Number of roots found */
double t; /* Parameter value of closest pt*/
QPointF v_arr[4];
for(int i=0; i<4; i++)
v_arr[i]=V[i];
/* Convert problem to 5th-degree Bezier form */
w = ConvertToBezierForm(P, v_arr);
/* Find all possible roots of 5th-degree equation */
n_solutions = FindRoots(w, W_DEGREE, t_candidate, 0);
free((char *)w);
/* Compare distances of P to all candidates, and to t=0, and t=1 */
{
double dist, new_dist;
QPointF p;
QPointF v;
int i;
/* Check distance to beginning of curve, where t = 0 */
dist = V2SquaredLength(V2Sub(&P, &v_arr[0], &v));
t = 0.0;
/* Find distances for candidate points */
for (i = 0; i < n_solutions; i++) {
p = Bezier(v_arr, DEGREE, t_candidate[i],
(QPointF *)NULL, (QPointF *)NULL);
new_dist = V2SquaredLength(V2Sub(&P, &p, &v));
if (new_dist < dist) {
dist = new_dist;
t = t_candidate[i];
}
}
/* Finally, look at distance to end point, where t = 1.0 */
new_dist = V2SquaredLength(V2Sub(&P, &V[DEGREE], &v));
if (new_dist < dist) {
dist = new_dist;
t = 1.0;
}
}
/* Return the point on the curve at parameter value t */
// printf("t : %4.12f\n", t);
QPointF b=Bezier(v_arr, DEGREE, t, (QPointF *)NULL, (QPointF *)NULL);
return V2DistanceBetween2Points(&P,&b);
}
/*
* 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);
}
/*
* 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);
}
/* returns length of input vector */
double V2Length(Vector2 *a) {
return(sqrt(V2SquaredLength(a)));
}
