/*
* NearestPointOnCurve :
* Compute the parameter value of the point on a Bezier
* curve segment closest to some arbtitrary, user-input point.
* Return the point on the curve at that parameter value.
*
Geom::Point P; The user-supplied point
Geom::Point *V; Control points of cubic Bezier
*/
double NearestPointOnCurve(Geom::Point P, Geom::Point *V)
{
double t_candidate[W_DEGREE]; /* Possible roots */
/* Convert problem to 5th-degree Bezier form */
Geom::Point *w = ConvertToBezierForm(P, V);
/* Find all possible roots of 5th-degree equation */
int n_solutions = FindRoots(w, W_DEGREE, t_candidate, 0);
std::free((char *)w);
/* Check distance to end of the curve, where t = 1 */
double dist = SquaredLength(P - V[DEGREE]);
double t = 1.0;
/* Find distances for candidate points */
for (int i = 0; i < n_solutions; i++) {
Geom::Point p = Bez(V, DEGREE, t_candidate[i], NULL, NULL);
double new_dist = SquaredLength(P - p);
if (new_dist < dist) {
dist = new_dist;
t = t_candidate[i];
}
}
/* Return the parameter value t */
return t;
}
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);
}
// 计算一点到三次贝塞尔曲线段上的最近点
// Parameters :
// pt: The user-supplied point
// pts: Control points of cubic Bezier
// nearpt: output the point on the curve at that parameter value
//
GEOMAPI void mgNearestOnBezier(
const Point2d& pt, const Point2d* pts, Point2d& nearpt)
{
Point2d w[W_DEGREE+1]; // Ctl pts for 5th-degree eqn
float t_candidate[W_DEGREE]; // Possible roots
int n_solutions; // Number of roots found
float t; // Parameter value of closest pt
// Convert problem to 5th-degree Bezier form
ConvertToBezierForm(pt, pts, w);
// Find all possible roots of 5th-degree equation
n_solutions = FindRoots(w, W_DEGREE, t_candidate, 0);
// Compare distances of pt to all candidates, and to t=0, and t=1
{
float dist, new_dist;
Point2d p;
int i;
// Check distance to beginning of curve, where t = 0
dist = (pt - pts[0]).lengthSqrd();
t = 0.0;
// Find distances for candidate points
for (i = 0; i < n_solutions; i++) {
p = BezierPoint(pts, DEGREE, t_candidate[i],
(Point2d *)NULL, (Point2d *)NULL);
new_dist = (pt - p).lengthSqrd();
if (new_dist < dist) {
dist = new_dist;
t = t_candidate[i];
}
}
// Finally, look at distance to end point, where t = 1.0
new_dist = (pt - pts[DEGREE]).lengthSqrd();
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);
nearpt = (BezierPoint(pts, DEGREE, t, (Point2d *)NULL, (Point2d *)NULL));
}