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add a utility function to Canvas to compute distance from a point to a line segment

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Paul Davis 2013-12-09 13:35:07 -05:00
parent 59da788793
commit 75b25cd913
2 changed files with 68 additions and 0 deletions
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2
libs/canvas/canvas/utils.h
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@ -28,5 +28,7 @@ namespace ArdourCanvas {
extern Color rgba_to_color (double r, double g, double b, double a);
extern void set_source_rgba (Cairo::RefPtr<Cairo::Context>, Color);
Distance distance_to_segment_squared (Duple const & p, Duple const & p1, Duple const & p2, double& t, Duple& at);
}

66
libs/canvas/utils.cc
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@ -154,3 +154,69 @@ ArdourCanvas::set_source_rgba (Cairo::RefPtr<Cairo::Context> context, Color colo
);
}
ArdourCanvas::Distance
ArdourCanvas::distance_to_segment_squared (Duple const & p, Duple const & p1, Duple const & p2, double& t, Duple& at)
{
static const double kMinSegmentLenSquared = 0.00000001; // adjust to suit. If you use float, you'll probably want something like 0.000001f
static const double kEpsilon = 1.0E-14; // adjust to suit. If you use floats, you'll probably want something like 1E-7f
double dx = p2.x - p1.x;
double dy = p2.y - p1.y;
double dp1x = p.x - p1.x;
double dp1y = p.y - p1.y;
const double segLenSquared = (dx * dx) + (dy * dy);
if (segLenSquared >= -kMinSegmentLenSquared && segLenSquared <= kMinSegmentLenSquared) {
// segment is a point.
at = p1;
t = 0.0;
return ((dp1x * dp1x) + (dp1y * dp1y));
}
// Project a line from p to the segment [p1,p2]. By considering the line
// extending the segment, parameterized as p1 + (t * (p2 - p1)),
// we find projection of point p onto the line.
// It falls where t = [(p - p1) . (p2 - p1)] / |p2 - p1|^2
t = ((dp1x * dx) + (dp1y * dy)) / segLenSquared;
if (t < kEpsilon) {
// intersects at or to the "left" of first segment vertex (p1.x, p1.y). If t is approximately 0.0, then
// intersection is at p1. If t is less than that, then there is no intersection (i.e. p is not within
// the 'bounds' of the segment)
if (t > -kEpsilon) {
// intersects at 1st segment vertex
t = 0.0;
}
// set our 'intersection' point to p1.
at = p1;
// Note: If you wanted the ACTUAL intersection point of where the projected lines would intersect if
// we were doing PointLineDistanceSquared, then qx would be (p1.x + (t * dx)) and qy would be (p1.y + (t * dy)).
} else if (t > (1.0 - kEpsilon)) {
// intersects at or to the "right" of second segment vertex (p2.x, p2.y). If t is approximately 1.0, then
// intersection is at p2. If t is greater than that, then there is no intersection (i.e. p is not within
// the 'bounds' of the segment)
if (t < (1.0 + kEpsilon)) {
// intersects at 2nd segment vertex
t = 1.0;
}
// set our 'intersection' point to p2.
at = p2;
// Note: If you wanted the ACTUAL intersection point of where the projected lines would intersect if
// we were doing PointLineDistanceSquared, then qx would be (p1.x + (t * dx)) and qy would be (p1.y + (t * dy)).
} else {
// The projection of the point to the point on the segment that is perpendicular succeeded and the point
// is 'within' the bounds of the segment. Set the intersection point as that projected point.
at = Duple (p1.x + (t * dx), p1.y + (t * dy));
}
// return the squared distance from p to the intersection point. Note that we return the squared distance
// as an optimization because many times you just need to compare relative distances and the squared values
// works fine for that. If you want the ACTUAL distance, just take the square root of this value.
double dpqx = p.x - at.x;
double dpqy = p.y - at.y;
return ((dpqx * dpqx) + (dpqy * dpqy));
}