2 Copyright (C) 2011-2013 Paul Davis
3 Author: Carl Hetherington <cth@carlh.net>
5 This program is free software; you can redistribute it and/or modify
6 it under the terms of the GNU General Public License as published by
7 the Free Software Foundation; either version 2 of the License, or
8 (at your option) any later version.
10 This program is distributed in the hope that it will be useful,
11 but WITHOUT ANY WARRANTY; without even the implied warranty of
12 MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
13 GNU General Public License for more details.
15 You should have received a copy of the GNU General Public License
16 along with this program; if not, write to the Free Software
17 Foundation, Inc., 675 Mass Ave, Cambridge, MA 02139, USA.
23 #include <cairomm/context.h>
25 #include "canvas/utils.h"
28 using namespace ArdourCanvas;
30 ArdourCanvas::Distance
31 ArdourCanvas::distance_to_segment_squared (Duple const & p, Duple const & p1, Duple const & p2, double& t, Duple& at)
33 static const double kMinSegmentLenSquared = 0.00000001; // adjust to suit. If you use float, you'll probably want something like 0.000001f
34 static const double kEpsilon = 1.0E-14; // adjust to suit. If you use floats, you'll probably want something like 1E-7f
35 double dx = p2.x - p1.x;
36 double dy = p2.y - p1.y;
37 double dp1x = p.x - p1.x;
38 double dp1y = p.y - p1.y;
39 const double segLenSquared = (dx * dx) + (dy * dy);
41 if (segLenSquared >= -kMinSegmentLenSquared && segLenSquared <= kMinSegmentLenSquared) {
42 // segment is a point.
45 return ((dp1x * dp1x) + (dp1y * dp1y));
49 // Project a line from p to the segment [p1,p2]. By considering the line
50 // extending the segment, parameterized as p1 + (t * (p2 - p1)),
51 // we find projection of point p onto the line.
52 // It falls where t = [(p - p1) . (p2 - p1)] / |p2 - p1|^2
54 t = ((dp1x * dx) + (dp1y * dy)) / segLenSquared;
57 // intersects at or to the "left" of first segment vertex (p1.x, p1.y). If t is approximately 0.0, then
58 // intersection is at p1. If t is less than that, then there is no intersection (i.e. p is not within
59 // the 'bounds' of the segment)
61 // intersects at 1st segment vertex
64 // set our 'intersection' point to p1.
66 // Note: If you wanted the ACTUAL intersection point of where the projected lines would intersect if
67 // we were doing PointLineDistanceSquared, then qx would be (p1.x + (t * dx)) and qy would be (p1.y + (t * dy)).
69 } else if (t > (1.0 - kEpsilon)) {
70 // intersects at or to the "right" of second segment vertex (p2.x, p2.y). If t is approximately 1.0, then
71 // intersection is at p2. If t is greater than that, then there is no intersection (i.e. p is not within
72 // the 'bounds' of the segment)
73 if (t < (1.0 + kEpsilon)) {
74 // intersects at 2nd segment vertex
77 // set our 'intersection' point to p2.
79 // Note: If you wanted the ACTUAL intersection point of where the projected lines would intersect if
80 // we were doing PointLineDistanceSquared, then qx would be (p1.x + (t * dx)) and qy would be (p1.y + (t * dy)).
82 // The projection of the point to the point on the segment that is perpendicular succeeded and the point
83 // is 'within' the bounds of the segment. Set the intersection point as that projected point.
84 at = Duple (p1.x + (t * dx), p1.y + (t * dy));
87 // return the squared distance from p to the intersection point. Note that we return the squared distance
88 // as an optimization because many times you just need to compare relative distances and the squared values
89 // works fine for that. If you want the ACTUAL distance, just take the square root of this value.
90 double dpqx = p.x - at.x;
91 double dpqy = p.y - at.y;
93 return ((dpqx * dpqx) + (dpqy * dpqy));