1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
|
#include <libnr/nr-point-fns.h>
#include <2geom/isnan.h>
using NR::Point;
/** Compute the L infinity, or maximum, norm of \a p. */
NR::Coord NR::LInfty(Point const &p) {
NR::Coord const a(fabs(p[0]));
NR::Coord const b(fabs(p[1]));
return ( a < b || IS_NAN(b)
? b
: a );
}
/** Returns true iff p is a zero vector, i.e.\ Point(0, 0).
*
* (NaN is considered non-zero.)
*/
bool
NR::is_zero(Point const &p)
{
return ( p[0] == 0 &&
p[1] == 0 );
}
bool
NR::is_unit_vector(Point const &p)
{
return fabs(1.0 - L2(p)) <= 1e-4;
/* The tolerance of 1e-4 is somewhat arbitrary. NR::Point::normalize is believed to return
points well within this tolerance. I'm not aware of any callers that want a small
tolerance; most callers would be ok with a tolerance of 0.25. */
}
NR::Coord NR::atan2(Point const p) {
return std::atan2(p[NR::Y], p[NR::X]);
}
/** Returns a version of \a a scaled to be a unit vector (within rounding error).
*
* The current version tries to handle infinite coordinates gracefully,
* but it's not clear that any callers need that.
*
* \pre a != Point(0, 0).
* \pre Neither coordinate is NaN.
* \post L2(ret) very near 1.0.
*/
Point NR::unit_vector(Point const &a)
{
Point ret(a);
ret.normalize();
return ret;
}
NR::Point abs(NR::Point const &b)
{
NR::Point ret;
for ( int i = 0 ; i < 2 ; i++ ) {
ret[i] = fabs(b[i]);
}
return ret;
}
NR::Point
snap_vector_midpoint (NR::Point p, NR::Point begin, NR::Point end, double snap)
{
double length = NR::L2(end - begin);
NR::Point be = (end - begin) / length;
double r = NR::dot(p - begin, be);
if (r < 0.0) return begin;
if (r > length) return end;
double snapdist = length * snap;
double r_snapped = (snap==0) ? r : floor(r/(snapdist + 0.5)) * snapdist;
return (begin + r_snapped * be);
}
double
get_offset_between_points (NR::Point p, NR::Point begin, NR::Point end)
{
double length = NR::L2(end - begin);
NR::Point be = (end - begin) / length;
double r = NR::dot(p - begin, be);
if (r < 0.0) return 0.0;
if (r > length) return 1.0;
return (r / length);
}
NR::Point
project_on_linesegment(NR::Point const p, NR::Point const p1, NR::Point const p2)
{
// p_proj = projection of p on the linesegment running from p1 to p2
// p_proj = p1 + u (p2 - p1)
// calculate u according to "Minimum Distance between a Point and a Line"
// see http://local.wasp.uwa.edu.au/~pbourke/geometry/pointline/
// Warning: projected points will not necessarily be in between the endpoints of the linesegments!
if (p1 == p2) { // to avoid div. by zero below
return p;
}
NR::Point const d1(p-p1); // delta 1
NR::Point const d2(p2-p1); // delta 2
double const u = (d1[NR::X] * d2[NR::X] + d1[NR::Y] * d2[NR::Y]) / (NR::L2(d2) * NR::L2(d2));
return (p1 + u*(p2-p1));
}
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :
|
