1 #include <2geom/point.h>
2 #include <assert.h>
3 #include <2geom/coord.h>
4 #include <2geom/isnan.h> //temporary fix for isnan()
5 #include <2geom/transforms.h>
7 namespace Geom {
9 /** \brief Scales this vector to make it a unit vector (within rounding error).
10 *
11 * The current version tries to handle infinite coordinates gracefully,
12 * but it's not clear that any callers need that.
13 *
14 * \pre \f$this \neq (0, 0)\f$
15 * \pre Neither component is NaN.
16 * \post \f$-\epsilon<\left|this\right|-1<\epsilon\f$
17 */
18 void Point::normalize() {
19 double len = hypot(_pt[0], _pt[1]);
20 if(len == 0) return;
21 if(IS_NAN(len)) return;
22 static double const inf = 1e400;
23 if(len != inf) {
24 *this /= len;
25 } else {
26 unsigned n_inf_coords = 0;
27 /* Delay updating pt in case neither coord is infinite. */
28 Point tmp;
29 for ( unsigned i = 0 ; i < 2 ; ++i ) {
30 if ( _pt[i] == inf ) {
31 ++n_inf_coords;
32 tmp[i] = 1.0;
33 } else if ( _pt[i] == -inf ) {
34 ++n_inf_coords;
35 tmp[i] = -1.0;
36 } else {
37 tmp[i] = 0.0;
38 }
39 }
40 switch (n_inf_coords) {
41 case 0: {
42 /* Can happen if both coords are near +/-DBL_MAX. */
43 *this /= 4.0;
44 len = hypot(_pt[0], _pt[1]);
45 assert(len != inf);
46 *this /= len;
47 break;
48 }
49 case 1: {
50 *this = tmp;
51 break;
52 }
53 case 2: {
54 *this = tmp * sqrt(0.5);
55 break;
56 }
57 }
58 }
59 }
61 /** Compute the L1 norm, or manhattan distance, of \a p. */
62 Coord L1(Point const &p) {
63 Coord d = 0;
64 for ( int i = 0 ; i < 2 ; i++ ) {
65 d += fabs(p[i]);
66 }
67 return d;
68 }
70 /** Compute the L infinity, or maximum, norm of \a p. */
71 Coord LInfty(Point const &p) {
72 Coord const a(fabs(p[0]));
73 Coord const b(fabs(p[1]));
74 return ( a < b || IS_NAN(b)
75 ? b
76 : a );
77 }
79 /** Returns true iff p is a zero vector, i.e.\ Point(0, 0).
80 *
81 * (NaN is considered non-zero.)
82 */
83 bool
84 is_zero(Point const &p)
85 {
86 return ( p[0] == 0 &&
87 p[1] == 0 );
88 }
90 bool
91 is_unit_vector(Point const &p)
92 {
93 return fabs(1.0 - L2(p)) <= 1e-4;
94 /* The tolerance of 1e-4 is somewhat arbitrary. Point::normalize is believed to return
95 points well within this tolerance. I'm not aware of any callers that want a small
96 tolerance; most callers would be ok with a tolerance of 0.25. */
97 }
99 Coord atan2(Point const p) {
100 return std::atan2(p[Y], p[X]);
101 }
103 /** compute the angle turning from a to b. This should give \f$\pi/2\f$ for angle_between(a, rot90(a));
104 * This works by projecting b onto the basis defined by a, rot90(a)
105 */
106 Coord angle_between(Point const a, Point const b) {
107 return std::atan2(cross(b,a), dot(b,a));
108 }
112 /** Returns a version of \a a scaled to be a unit vector (within rounding error).
113 *
114 * The current version tries to handle infinite coordinates gracefully,
115 * but it's not clear that any callers need that.
116 *
117 * \pre a != Point(0, 0).
118 * \pre Neither coordinate is NaN.
119 * \post L2(ret) very near 1.0.
120 */
121 Point unit_vector(Point const &a)
122 {
123 Point ret(a);
124 ret.normalize();
125 return ret;
126 }
128 Point abs(Point const &b)
129 {
130 Point ret;
131 for ( int i = 0 ; i < 2 ; i++ ) {
132 ret[i] = fabs(b[i]);
133 }
134 return ret;
135 }
137 Point operator*(Point const &v, Matrix const &m) {
138 Point ret;
139 for(int i = 0; i < 2; i++) {
140 ret[i] = v[X] * m[i] + v[Y] * m[i + 2] + m[i + 4];
141 }
142 return ret;
143 }
145 Point operator/(Point const &p, Matrix const &m) { return p * m.inverse(); }
147 Point &Point::operator*=(Matrix const &m)
148 {
149 *this = *this * m;
150 return *this;
151 }
153 Point constrain_angle(Point const &ref, Point const &pt, unsigned int n, Point const &dir)
154 {
155 // for special cases we could perhaps use faster routines
156 if (n == 0.0) {
157 return pt;
158 }
159 Point diff(pt - ref);
160 double angle = -angle_between(diff, dir);
161 double k = round(angle * (double)n / (2.0*M_PI));
162 return ref + dir * Rotate(k * 2.0 * M_PI / (double)n) * L2(diff);
163 }
165 } //Namespace Geom
167 /*
168 Local Variables:
169 mode:c++
170 c-file-style:"stroustrup"
171 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
172 indent-tabs-mode:nil
173 fill-column:99
174 End:
175 */
176 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :