1 #ifndef SEEN_Geom_POINT_H
2 #define SEEN_Geom_POINT_H
4 /**
5 * \file
6 * \brief Defines a Cartesian 2D Point class.
7 */
9 #include <iostream>
11 #include <2geom/coord.h>
12 #include <2geom/isnan.h>
13 #include <2geom/utils.h>
15 namespace Geom {
17 enum Dim2 { X=0, Y=1 };
19 class Matrix;
21 /// Cartesian 2D point.
22 class Point {
23 Coord _pt[2];
25 public:
26 /// The default constructor creates an Point(0,0) DO NOT RELY ON THIS, BEST NOT TO USE THIS CONSTRUCTOR
27 inline Point()
28 { _pt[X] = _pt[Y] = 0; }
30 inline Point(Coord x, Coord y) {
31 _pt[X] = x; _pt[Y] = y;
32 }
34 inline Point(Point const &p) {
35 for (unsigned i = 0; i < 2; ++i)
36 _pt[i] = p._pt[i];
37 }
39 inline Point &operator=(Point const &p) {
40 for (unsigned i = 0; i < 2; ++i)
41 _pt[i] = p._pt[i];
42 return *this;
43 }
45 inline Coord operator[](unsigned i) const { return _pt[i]; }
46 inline Coord &operator[](unsigned i) { return _pt[i]; }
48 Coord operator[](Dim2 d) const throw() { return _pt[d]; }
49 Coord &operator[](Dim2 d) throw() { return _pt[d]; }
51 static inline Point polar(Coord angle, Coord radius) {
52 return Point(radius * std::cos(angle), radius * std::sin(angle));
53 }
55 inline Coord length() const { return hypot(_pt[0], _pt[1]); }
57 /** Return a point like this point but rotated -90 degrees.
58 (If the y axis grows downwards and the x axis grows to the
59 right, then this is 90 degrees counter-clockwise.)
60 **/
61 Point ccw() const {
62 return Point(_pt[Y], -_pt[X]);
63 }
65 /** Return a point like this point but rotated +90 degrees.
66 (If the y axis grows downwards and the x axis grows to the
67 right, then this is 90 degrees clockwise.)
68 **/
69 Point cw() const {
70 return Point(-_pt[Y], _pt[X]);
71 }
73 /**
74 \brief A function to lower the precision of the point
75 \param places The number of decimal places that should be in
76 the final number.
77 */
78 inline void round (int places = 0) {
79 _pt[X] = (Coord)(decimal_round((double)_pt[X], places));
80 _pt[Y] = (Coord)(decimal_round((double)_pt[Y], places));
81 return;
82 }
84 void normalize();
86 inline bool isFinite() const {
87 for ( unsigned i = 0 ; i < 2 ; ++i ) {
88 if(!IS_FINITE(_pt[i])) return false;
89 }
90 return true;
91 }
93 inline Point operator+(Point const &o) const {
94 return Point(_pt[X] + o._pt[X], _pt[Y] + o._pt[Y]);
95 }
96 inline Point operator-(Point const &o) const {
97 return Point(_pt[X] - o._pt[X], _pt[Y] - o._pt[Y]);
98 }
99 inline Point &operator+=(Point const &o) {
100 for ( unsigned i = 0 ; i < 2 ; ++i ) {
101 _pt[i] += o._pt[i];
102 }
103 return *this;
104 }
105 inline Point &operator-=(Point const &o) {
106 for ( unsigned i = 0 ; i < 2 ; ++i ) {
107 _pt[i] -= o._pt[i];
108 }
109 return *this;
110 }
112 inline Point operator-() const {
113 return Point(-_pt[X], -_pt[Y]);
114 }
115 inline Point operator*(double const s) const {
116 return Point(_pt[X] * s, _pt[Y] * s);
117 }
118 inline Point operator/(double const s) const {
119 //TODO: s == 0?
120 return Point(_pt[X] / s, _pt[Y] / s);
121 }
122 inline Point &operator*=(double const s) {
123 for ( unsigned i = 0 ; i < 2 ; ++i ) _pt[i] *= s;
124 return *this;
125 }
126 inline Point &operator/=(double const s) {
127 //TODO: s == 0?
128 for ( unsigned i = 0 ; i < 2 ; ++i ) _pt[i] /= s;
129 return *this;
130 }
132 Point &operator*=(Matrix const &m);
134 inline int operator == (const Point &in_pnt) {
135 return ((_pt[X] == in_pnt[X]) && (_pt[Y] == in_pnt[Y]));
136 }
138 friend inline std::ostream &operator<< (std::ostream &out_file, const Geom::Point &in_pnt);
139 };
141 inline Point operator*(double const s, Point const &p) { return p * s; }
143 /** A function to print out the Point. It just prints out the coords
144 on the given output stream */
145 inline std::ostream &operator<< (std::ostream &out_file, const Geom::Point &in_pnt) {
146 out_file << "X: " << in_pnt[X] << " Y: " << in_pnt[Y];
147 return out_file;
148 }
150 /** This is a rotation (sort of). */
151 inline Point operator^(Point const &a, Point const &b) {
152 Point const ret(a[0] * b[0] - a[1] * b[1],
153 a[1] * b[0] + a[0] * b[1]);
154 return ret;
155 }
157 //IMPL: boost::EqualityComparableConcept
158 inline bool operator==(Point const &a, Point const &b) {
159 return (a[X] == b[X]) && (a[Y] == b[Y]);
160 }
161 inline bool operator!=(Point const &a, Point const &b) {
162 return (a[X] != b[X]) || (a[Y] != b[Y]);
163 }
165 /** This is a lexicographical ordering for points. It is remarkably useful for sweepline algorithms*/
166 inline bool operator<=(Point const &a, Point const &b) {
167 return ( ( a[Y] < b[Y] ) ||
168 (( a[Y] == b[Y] ) && ( a[X] < b[X] )));
169 }
171 Coord L1(Point const &p);
173 /** Compute the L2, or euclidean, norm of \a p. */
174 inline Coord L2(Point const &p) { return p.length(); }
176 /** Compute the square of L2 norm of \a p. Warning: this can overflow where L2 won't.*/
177 inline Coord L2sq(Point const &p) { return p[0]*p[0] + p[1]*p[1]; }
179 double LInfty(Point const &p);
180 bool is_zero(Point const &p);
181 bool is_unit_vector(Point const &p);
183 extern double atan2(Point const p);
184 /** compute the angle turning from a to b (signed). */
185 extern double angle_between(Point const a, Point const b);
187 //IMPL: NearConcept
188 inline bool are_near(Point const &a, Point const &b, double const eps=EPSILON) {
189 return ( are_near(a[X],b[X],eps) && are_near(a[Y],b[Y],eps) );
190 }
192 inline
193 Point middle_point(Point const& P1, Point const& P2)
194 {
195 return (P1 + P2) / 2;
196 }
198 /** Returns p * Geom::rotate_degrees(90), but more efficient.
199 *
200 * Angle direction in Inkscape code: If you use the traditional mathematics convention that y
201 * increases upwards, then positive angles are anticlockwise as per the mathematics convention. If
202 * you take the common non-mathematical convention that y increases downwards, then positive angles
203 * are clockwise, as is common outside of mathematics.
204 *
205 * There is no rot_neg90 function: use -rot90(p) instead.
206 */
207 inline Point rot90(Point const &p) { return Point(-p[Y], p[X]); }
209 /** Given two points and a parameter t \in [0, 1], return a point
210 * proportionally from a to b by t. Akin to 1 degree bezier.*/
211 inline Point lerp(double const t, Point const a, Point const b) { return (a * (1 - t) + b * t); }
213 Point unit_vector(Point const &a);
215 /** compute the dot product (inner product) between the vectors a and b. */
216 inline Coord dot(Point const &a, Point const &b) { return a[0] * b[0] + a[1] * b[1]; }
217 /** Defined as dot(a, b.cw()). */
218 inline Coord cross(Point const &a, Point const &b) { return dot(a, b.cw()); }
220 /** compute the euclidean distance between points a and b. TODO: hypot safer/faster? */
221 inline Coord distance (Point const &a, Point const &b) { return L2(a - b); }
223 /** compute the square of the distance between points a and b. */
224 inline Coord distanceSq (Point const &a, Point const &b) { return L2sq(a - b); }
226 Point abs(Point const &b);
228 Point operator*(Point const &v, Matrix const &m);
230 Point operator/(Point const &p, Matrix const &m);
232 /** Constrains the angle (with respect to dir) of the line
233 * joining A and B to a multiple of pi/n.
234 */
235 Point constrain_angle(Point const &A, Point const &B, unsigned int n = 4, Geom::Point const &dir = Geom::Point(1,0));
237 } /* namespace Geom */
239 #endif /* !SEEN_Geom_POINT_H */
241 /*
242 Local Variables:
243 mode:c++
244 c-file-style:"stroustrup"
245 c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
246 indent-tabs-mode:nil
247 fill-column:99
248 End:
249 */
250 // vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:encoding=utf-8:textwidth=99 :