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1// Copyright (C) 2002-2012 Nikolaus Gebhardt
2// This file is part of the "Irrlicht Engine".
3// For conditions of distribution and use, see copyright notice in irrlicht.h
4
5#ifndef __IRR_LINE_2D_H_INCLUDED__
6#define __IRR_LINE_2D_H_INCLUDED__
7
8#include "irrTypes.h"
9#include "vector2d.h"
10
11namespace irr
12{
13namespace core
14{
15
16//! 2D line between two points with intersection methods.
17template <class T>
18class line2d
19{
20 public:
21 //! Default constructor for line going from (0,0) to (1,1).
22 line2d() : start(0,0), end(1,1) {}
23 //! Constructor for line between the two points.
24 line2d(T xa, T ya, T xb, T yb) : start(xa, ya), end(xb, yb) {}
25 //! Constructor for line between the two points given as vectors.
26 line2d(const vector2d<T>& start, const vector2d<T>& end) : start(start), end(end) {}
27 //! Copy constructor.
28 line2d(const line2d<T>& other) : start(other.start), end(other.end) {}
29
30 // operators
31
32 line2d<T> operator+(const vector2d<T>& point) const { return line2d<T>(start + point, end + point); }
33 line2d<T>& operator+=(const vector2d<T>& point) { start += point; end += point; return *this; }
34
35 line2d<T> operator-(const vector2d<T>& point) const { return line2d<T>(start - point, end - point); }
36 line2d<T>& operator-=(const vector2d<T>& point) { start -= point; end -= point; return *this; }
37
38 bool operator==(const line2d<T>& other) const
39 { return (start==other.start && end==other.end) || (end==other.start && start==other.end);}
40 bool operator!=(const line2d<T>& other) const
41 { return !(start==other.start && end==other.end) || (end==other.start && start==other.end);}
42
43 // functions
44 //! Set this line to new line going through the two points.
45 void setLine(const T& xa, const T& ya, const T& xb, const T& yb){start.set(xa, ya); end.set(xb, yb);}
46 //! Set this line to new line going through the two points.
47 void setLine(const vector2d<T>& nstart, const vector2d<T>& nend){start.set(nstart); end.set(nend);}
48 //! Set this line to new line given as parameter.
49 void setLine(const line2d<T>& line){start.set(line.start); end.set(line.end);}
50
51 //! Get length of line
52 /** \return Length of the line. */
53 T getLength() const { return start.getDistanceFrom(end); }
54
55 //! Get squared length of the line
56 /** \return Squared length of line. */
57 T getLengthSQ() const { return start.getDistanceFromSQ(end); }
58
59 //! Get middle of the line
60 /** \return center of the line. */
61 vector2d<T> getMiddle() const
62 {
63 return (start + end)/(T)2;
64 }
65
66 //! Get the vector of the line.
67 /** \return The vector of the line. */
68 vector2d<T> getVector() const { return vector2d<T>(end.X - start.X, end.Y - start.Y); }
69
70 //! Tests if this line intersects with another line.
71 /** \param l: Other line to test intersection with.
72 \param checkOnlySegments: Default is to check intersection between the begin and endpoints.
73 When set to false the function will check for the first intersection point when extending the lines.
74 \param out: If there is an intersection, the location of the
75 intersection will be stored in this vector.
76 \return True if there is an intersection, false if not. */
77 bool intersectWith(const line2d<T>& l, vector2d<T>& out, bool checkOnlySegments=true) const
78 {
79 // Uses the method given at:
80 // http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/
81 const f32 commonDenominator = (f32)(l.end.Y - l.start.Y)*(end.X - start.X) -
82 (l.end.X - l.start.X)*(end.Y - start.Y);
83
84 const f32 numeratorA = (f32)(l.end.X - l.start.X)*(start.Y - l.start.Y) -
85 (l.end.Y - l.start.Y)*(start.X -l.start.X);
86
87 const f32 numeratorB = (f32)(end.X - start.X)*(start.Y - l.start.Y) -
88 (end.Y - start.Y)*(start.X -l.start.X);
89
90 if(equals(commonDenominator, 0.f))
91 {
92 // The lines are either coincident or parallel
93 // if both numerators are 0, the lines are coincident
94 if(equals(numeratorA, 0.f) && equals(numeratorB, 0.f))
95 {
96 // Try and find a common endpoint
97 if(l.start == start || l.end == start)
98 out = start;
99 else if(l.end == end || l.start == end)
100 out = end;
101 // now check if the two segments are disjunct
102 else if (l.start.X>start.X && l.end.X>start.X && l.start.X>end.X && l.end.X>end.X)
103 return false;
104 else if (l.start.Y>start.Y && l.end.Y>start.Y && l.start.Y>end.Y && l.end.Y>end.Y)
105 return false;
106 else if (l.start.X<start.X && l.end.X<start.X && l.start.X<end.X && l.end.X<end.X)
107 return false;
108 else if (l.start.Y<start.Y && l.end.Y<start.Y && l.start.Y<end.Y && l.end.Y<end.Y)
109 return false;
110 // else the lines are overlapping to some extent
111 else
112 {
113 // find the points which are not contributing to the
114 // common part
115 vector2d<T> maxp;
116 vector2d<T> minp;
117 if ((start.X>l.start.X && start.X>l.end.X && start.X>end.X) || (start.Y>l.start.Y && start.Y>l.end.Y && start.Y>end.Y))
118 maxp=start;
119 else if ((end.X>l.start.X && end.X>l.end.X && end.X>start.X) || (end.Y>l.start.Y && end.Y>l.end.Y && end.Y>start.Y))
120 maxp=end;
121 else if ((l.start.X>start.X && l.start.X>l.end.X && l.start.X>end.X) || (l.start.Y>start.Y && l.start.Y>l.end.Y && l.start.Y>end.Y))
122 maxp=l.start;
123 else
124 maxp=l.end;
125 if (maxp != start && ((start.X<l.start.X && start.X<l.end.X && start.X<end.X) || (start.Y<l.start.Y && start.Y<l.end.Y && start.Y<end.Y)))
126 minp=start;
127 else if (maxp != end && ((end.X<l.start.X && end.X<l.end.X && end.X<start.X) || (end.Y<l.start.Y && end.Y<l.end.Y && end.Y<start.Y)))
128 minp=end;
129 else if (maxp != l.start && ((l.start.X<start.X && l.start.X<l.end.X && l.start.X<end.X) || (l.start.Y<start.Y && l.start.Y<l.end.Y && l.start.Y<end.Y)))
130 minp=l.start;
131 else
132 minp=l.end;
133
134 // one line is contained in the other. Pick the center
135 // of the remaining points, which overlap for sure
136 out = core::vector2d<T>();
137 if (start != maxp && start != minp)
138 out += start;
139 if (end != maxp && end != minp)
140 out += end;
141 if (l.start != maxp && l.start != minp)
142 out += l.start;
143 if (l.end != maxp && l.end != minp)
144 out += l.end;
145 out.X = (T)(out.X/2);
146 out.Y = (T)(out.Y/2);
147 }
148
149 return true; // coincident
150 }
151
152 return false; // parallel
153 }
154
155 // Get the point of intersection on this line, checking that
156 // it is within the line segment.
157 const f32 uA = numeratorA / commonDenominator;
158 if(checkOnlySegments && (uA < 0.f || uA > 1.f) )
159 return false; // Outside the line segment
160
161 const f32 uB = numeratorB / commonDenominator;
162 if(checkOnlySegments && (uB < 0.f || uB > 1.f))
163 return false; // Outside the line segment
164
165 // Calculate the intersection point.
166 out.X = (T)(start.X + uA * (end.X - start.X));
167 out.Y = (T)(start.Y + uA * (end.Y - start.Y));
168 return true;
169 }
170
171 //! Get unit vector of the line.
172 /** \return Unit vector of this line. */
173 vector2d<T> getUnitVector() const
174 {
175 T len = (T)(1.0 / getLength());
176 return vector2d<T>((end.X - start.X) * len, (end.Y - start.Y) * len);
177 }
178
179 //! Get angle between this line and given line.
180 /** \param l Other line for test.
181 \return Angle in degrees. */
182 f64 getAngleWith(const line2d<T>& l) const
183 {
184 vector2d<T> vect = getVector();
185 vector2d<T> vect2 = l.getVector();
186 return vect.getAngleWith(vect2);
187 }
188
189 //! Tells us if the given point lies to the left, right, or on the line.
190 /** \return 0 if the point is on the line
191 <0 if to the left, or >0 if to the right. */
192 T getPointOrientation(const vector2d<T>& point) const
193 {
194 return ( (end.X - start.X) * (point.Y - start.Y) -
195 (point.X - start.X) * (end.Y - start.Y) );
196 }
197
198 //! Check if the given point is a member of the line
199 /** \return True if point is between start and end, else false. */
200 bool isPointOnLine(const vector2d<T>& point) const
201 {
202 T d = getPointOrientation(point);
203 return (d == 0 && point.isBetweenPoints(start, end));
204 }
205
206 //! Check if the given point is between start and end of the line.
207 /** Assumes that the point is already somewhere on the line. */
208 bool isPointBetweenStartAndEnd(const vector2d<T>& point) const
209 {
210 return point.isBetweenPoints(start, end);
211 }
212
213 //! Get the closest point on this line to a point
214 /** \param checkOnlySegments: Default (true) is to return a point on the line-segment (between begin and end) of the line.
215 When set to false the function will check for the first the closest point on the the line even when outside the segment. */
216 vector2d<T> getClosestPoint(const vector2d<T>& point, bool checkOnlySegments=true) const
217 {
218 vector2d<f64> c((f64)(point.X-start.X), (f64)(point.Y- start.Y));
219 vector2d<f64> v((f64)(end.X-start.X), (f64)(end.Y-start.Y));
220 f64 d = v.getLength();
221 if ( d == 0 ) // can't tell much when the line is just a single point
222 return start;
223 v /= d;
224 f64 t = v.dotProduct(c);
225
226 if ( checkOnlySegments )
227 {
228 if (t < 0) return vector2d<T>((T)start.X, (T)start.Y);
229 if (t > d) return vector2d<T>((T)end.X, (T)end.Y);
230 }
231
232 v *= t;
233 return vector2d<T>((T)(start.X + v.X), (T)(start.Y + v.Y));
234 }
235
236 //! Start point of the line.
237 vector2d<T> start;
238 //! End point of the line.
239 vector2d<T> end;
240};
241
242 // partial specialization to optimize <f32> lines (avoiding casts)
243 template <>
244 inline vector2df line2d<irr::f32>::getClosestPoint(const vector2df& point, bool checkOnlySegments) const
245 {
246 vector2df c = point - start;
247 vector2df v = end - start;
248 f32 d = (f32)v.getLength();
249 if ( d == 0 ) // can't tell much when the line is just a single point
250 return start;
251 v /= d;
252 f32 t = v.dotProduct(c);
253
254 if ( checkOnlySegments )
255 {
256 if (t < 0) return start;
257 if (t > d) return end;
258 }
259
260 v *= t;
261 return start + v;
262 }
263
264
265 //! Typedef for an f32 line.
266 typedef line2d<f32> line2df;
267 //! Typedef for an integer line.
268 typedef line2d<s32> line2di;
269
270} // end namespace core
271} // end namespace irr
272
273#endif
274
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