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line2d.h
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    00001 // Copyright (C) 2002-2012 Nikolaus Gebhardt
    00002 // This file is part of the "Irrlicht Engine".
    00003 // For conditions of distribution and use, see copyright notice in irrlicht.h
    00004
    00005 #ifndef __IRR_LINE_2D_H_INCLUDED__
    00006 #define __IRR_LINE_2D_H_INCLUDED__
    00007
    00008 #include "irrTypes.h"
    00009 #include "vector2d.h"
    00010
    00011 namespace irr
    00012 {
    00013 namespace core
    00014 {
    00015
    00017 template <class T>
    00018 class line2d
    00019 {
    00020     public:
    00022         line2d() : start(0,0), end(1,1) {}
    00024         line2d(T xa, T ya, T xb, T yb) : start(xa, ya), end(xb, yb) {}
    00026         line2d(const vector2d<T>& start, const vector2d<T>& end) : start(start), end(end) {}
    00028         line2d(const line2d<T>& other) : start(other.start), end(other.end) {}
    00029
    00030         // operators
    00031
    00032         line2d<T> operator+(const vector2d<T>& point) const { return line2d<T>(start + point, end + point); }
    00033         line2d<T>& operator+=(const vector2d<T>& point) { start += point; end += point; return *this; }
    00034
    00035         line2d<T> operator-(const vector2d<T>& point) const { return line2d<T>(start - point, end - point); }
    00036         line2d<T>& operator-=(const vector2d<T>& point) { start -= point; end -= point; return *this; }
    00037
    00038         bool operator==(const line2d<T>& other) const
    00039         { return (start==other.start && end==other.end) || (end==other.start && start==other.end);}
    00040         bool operator!=(const line2d<T>& other) const
    00041         { return !(start==other.start && end==other.end) || (end==other.start && start==other.end);}
    00042
    00043         // functions
    00045         void setLine(const T& xa, const T& ya, const T& xb, const T& yb){start.set(xa, ya); end.set(xb, yb);}
    00047         void setLine(const vector2d<T>& nstart, const vector2d<T>& nend){start.set(nstart); end.set(nend);}
    00049         void setLine(const line2d<T>& line){start.set(line.start); end.set(line.end);}
    00050
    00052
    00053         T getLength() const { return start.getDistanceFrom(end); }
    00054
    00056
    00057         T getLengthSQ() const { return start.getDistanceFromSQ(end); }
    00058
    00060
    00061         vector2d<T> getMiddle() const
    00062         {
    00063             return (start + end)/(T)2;
    00064         }
    00065
    00067
    00068         vector2d<T> getVector() const { return vector2d<T>(end.X - start.X, end.Y - start.Y); }
    00069
    00071
    00077         bool intersectWith(const line2d<T>& l, vector2d<T>& out, bool checkOnlySegments=true) const
    00078         {
    00079             // Uses the method given at:
    00080             // http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/
    00081             const f32 commonDenominator = (f32)(l.end.Y - l.start.Y)*(end.X - start.X) -
    00082                                             (l.end.X - l.start.X)*(end.Y - start.Y);
    00083
    00084             const f32 numeratorA = (f32)(l.end.X - l.start.X)*(start.Y - l.start.Y) -
    00085                                             (l.end.Y - l.start.Y)*(start.X -l.start.X);
    00086
    00087             const f32 numeratorB = (f32)(end.X - start.X)*(start.Y - l.start.Y) -
    00088                                             (end.Y - start.Y)*(start.X -l.start.X);
    00089
    00090             if(equals(commonDenominator, 0.f))
    00091             {
    00092                 // The lines are either coincident or parallel
    00093                 // if both numerators are 0, the lines are coincident
    00094                 if(equals(numeratorA, 0.f) && equals(numeratorB, 0.f))
    00095                 {
    00096                     // Try and find a common endpoint
    00097                     if(l.start == start || l.end == start)
    00098                         out = start;
    00099                     else if(l.end == end || l.start == end)
    00100                         out = end;
    00101                     // now check if the two segments are disjunct
    00102                     else if (l.start.X>start.X && l.end.X>start.X && l.start.X>end.X && l.end.X>end.X)
    00103                         return false;
    00104                     else if (l.start.Y>start.Y && l.end.Y>start.Y && l.start.Y>end.Y && l.end.Y>end.Y)
    00105                         return false;
    00106                     else if (l.start.X<start.X && l.end.X<start.X && l.start.X<end.X && l.end.X<end.X)
    00107                         return false;
    00108                     else if (l.start.Y<start.Y && l.end.Y<start.Y && l.start.Y<end.Y && l.end.Y<end.Y)
    00109                         return false;
    00110                     // else the lines are overlapping to some extent
    00111                     else
    00112                     {
    00113                         // find the points which are not contributing to the
    00114                         // common part
    00115                         vector2d<T> maxp;
    00116                         vector2d<T> minp;
    00117                         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))
    00118                             maxp=start;
    00119                         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))
    00120                             maxp=end;
    00121                         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))
    00122                             maxp=l.start;
    00123                         else
    00124                             maxp=l.end;
    00125                         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)))
    00126                             minp=start;
    00127                         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)))
    00128                             minp=end;
    00129                         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)))
    00130                             minp=l.start;
    00131                         else
    00132                             minp=l.end;
    00133
    00134                         // one line is contained in the other. Pick the center
    00135                         // of the remaining points, which overlap for sure
    00136                         out = core::vector2d<T>();
    00137                         if (start != maxp && start != minp)
    00138                             out += start;
    00139                         if (end != maxp && end != minp)
    00140                             out += end;
    00141                         if (l.start != maxp && l.start != minp)
    00142                             out += l.start;
    00143                         if (l.end != maxp && l.end != minp)
    00144                             out += l.end;
    00145                         out.X = (T)(out.X/2);
    00146                         out.Y = (T)(out.Y/2);
    00147                     }
    00148
    00149                     return true; // coincident
    00150                 }
    00151
    00152                 return false; // parallel
    00153             }
    00154
    00155             // Get the point of intersection on this line, checking that
    00156             // it is within the line segment.
    00157             const f32 uA = numeratorA / commonDenominator;
    00158             if(checkOnlySegments && (uA < 0.f || uA > 1.f) )
    00159                 return false; // Outside the line segment
    00160
    00161             const f32 uB = numeratorB / commonDenominator;
    00162             if(checkOnlySegments && (uB < 0.f || uB > 1.f))
    00163                 return false; // Outside the line segment
    00164
    00165             // Calculate the intersection point.
    00166             out.X = (T)(start.X + uA * (end.X - start.X));
    00167             out.Y = (T)(start.Y + uA * (end.Y - start.Y));
    00168             return true;
    00169         }
    00170
    00172
    00173         vector2d<T> getUnitVector() const
    00174         {
    00175             T len = (T)(1.0 / getLength());
    00176             return vector2d<T>((end.X - start.X) * len, (end.Y - start.Y) * len);
    00177         }
    00178
    00180
    00182         f64 getAngleWith(const line2d<T>& l) const
    00183         {
    00184             vector2d<T> vect = getVector();
    00185             vector2d<T> vect2 = l.getVector();
    00186             return vect.getAngleWith(vect2);
    00187         }
    00188
    00190
    00192         T getPointOrientation(const vector2d<T>& point) const
    00193         {
    00194             return ( (end.X - start.X) * (point.Y - start.Y) -
    00195                     (point.X - start.X) * (end.Y - start.Y) );
    00196         }
    00197
    00199
    00200         bool isPointOnLine(const vector2d<T>& point) const
    00201         {
    00202             T d = getPointOrientation(point);
    00203             return (d == 0 && point.isBetweenPoints(start, end));
    00204         }
    00205
    00207
    00208         bool isPointBetweenStartAndEnd(const vector2d<T>& point) const
    00209         {
    00210             return point.isBetweenPoints(start, end);
    00211         }
    00212
    00214
    00216         vector2d<T> getClosestPoint(const vector2d<T>& point, bool checkOnlySegments=true) const
    00217         {
    00218             vector2d<f64> c((f64)(point.X-start.X), (f64)(point.Y- start.Y));
    00219             vector2d<f64> v((f64)(end.X-start.X), (f64)(end.Y-start.Y));
    00220             f64 d = v.getLength();
    00221             if ( d == 0 )   // can't tell much when the line is just a single point
    00222                 return start;
    00223             v /= d;
    00224             f64 t = v.dotProduct(c);
    00225
    00226             if ( checkOnlySegments )
    00227             {
    00228                 if (t < 0) return vector2d<T>((T)start.X, (T)start.Y);
    00229                 if (t > d) return vector2d<T>((T)end.X, (T)end.Y);
    00230             }
    00231
    00232             v *= t;
    00233             return vector2d<T>((T)(start.X + v.X), (T)(start.Y + v.Y));
    00234         }
    00235
    00237         vector2d<T> start;
    00239         vector2d<T> end;
    00240 };
    00241
    00242     // partial specialization to optimize <f32> lines (avoiding casts)
    00243     template <>
    00244     inline vector2df line2d<irr::f32>::getClosestPoint(const vector2df& point, bool checkOnlySegments) const
    00245     {
    00246         vector2df c = point - start;
    00247         vector2df v = end - start;
    00248         f32 d = (f32)v.getLength();
    00249         if ( d == 0 )   // can't tell much when the line is just a single point
    00250             return start;
    00251         v /= d;
    00252         f32 t = v.dotProduct(c);
    00253
    00254         if ( checkOnlySegments )
    00255         {
    00256             if (t < 0) return start;
    00257             if (t > d) return end;
    00258         }
    00259
    00260         v *= t;
    00261         return start + v;
    00262     }
    00263
    00264
    00266     typedef line2d<f32> line2df;
    00268     typedef line2d<s32> line2di;
    00269
    00270 } // end namespace core
    00271 } // end namespace irr
    00272
    00273 #endif
    00274