201 lines
6.9 KiB
C++
201 lines
6.9 KiB
C++
// Copyright (C) 2002-2009 Nikolaus Gebhardt
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// This file is part of the "Irrlicht Engine".
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// For conditions of distribution and use, see copyright notice in irrlicht.h
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#ifndef __IRR_LINE_2D_H_INCLUDED__
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#define __IRR_LINE_2D_H_INCLUDED__
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#include "irrTypes.h"
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#include "vector2d.h"
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namespace irr
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{
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namespace core
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{
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//! 2D line between two points with intersection methods.
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template <class T>
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class line2d
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{
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public:
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//! Default constructor for line going from (0,0) to (1,1).
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line2d() : start(0,0), end(1,1) {}
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//! Constructor for line between the two points.
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line2d(T xa, T ya, T xb, T yb) : start(xa, ya), end(xb, yb) {}
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//! Constructor for line between the two points given as vectors.
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line2d(const vector2d<T>& start, const vector2d<T>& end) : start(start), end(end) {}
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//! Copy constructor.
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line2d(const line2d<T>& other) : start(other.start), end(other.end) {}
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// operators
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line2d<T> operator+(const vector2d<T>& point) const { return line2d<T>(start + point, end + point); }
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line2d<T>& operator+=(const vector2d<T>& point) { start += point; end += point; return *this; }
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line2d<T> operator-(const vector2d<T>& point) const { return line2d<T>(start - point, end - point); }
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line2d<T>& operator-=(const vector2d<T>& point) { start -= point; end -= point; return *this; }
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bool operator==(const line2d<T>& other) const
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{ return (start==other.start && end==other.end) || (end==other.start && start==other.end);}
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bool operator!=(const line2d<T>& other) const
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{ return !(start==other.start && end==other.end) || (end==other.start && start==other.end);}
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// functions
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//! Set this line to new line going through the two points.
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void setLine(const T& xa, const T& ya, const T& xb, const T& yb){start.set(xa, ya); end.set(xb, yb);}
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//! Set this line to new line going through the two points.
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void setLine(const vector2d<T>& nstart, const vector2d<T>& nend){start.set(nstart); end.set(nend);}
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//! Set this line to new line given as parameter.
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void setLine(const line2d<T>& line){start.set(line.start); end.set(line.end);}
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//! Get length of line
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/** \return Length of the line. */
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f64 getLength() const { return start.getDistanceFrom(end); }
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//! Get squared length of the line
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/** \return Squared length of line. */
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T getLengthSQ() const { return start.getDistanceFromSQ(end); }
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//! Get middle of the line
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/** \return center of the line. */
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vector2d<T> getMiddle() const
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{
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return (start + end) * (T)0.5;
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}
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//! Get the vector of the line.
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/** \return The vector of the line. */
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vector2d<T> getVector() const { return vector2d<T>(end.X - start.X, end.Y - start.Y); }
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//! Tests if this line intersects with another line.
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/** \param l: Other line to test intersection with.
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\param checkOnlySegments: Default is to check intersection between the begin and endpoints.
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When set to false the function will check for the first intersection point when extending the lines.
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\param out: If there is an intersection, the location of the
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intersection will be stored in this vector.
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\return True if there is an intersection, false if not. */
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bool intersectWith(const line2d<T>& l, vector2d<T>& out, bool checkOnlySegments=true) const
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{
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// Uses the method given at:
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// http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/
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const f32 commonDenominator = (l.end.Y - l.start.Y)*(end.X - start.X) -
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(l.end.X - l.start.X)*(end.Y - start.Y);
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const f32 numeratorA = (l.end.X - l.start.X)*(start.Y - l.start.Y) -
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(l.end.Y - l.start.Y)*(start.X -l.start.X);
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const f32 numeratorB = (end.X - start.X)*(start.Y - l.start.Y) -
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(end.Y - start.Y)*(start.X -l.start.X);
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if(equals(commonDenominator, 0.f))
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{
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// The lines are either coincident or parallel
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if(equals(numeratorA, 0.f) && equals(numeratorB, 0.f))
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{
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// Try and find a common endpoint
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if(l.start == start || l.end == start)
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out = start;
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else if(l.end == end || l.start == end)
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out = end;
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else
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// one line is contained in the other, so for lack of a better
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// answer, pick the average of both lines
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out = ((start + end + l.start + l.end) * 0.25f);
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return true; // coincident
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}
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return false; // parallel
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}
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// Get the point of intersection on this line, checking that
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// it is within the line segment.
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const f32 uA = numeratorA / commonDenominator;
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if(checkOnlySegments && (uA < 0.f || uA > 1.f) )
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return false; // Outside the line segment
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const f32 uB = numeratorB / commonDenominator;
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if(checkOnlySegments && (uB < 0.f || uB > 1.f))
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return false; // Outside the line segment
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// Calculate the intersection point.
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out.X = start.X + uA * (end.X - start.X);
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out.Y = start.Y + uA * (end.Y - start.Y);
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return true;
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}
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//! Get unit vector of the line.
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/** \return Unit vector of this line. */
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vector2d<T> getUnitVector() const
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{
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T len = (T)(1.0 / getLength());
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return vector2d<T>((end.X - start.X) * len, (end.Y - start.Y) * len);
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}
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//! Get angle between this line and given line.
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/** \param l Other line for test.
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\return Angle in degrees. */
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f64 getAngleWith(const line2d<T>& l) const
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{
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vector2d<T> vect = getVector();
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vector2d<T> vect2 = l.getVector();
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return vect.getAngleWith(vect2);
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}
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//! Tells us if the given point lies to the left, right, or on the line.
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/** \return 0 if the point is on the line
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<0 if to the left, or >0 if to the right. */
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T getPointOrientation(const vector2d<T>& point) const
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{
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return ( (end.X - start.X) * (point.Y - start.Y) -
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(point.X - start.X) * (end.Y - start.Y) );
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}
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//! Check if the given point is a member of the line
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/** \return True if point is between start and end, else false. */
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bool isPointOnLine(const vector2d<T>& point) const
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{
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T d = getPointOrientation(point);
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return (d == 0 && point.isBetweenPoints(start, end));
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}
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//! Check if the given point is between start and end of the line.
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/** Assumes that the point is already somewhere on the line. */
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bool isPointBetweenStartAndEnd(const vector2d<T>& point) const
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{
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return point.isBetweenPoints(start, end);
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}
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//! Get the closest point on this line to a point
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vector2d<T> getClosestPoint(const vector2d<T>& point) const
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{
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vector2d<T> c = point - start;
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vector2d<T> v = end - start;
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T d = (T)v.getLength();
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v /= d;
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T t = v.dotProduct(c);
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if (t < (T)0.0) return start;
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if (t > d) return end;
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v *= t;
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return start + v;
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}
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//! Start point of the line.
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vector2d<T> start;
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//! End point of the line.
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vector2d<T> end;
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};
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//! Typedef for an f32 line.
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typedef line2d<f32> line2df;
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//! Typedef for an integer line.
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typedef line2d<s32> line2di;
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} // end namespace core
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} // end namespace irr
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#endif
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