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./aip/1.8aipmod/include/line2d.h :


// Copyright (C) 2002-2011 Nikolaus Gebhardt

// This file is part of the "Irrlicht Engine".

// For conditions of distribution and use, see copyright notice in irrlicht.h


#ifndef __IRR_LINE_2D_H_INCLUDED__
#define __IRR_LINE_2D_H_INCLUDED__

#include "irrTypes.h"
#include "vector2d.h"

namespace irr
{
namespace core
{

//! 2D line between two points with intersection methods.

template <class T>
class line2d
{
	public:
		//! Default constructor for line going from (0,0) to (1,1).

		line2d() : start(0,0), end(1,1) {}
		//! Constructor for line between the two points.

		line2d(T xa, T ya, T xb, T yb) : start(xa, ya), end(xb, yb) {}
		//! Constructor for line between the two points given as vectors.

		line2d(const vector2d<T>& start, const vector2d<T>& end) : start(start), end(end) {}
		//! Copy constructor.

		line2d(const line2d<T>& other) : start(other.start), end(other.end) {}

		// operators


		line2d<T> operator+(const vector2d<T>& point) const { return line2d<T>(start + point, end + point); }
		line2d<T>& operator+=(const vector2d<T>& point) { start += point; end += point; return *this; }

		line2d<T> operator-(const vector2d<T>& point) const { return line2d<T>(start - point, end - point); }
		line2d<T>& operator-=(const vector2d<T>& point) { start -= point; end -= point; return *this; }

		bool operator==(const line2d<T>& other) const
		{ return (start==other.start && end==other.end) || (end==other.start && start==other.end);}
		bool operator!=(const line2d<T>& other) const
		{ return !(start==other.start && end==other.end) || (end==other.start && start==other.end);}

		// functions

		//! Set this line to new line going through the two points.

		void setLine(const T& xa, const T& ya, const T& xb, const T& yb){start.set(xa, ya); end.set(xb, yb);}
		//! Set this line to new line going through the two points.

		void setLine(const vector2d<T>& nstart, const vector2d<T>& nend){start.set(nstart); end.set(nend);}
		//! Set this line to new line given as parameter.

		void setLine(const line2d<T>& line){start.set(line.start); end.set(line.end);}

		//! Get length of line

		/** \return Length of the line. */
		f64 getLength() const { return start.getDistanceFrom(end); }

		//! Get squared length of the line

		/** \return Squared length of line. */
		T getLengthSQ() const { return start.getDistanceFromSQ(end); }

		//! Get middle of the line

		/** \return center of the line. */
		vector2d<T> getMiddle() const
		{
			return (start + end) * (T)0.5;
		}

		//! Get the vector of the line.

		/** \return The vector of the line. */
		vector2d<T> getVector() const { return vector2d<T>(end.X - start.X, end.Y - start.Y); }

		//! Tests if this line intersects with another line.

		/** \param l: Other line to test intersection with.
		\param checkOnlySegments: Default is to check intersection between the begin and endpoints.
		When set to false the function will check for the first intersection point when extending the lines.
		\param out: If there is an intersection, the location of the
		intersection will be stored in this vector.
		\return True if there is an intersection, false if not. */
		bool intersectWith(const line2d<T>& l, vector2d<T>& out, bool checkOnlySegments=true) const
		{
			// Uses the method given at:

			// http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/

			const f32 commonDenominator = (l.end.Y - l.start.Y)*(end.X - start.X) -
											(l.end.X - l.start.X)*(end.Y - start.Y);

			const f32 numeratorA = (l.end.X - l.start.X)*(start.Y - l.start.Y) -
											(l.end.Y - l.start.Y)*(start.X -l.start.X);

			const f32 numeratorB = (end.X - start.X)*(start.Y - l.start.Y) -
											(end.Y - start.Y)*(start.X -l.start.X);

			if(equals(commonDenominator, 0.f))
			{
				// The lines are either coincident or parallel

				// if both numerators are 0, the lines are coincident

				if(equals(numeratorA, 0.f) && equals(numeratorB, 0.f))
				{
					// Try and find a common endpoint

					if(l.start == start || l.end == start)
						out = start;
					else if(l.end == end || l.start == end)
						out = end;
					// now check if the two segments are disjunct

					else if (l.start.X>start.X && l.end.X>start.X && l.start.X>end.X && l.end.X>end.X)
						return false;
					else if (l.start.Y>start.Y && l.end.Y>start.Y && l.start.Y>end.Y && l.end.Y>end.Y)
						return false;
					else if (l.start.X<start.X && l.end.X<start.X && l.start.X<end.X && l.end.X<end.X)
						return false;
					else if (l.start.Y<start.Y && l.end.Y<start.Y && l.start.Y<end.Y && l.end.Y<end.Y)
						return false;
					// else the lines are overlapping to some extent

					else
					{
						// find the points which are not contributing to the

						// common part

						vector2d<T> maxp;
						vector2d<T> minp;
						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))
							maxp=start;
						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))
							maxp=end;
						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))
							maxp=l.start;
						else
							maxp=l.end;
						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)))
							minp=start;
						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)))
							minp=end;
						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)))
							minp=l.start;
						else
							minp=l.end;

						// one line is contained in the other. Pick the center

						// of the remaining points, which overlap for sure

						out = core::vector2d<T>();
						if (start != maxp && start != minp)
							out += start;
						if (end != maxp && end != minp)
							out += end;
						if (l.start != maxp && l.start != minp)
							out += l.start;
						if (l.end != maxp && l.end != minp)
							out += l.end;
						out *= 0.5f;
					}

					return true; // coincident

				}

				return false; // parallel

			}

			// Get the point of intersection on this line, checking that

			// it is within the line segment.

			const f32 uA = numeratorA / commonDenominator;
			if(checkOnlySegments && (uA < 0.f || uA > 1.f) )
				return false; // Outside the line segment


			const f32 uB = numeratorB / commonDenominator;
			if(checkOnlySegments && (uB < 0.f || uB > 1.f))
				return false; // Outside the line segment


			// Calculate the intersection point.

			out.X = start.X + uA * (end.X - start.X);
			out.Y = start.Y + uA * (end.Y - start.Y);
			return true;
		}

		//! Get unit vector of the line.

		/** \return Unit vector of this line. */
		vector2d<T> getUnitVector() const
		{
			T len = (T)(1.0 / getLength());
			return vector2d<T>((end.X - start.X) * len, (end.Y - start.Y) * len);
		}

		//! Get angle between this line and given line.

		/** \param l Other line for test.
		\return Angle in degrees. */
		f64 getAngleWith(const line2d<T>& l) const
		{
			vector2d<T> vect = getVector();
			vector2d<T> vect2 = l.getVector();
			return vect.getAngleWith(vect2);
		}

		//! Tells us if the given point lies to the left, right, or on the line.

		/** \return 0 if the point is on the line
		<0 if to the left, or >0 if to the right. */
		T getPointOrientation(const vector2d<T>& point) const
		{
			return ( (end.X - start.X) * (point.Y - start.Y) -
					(point.X - start.X) * (end.Y - start.Y) );
		}

		//! Check if the given point is a member of the line

		/** \return True if point is between start and end, else false. */
		bool isPointOnLine(const vector2d<T>& point) const
		{
			T d = getPointOrientation(point);
			return (d == 0 && point.isBetweenPoints(start, end));
		}

		//! Check if the given point is between start and end of the line.

		/** Assumes that the point is already somewhere on the line. */
		bool isPointBetweenStartAndEnd(const vector2d<T>& point) const
		{
			return point.isBetweenPoints(start, end);
		}

		//! Get the closest point on this line to a point

		vector2d<T> getClosestPoint(const vector2d<T>& point) const
		{
			vector2d<T> c = point - start;
			vector2d<T> v = end - start;
			T d = (T)v.getLength();
			v /= d;
			T t = v.dotProduct(c);

			if (t < (T)0.0) return start;
			if (t > d) return end;

			v *= t;
			return start + v;
		}

		//! Start point of the line.

		vector2d<T> start;
		//! End point of the line.

		vector2d<T> end;
};

	//! Typedef for an f32 line.

	typedef line2d<f32> line2df;
	//! Typedef for an integer line.

	typedef line2d<s32> line2di;

} // end namespace core

} // end namespace irr


#endif

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