358 lines
13 KiB
C++
358 lines
13 KiB
C++
// Copyright (C) 2002-2012 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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#pragma once
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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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// 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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T 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)2;
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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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/*! Check if this segment intersects another segment,
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or if segments are coincident (colinear). */
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bool intersectAsSegments( const line2d<T>& other) const
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{
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// Taken from:
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// http://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
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// Find the four orientations needed for general and
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// special cases
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s32 o1 = start.checkOrientation( end, other.start);
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s32 o2 = start.checkOrientation( end, other.end);
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s32 o3 = other.start.checkOrientation( other.end, start);
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s32 o4 = other.start.checkOrientation( other.end, end);
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// General case
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if (o1 != o2 && o3 != o4)
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return true;
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// Special Cases to check if segments are colinear
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if (o1 == 0 && other.start.isBetweenPoints( start, end)) return true;
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if (o2 == 0 && other.end.isBetweenPoints( start, end)) return true;
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if (o3 == 0 && start.isBetweenPoints( other.start, other.end)) return true;
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if (o4 == 0 && end.isBetweenPoints( other.start, other.end)) return true;
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return false; // Doesn't fall in any of the above cases
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}
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/*! Check if 2 segments are incident (intersects in exactly 1 point).*/
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bool incidentSegments( const line2d<T>& other) const
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{
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return
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start.checkOrientation( end, other.start) != start.checkOrientation( end, other.end)
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&& other.start.checkOrientation( other.end, start) != other.start.checkOrientation( other.end, end);
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}
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/*! Check if 2 lines/segments are parallel or nearly parallel.*/
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bool nearlyParallel( const line2d<T>& line, const T factor = relativeErrorFactor<T>()) const
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{
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const vector2d<T> a = getVector();
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const vector2d<T> b = line.getVector();
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return a.nearlyParallel( b, factor);
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}
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/*! returns a intersection point of 2 lines (if lines are not parallel). Behaviour
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undefined if lines are parallel or coincident.
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It's on optimized intersectWith with checkOnlySegments=false and ignoreCoincidentLines=true
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*/
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vector2d<T> fastLinesIntersection( const line2d<T>& l) const
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{
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const f32 commonDenominator = (f32)((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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if ( commonDenominator != 0.f )
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{
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const f32 numeratorA = (f32)((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 uA = numeratorA / commonDenominator;
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// Calculate the intersection point.
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return vector2d<T> (
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(T)(start.X + uA * (end.X - start.X)),
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(T)(start.Y + uA * (end.Y - start.Y))
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);
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}
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else
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return l.start;
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}
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/*! Check if this line intersect a segment. The eventual intersection point is returned in "out".*/
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bool lineIntersectSegment( const line2d<T>& segment, vector2d<T> & out) const
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{
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if (nearlyParallel( segment))
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return false;
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out = fastLinesIntersection( segment);
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return out.isBetweenPoints( segment.start, segment.end);
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}
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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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\param ignoreCoincidentLines: When true coincident lines (lines above each other) are never considered as intersecting.
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When false the center of the overlapping part is returned.
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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, bool ignoreCoincidentLines=false) 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 = (f32)((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 = (f32)((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 = (f32)((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 both numerators are 0, the lines are coincident
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if(!ignoreCoincidentLines && 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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// now check if the two segments are disjunct
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else if (l.start.X>start.X && l.end.X>start.X && l.start.X>end.X && l.end.X>end.X)
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return false;
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else if (l.start.Y>start.Y && l.end.Y>start.Y && l.start.Y>end.Y && l.end.Y>end.Y)
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return false;
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else if (l.start.X<start.X && l.end.X<start.X && l.start.X<end.X && l.end.X<end.X)
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return false;
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else if (l.start.Y<start.Y && l.end.Y<start.Y && l.start.Y<end.Y && l.end.Y<end.Y)
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return false;
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// else the lines are overlapping to some extent
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else
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{
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// find the points which are not contributing to the
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// common part
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vector2d<T> maxp;
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vector2d<T> minp;
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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))
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maxp=start;
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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))
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maxp=end;
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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))
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maxp=l.start;
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else
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maxp=l.end;
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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)))
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minp=start;
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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)))
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minp=end;
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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)))
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minp=l.start;
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else
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minp=l.end;
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// one line is contained in the other. Pick the center
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// of the remaining points, which overlap for sure
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out = core::vector2d<T>();
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if (start != maxp && start != minp)
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out += start;
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if (end != maxp && end != minp)
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out += end;
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if (l.start != maxp && l.start != minp)
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out += l.start;
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if (l.end != maxp && l.end != minp)
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out += l.end;
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out.X = (T)(out.X/2);
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out.Y = (T)(out.Y/2);
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}
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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)
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{
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if(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(uB < 0.f || uB > 1.f)
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return false; // Outside the line segment
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}
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// Calculate the intersection point.
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out.X = (T)(start.X + uA * (end.X - start.X));
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out.Y = (T)(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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/** \param point: Starting search at this point
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\param checkOnlySegments: Default (true) is to return a point on the line-segment (between begin and end) of the line.
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When set to false the function will check for the first the closest point on the the line even when outside the segment. */
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vector2d<T> getClosestPoint(const vector2d<T>& point, bool checkOnlySegments=true) const
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{
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vector2d<f64> c((f64)(point.X-start.X), (f64)(point.Y- start.Y));
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vector2d<f64> v((f64)(end.X-start.X), (f64)(end.Y-start.Y));
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f64 d = v.getLength();
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if ( d == 0 ) // can't tell much when the line is just a single point
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return start;
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v /= d;
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f64 t = v.dotProduct(c);
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if ( checkOnlySegments )
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{
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if (t < 0) return vector2d<T>((T)start.X, (T)start.Y);
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if (t > d) return vector2d<T>((T)end.X, (T)end.Y);
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}
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v *= t;
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return vector2d<T>((T)(start.X + v.X), (T)(start.Y + v.Y));
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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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// partial specialization to optimize <f32> lines (avoiding casts)
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template <>
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inline vector2df line2d<irr::f32>::getClosestPoint(const vector2df& point, bool checkOnlySegments) const
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{
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const vector2df c = point - start;
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vector2df v = end - start;
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const f32 d = (f32)v.getLength();
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if ( d == 0 ) // can't tell much when the line is just a single point
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return start;
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v /= d;
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const f32 t = v.dotProduct(c);
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if ( checkOnlySegments )
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{
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if (t < 0) return start;
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if (t > d) return end;
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}
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v *= t;
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return start + v;
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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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