line2d.hpp

// Copyright (C) 2002-2012 Nikolaus Gebhardt
// This file is part of the "Irrlicht Engine".
// For conditions of distribution and use, see copyright notice in nirtcpp/nirtcpp.hpp
 
#ifndef NIRT_LINE_2D_HPP_INCLUDED
#define NIRT_LINE_2D_HPP_INCLUDED
 
#include <nirtcpp/core/engine/nirt_types.hpp>
#include <nirtcpp/core/engine/vector2d.hpp>
 
namespace nirt
{
namespace core
{
 
template <class T>
class line2d
{
    public:
        line2d() : start(0,0), end(1,1) {}
        line2d(T xa, T ya, T xb, T yb) : start(xa, ya), end(xb, yb) {}
        line2d(const vector2d<T>& start, const vector2d<T>& end) : start(start), end(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
        void setLine(const T& xa, const T& ya, const T& xb, const T& yb){start.set(xa, ya); end.set(xb, yb);}
        void setLine(const vector2d<T>& nstart, const vector2d<T>& nend){start.set(nstart); end.set(nend);}
        void setLine(const line2d<T>& line){start.set(line.start); end.set(line.end);}
 
 
        T getLength() const { return start.getDistanceFrom(end); }
 
 
        T getLengthSQ() const { return start.getDistanceFromSQ(end); }
 
 
        vector2d<T> getMiddle() const
        {
            return (start + end)/(T)2;
        }
 
 
        vector2d<T> getVector() const { return vector2d<T>( end.X - start.X, end.Y - start.Y); }
 
        bool intersectAsSegments( const line2d<T>& other) const
        {
            // Taken from:
            // http://www.geeksforgeeks.org/check-if-two-given-line-segments-intersect/
 
            // Find the four orientations needed for general and
            // special cases
            s32 o1 = start.checkOrientation( end, other.start);
            s32 o2 = start.checkOrientation( end, other.end);
            s32 o3 = other.start.checkOrientation( other.end, start);
            s32 o4 = other.start.checkOrientation( other.end, end);
 
            // General case
            if (o1 != o2 && o3 != o4)
                return true;
 
            // Special Cases to check if segments are coolinear
            if (o1 == 0 && other.start.isBetweenPoints( start, end)) return true;
            if (o2 == 0 && other.end.isBetweenPoints( start, end)) return true;
            if (o3 == 0 && start.isBetweenPoints( other.start, other.end)) return true;
            if (o4 == 0 && end.isBetweenPoints( other.start, other.end)) return true;
 
            return false; // Doesn't fall in any of the above cases
        }
 
        bool incidentSegments( const line2d<T>& other) const
        {
            return
                start.checkOrientation( end, other.start) != start.checkOrientation( end, other.end)
            &&  other.start.checkOrientation( other.end, start) != other.start.checkOrientation( other.end, end);
        }
 
        bool nearlyParallel( const line2d<T>& line, const T factor = relativeErrorFactor<T>()) const
        {
            const vector2d<T> a = getVector();
            const vector2d<T> b = line.getVector();
 
            return a.nearlyParallel( b, factor);
        }
 
        vector2d<T> fastLinesIntersection( const line2d<T>& l) const
        {
            const f32 commonDenominator = (f32)((l.end.Y - l.start.Y)*(end.X - start.X) -
                (l.end.X - l.start.X)*(end.Y - start.Y));
 
            if ( commonDenominator != 0.f )
            {
                const f32 numeratorA = (f32)((l.end.X - l.start.X)*(start.Y - l.start.Y) -
                    (l.end.Y - l.start.Y)*(start.X - l.start.X));
 
                const f32 uA = numeratorA / commonDenominator;
 
                // Calculate the intersection point.
                return vector2d<T> (
                    (T)(start.X + uA * (end.X - start.X)),
                    (T)(start.Y + uA * (end.Y - start.Y))
                    );
            }
            else
                return l.start;
        }
 
        bool lineIntersectSegment( const line2d<T>& segment, vector2d<T> & out) const
        {
            if (nearlyParallel( segment))
                return false;
 
            out = fastLinesIntersection( segment);
 
            return out.isBetweenPoints( segment.start, segment.end);
        }
 
 
        bool intersectWith(const line2d<T>& l, vector2d<T>& out, bool checkOnlySegments=true, bool ignoreCoincidentLines=false) const
        {
            // Uses the method given at:
            // http://local.wasp.uwa.edu.au/~pbourke/geometry/lineline2d/
            const f64 commonDenominator = (f64)((l.end.Y - l.start.Y)*(end.X - start.X) -
                                            (l.end.X - l.start.X)*(end.Y - start.Y));
 
            const f64 numeratorA = (f64)((l.end.X - l.start.X)*(start.Y - l.start.Y) -
                                            (l.end.Y - l.start.Y)*(start.X -l.start.X));
 
            const f64 numeratorB = (f64)((end.X - start.X)*(start.Y - l.start.Y) -
                                            (end.Y - start.Y)*(start.X -l.start.X));
 
            if(equals(commonDenominator, 0.0))
            {
                // The lines are either coincident or parallel
                // if both numerators are 0, the lines are coincident
                if(!ignoreCoincidentLines && equals(numeratorA, 0.0) && equals(numeratorB, 0.0))
                {
                    // 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.X = (T)(out.X/2);
                        out.Y = (T)(out.Y/2);
                    }
 
                    return true; // coincident
                }
 
                return false; // parallel
            }
 
            // Get the point of intersection on this line, checking that
            // it is within the line segment.
            const f64 uA = numeratorA / commonDenominator;
            if (checkOnlySegments)
            {
                if(uA < 0.0 || uA > 1.0)
                    return false; // Outside the line segment
 
                const f64 uB = numeratorB / commonDenominator;
                if(uB < 0.0 || uB > 1.0)
                    return false; // Outside the line segment
            }
 
            // Calculate the intersection point.
            out.X = (T)(start.X + uA * (end.X - start.X));
            out.Y = (T)(start.Y + uA * (end.Y - start.Y));
            return true;
        }
 
 
        vector2d<T> getUnitVector() const
        {
            T len = (T)(1.0 / getLength());
            return vector2d<T>((end.X - start.X) * len, (end.Y - start.Y) * len);
        }
 
 
        f64 getAngleWith(const line2d<T>& l) const
        {
            vector2d<T> vect = getVector();
            vector2d<T> vect2 = l.getVector();
            return vect.getAngleWith(vect2);
        }
 
 
        T getPointOrientation(const vector2d<T>& point) const
        {
            return ( (end.X - start.X) * (point.Y - start.Y) -
                    (point.X - start.X) * (end.Y - start.Y) );
        }
 
 
        bool isPointOnLine(const vector2d<T>& point) const
        {
            T d = getPointOrientation(point);
            return (d == 0 && point.isBetweenPoints(start, end));
        }
 
 
        bool isPointBetweenStartAndEnd(const vector2d<T>& point) const
        {
            return point.isBetweenPoints(start, end);
        }
 
 
        vector2d<T> getClosestPoint(const vector2d<T>& point, bool checkOnlySegments=true) const
        {
            vector2d<f64> c((f64)(point.X-start.X), (f64)(point.Y- start.Y));
            vector2d<f64> v((f64)(end.X-start.X), (f64)(end.Y-start.Y));
            f64 d = v.getLength();
            if ( d == 0 ) // can't tell much when the line is just a single point
                return start;
            v /= d;
            f64 t = v.dotProduct(c);
 
            if ( checkOnlySegments )
            {
                if (t < 0) return vector2d<T>((T)start.X, (T)start.Y);
                if (t > d) return vector2d<T>((T)end.X, (T)end.Y);
            }
 
            v *= t;
            return vector2d<T>((T)(start.X + v.X), (T)(start.Y + v.Y));
        }
 
        vector2d<T> start;
        vector2d<T> end;
};
 
    // partial specialization to optimize <f32> lines (avoiding casts)
    template <>
    inline vector2df line2d<nirt::f32>::getClosestPoint(const vector2df& point, bool checkOnlySegments) const
    {
        const vector2df c = point - start;
        vector2df v = end - start;
        const f32 d = (f32)v.getLength();
        if ( d == 0 ) // can't tell much when the line is just a single point
            return start;
        v /= d;
        const f32 t = v.dotProduct(c);
 
        if ( checkOnlySegments )
        {
            if (t < 0) return start;
            if (t > d) return end;
        }
 
        v *= t;
        return start + v;
    }
 
 
    using line2df = line2d<f32>;
    using line2di = line2d<s32>;
 
} // end namespace core
} // end namespace nirt
 
#endif