vector2d.h

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// Copyright (C) 2002-2012 Nikolaus Gebhardt
// This file is part of the "Irrlicht Engine".
// For conditions of distribution and use, see copyright notice in irrlicht.h

#ifndef __IRR_POINT_2D_H_INCLUDED__
#define __IRR_POINT_2D_H_INCLUDED__

#include "irrMath.h"
#include "dimension2d.h"

namespace irr
{
namespace core
{



template <class T>
class vector2d
{
public:
        vector2d() : X(0), Y(0) {}
        vector2d(T nx, T ny) : X(nx), Y(ny) {}
        explicit vector2d(T n) : X(n), Y(n) {}
        vector2d(const vector2d<T>& other) : X(other.X), Y(other.Y) {}

        vector2d(const dimension2d<T>& other) : X(other.Width), Y(other.Height) {}

        // operators

        vector2d<T> operator-() const { return vector2d<T>(-X, -Y); }

        vector2d<T>& operator=(const vector2d<T>& other) { X = other.X; Y = other.Y; return *this; }

        vector2d<T>& operator=(const dimension2d<T>& other) { X = other.Width; Y = other.Height; return *this; }

        vector2d<T> operator+(const vector2d<T>& other) const { return vector2d<T>(X + other.X, Y + other.Y); }
        vector2d<T> operator+(const dimension2d<T>& other) const { return vector2d<T>(X + other.Width, Y + other.Height); }
        vector2d<T>& operator+=(const vector2d<T>& other) { X+=other.X; Y+=other.Y; return *this; }
        vector2d<T> operator+(const T v) const { return vector2d<T>(X + v, Y + v); }
        vector2d<T>& operator+=(const T v) { X+=v; Y+=v; return *this; }
        vector2d<T>& operator+=(const dimension2d<T>& other) { X += other.Width; Y += other.Height; return *this;  }

        vector2d<T> operator-(const vector2d<T>& other) const { return vector2d<T>(X - other.X, Y - other.Y); }
        vector2d<T> operator-(const dimension2d<T>& other) const { return vector2d<T>(X - other.Width, Y - other.Height); }
        vector2d<T>& operator-=(const vector2d<T>& other) { X-=other.X; Y-=other.Y; return *this; }
        vector2d<T> operator-(const T v) const { return vector2d<T>(X - v, Y - v); }
        vector2d<T>& operator-=(const T v) { X-=v; Y-=v; return *this; }
        vector2d<T>& operator-=(const dimension2d<T>& other) { X -= other.Width; Y -= other.Height; return *this;  }

        vector2d<T> operator*(const vector2d<T>& other) const { return vector2d<T>(X * other.X, Y * other.Y); }
        vector2d<T>& operator*=(const vector2d<T>& other) { X*=other.X; Y*=other.Y; return *this; }
        vector2d<T> operator*(const T v) const { return vector2d<T>(X * v, Y * v); }
        vector2d<T>& operator*=(const T v) { X*=v; Y*=v; return *this; }

        vector2d<T> operator/(const vector2d<T>& other) const { return vector2d<T>(X / other.X, Y / other.Y); }
        vector2d<T>& operator/=(const vector2d<T>& other) { X/=other.X; Y/=other.Y; return *this; }
        vector2d<T> operator/(const T v) const { return vector2d<T>(X / v, Y / v); }
        vector2d<T>& operator/=(const T v) { X/=v; Y/=v; return *this; }

        T& operator [](u32 index)
        {
                _IRR_DEBUG_BREAK_IF(index>1) // access violation

                return *(&X+index);
        }

        const T& operator [](u32 index) const
        {
                _IRR_DEBUG_BREAK_IF(index>1) // access violation

                return *(&X+index);
        }

        bool operator<=(const vector2d<T>&other) const
        {
                return (X<other.X || core::equals(X, other.X)) ||
                                (core::equals(X, other.X) && (Y<other.Y || core::equals(Y, other.Y)));
        }

        bool operator>=(const vector2d<T>&other) const
        {
                return (X>other.X || core::equals(X, other.X)) ||
                                (core::equals(X, other.X) && (Y>other.Y || core::equals(Y, other.Y)));
        }

        bool operator<(const vector2d<T>&other) const
        {
                return (X<other.X && !core::equals(X, other.X)) ||
                                (core::equals(X, other.X) && Y<other.Y && !core::equals(Y, other.Y));
        }

        bool operator>(const vector2d<T>&other) const
        {
                return (X>other.X && !core::equals(X, other.X)) ||
                                (core::equals(X, other.X) && Y>other.Y && !core::equals(Y, other.Y));
        }

        bool operator==(const vector2d<T>& other) const { return equals(other); }
        bool operator!=(const vector2d<T>& other) const { return !equals(other); }

        // functions


        bool equals(const vector2d<T>& other, const T tolerance = (T)ROUNDING_ERROR_f32 ) const
        {
                return core::equals(X, other.X, tolerance) && core::equals(Y, other.Y, tolerance);
        }

        vector2d<T>& set(T nx, T ny) {X=nx; Y=ny; return *this; }
        vector2d<T>& set(const vector2d<T>& p) { X=p.X; Y=p.Y; return *this; }


        T getLength() const { return core::squareroot( X*X + Y*Y ); }


        T getLengthSQ() const { return X*X + Y*Y; }


        T dotProduct(const vector2d<T>& other) const
        {
                return X*other.X + Y*other.Y;
        }

        bool nearlyParallel( const vector2d<T> & other, const T factor = relativeErrorFactor<T>()) const
        {
                // https://eagergames.wordpress.com/2017/04/01/fast-parallel-lines-and-vectors-test/
                // if a || b then  a.x/a.y = b.x/b.y (similiar triangles)
                // if a || b then either both x are 0 or both y are 0.

                return  equalsRelative( X*other.Y, other.X* Y, factor)
                && // a bit counterintuitive, but makes sure  that
                   // only y or only x are 0, and at same time deals
                   // with the case where one vector is zero vector.
                        (X*other.X + Y*other.Y) != 0;
        }


        T getDistanceFrom(const vector2d<T>& other) const
        {
                return vector2d<T>(X - other.X, Y - other.Y).getLength();
        }


        T getDistanceFromSQ(const vector2d<T>& other) const
        {
                return vector2d<T>(X - other.X, Y - other.Y).getLengthSQ();
        }


        vector2d<T>& rotateBy(f64 degrees, const vector2d<T>& center=vector2d<T>())
        {
                degrees *= DEGTORAD64;
                const f64 cs = cos(degrees);
                const f64 sn = sin(degrees);

                X -= center.X;
                Y -= center.Y;

                set((T)(X*cs - Y*sn), (T)(X*sn + Y*cs));

                X += center.X;
                Y += center.Y;
                return *this;
        }


        vector2d<T>& normalize()
        {
                f32 length = (f32)(X*X + Y*Y);
                if ( length == 0 )
                        return *this;
                length = core::reciprocal_squareroot ( length );
                X = (T)(X * length);
                Y = (T)(Y * length);
                return *this;
        }


        f64 getAngleTrig() const
        {
                if (Y == 0)
                        return X < 0 ? 180 : 0;
                else
                if (X == 0)
                        return Y < 0 ? 270 : 90;

                if ( Y > 0)
                        if (X > 0)
                                return atan((irr::f64)Y/(irr::f64)X) * RADTODEG64;
                        else
                                return 180.0-atan((irr::f64)Y/-(irr::f64)X) * RADTODEG64;
                else
                        if (X > 0)
                                return 360.0-atan(-(irr::f64)Y/(irr::f64)X) * RADTODEG64;
                        else
                                return 180.0+atan(-(irr::f64)Y/-(irr::f64)X) * RADTODEG64;
        }


        inline f64 getAngle() const
        {
                if (Y == 0) // corrected thanks to a suggestion by Jox
                        return X < 0 ? 180 : 0;
                else if (X == 0)
                        return Y < 0 ? 90 : 270;

                // don't use getLength here to avoid precision loss with s32 vectors
                // avoid floating-point trouble as sqrt(y*y) is occasionally larger than y, so clamp
                const f64 tmp = core::clamp(Y / sqrt((f64)(X*X + Y*Y)), -1.0, 1.0);
                const f64 angle = atan( core::squareroot(1 - tmp*tmp) / tmp) * RADTODEG64;

                if (X>0 && Y>0)
                        return angle + 270;
                else
                if (X>0 && Y<0)
                        return angle + 90;
                else
                if (X<0 && Y<0)
                        return 90 - angle;
                else
                if (X<0 && Y>0)
                        return 270 - angle;

                return angle;
        }


        inline f64 getAngleWith(const vector2d<T>& b) const
        {
                f64 tmp = (f64)(X*b.X + Y*b.Y);

                if (tmp == 0.0)
                        return 90.0;

                tmp = tmp / core::squareroot((f64)((X*X + Y*Y) * (b.X*b.X + b.Y*b.Y)));
                if (tmp < 0.0)
                        tmp = -tmp;
                if ( tmp > 1.0 ) //   avoid floating-point trouble
                        tmp = 1.0;

                return atan(sqrt(1 - tmp*tmp) / tmp) * RADTODEG64;
        }


        bool isBetweenPoints(const vector2d<T>& begin, const vector2d<T>& end) const
        {
                //             .  end
                //            /
                //           /
                //          /
                //         . begin
                //        -
                //       -
                //      . this point (am I inside or outside)?
                //
                if (begin.X != end.X)
                {
                        return ((begin.X <= X && X <= end.X) ||
                                        (begin.X >= X && X >= end.X));
                }
                else
                {
                        return ((begin.Y <= Y && Y <= end.Y) ||
                                        (begin.Y >= Y && Y >= end.Y));
                }
        }


        vector2d<T> getInterpolated(const vector2d<T>& other, f64 d) const
        {
                const f64 inv = 1.0f - d;
                return vector2d<T>((T)(other.X*inv + X*d), (T)(other.Y*inv + Y*d));
        }


        vector2d<T> getInterpolated_quadratic(const vector2d<T>& v2, const vector2d<T>& v3, f64 d) const
        {
                // this*(1-d)*(1-d) + 2 * v2 * (1-d) + v3 * d * d;
                const f64 inv = 1.0f - d;
                const f64 mul0 = inv * inv;
                const f64 mul1 = 2.0f * d * inv;
                const f64 mul2 = d * d;

                return vector2d<T> ( (T)(X * mul0 + v2.X * mul1 + v3.X * mul2),
                                        (T)(Y * mul0 + v2.Y * mul1 + v3.Y * mul2));
        }

        s32 checkOrientation( const vector2d<T> & b, const vector2d<T> & c) const
        {
                // Example of clockwise points
                //
                //   ^ Y
                //   |       A
                //   |      . .
                //   |     .   .
                //   |    C.....B
                //   +---------------> X

                T val = (b.Y - Y) * (c.X - b.X) -
                        (b.X - X) * (c.Y - b.Y);

                if (val == 0) return 0;  // colinear

                return (val > 0) ? 1 : 2; // clock or counterclock wise
        }

        inline bool areClockwise( const vector2d<T> & b, const vector2d<T> & c) const
        {
                T val = (b.Y - Y) * (c.X - b.X) -
                        (b.X - X) * (c.Y - b.Y);

                return val > 0;
        }

        inline bool areCounterClockwise( const vector2d<T> & b, const vector2d<T> & c) const
        {
                T val = (b.Y - Y) * (c.X - b.X) -
                        (b.X - X) * (c.Y - b.Y);

                return val < 0;
        }


        vector2d<T>& interpolate( const vector2d<T>& a, const vector2d<T>& b, f64 d)
        {
                X = (T)((f64)b.X + ( ( a.X - b.X ) * d ));
                Y = (T)((f64)b.Y + ( ( a.Y - b.Y ) * d ));
                return *this;
        }

        T X;

        T Y;
};

        typedef vector2d<f32> vector2df;

        typedef vector2d<s32> vector2di;

        template<class S, class T>
        vector2d<T> operator*(const S scalar, const vector2d<T>& vector) { return vector*scalar; }

        // These methods are declared in dimension2d, but need definitions of vector2d
        template<class T>
        dimension2d<T>::dimension2d(const vector2d<T>& other) : Width(other.X), Height(other.Y) { }

        template<class T>
        bool dimension2d<T>::operator==(const vector2d<T>& other) const { return Width == other.X && Height == other.Y; }

} // end namespace core
} // end namespace irr

#endif