OgreVector3.h

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/*
-----------------------------------------------------------------------------
This source file is part of OGRE
    (Object-oriented Graphics Rendering Engine)
For the latest info, see http://www.ogre3d.org/

Copyright (c) 2000-2014 Torus Knot Software Ltd

Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in
all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
THE SOFTWARE.
-----------------------------------------------------------------------------
*/
#ifndef __Vector3_H__
#define __Vector3_H__

#include "OgrePrerequisites.h"
#include "OgreMath.h"
#include "OgreQuaternion.h"

namespace Ogre
{

    class _OgreExport Vector3
    {
    public:
        Real x, y, z;

    public:
        inline Vector3()
        {
        }

        inline Vector3( const Real fX, const Real fY, const Real fZ )
            : x( fX ), y( fY ), z( fZ )
        {
        }

        inline explicit Vector3( const Real afCoordinate[3] )
            : x( afCoordinate[0] ),
              y( afCoordinate[1] ),
              z( afCoordinate[2] )
        {
        }

        inline explicit Vector3( const int afCoordinate[3] )
        {
            x = (Real)afCoordinate[0];
            y = (Real)afCoordinate[1];
            z = (Real)afCoordinate[2];
        }

        inline explicit Vector3( Real* const r )
            : x( r[0] ), y( r[1] ), z( r[2] )
        {
        }

        inline explicit Vector3( const Real scaler )
            : x( scaler )
            , y( scaler )
            , z( scaler )
        {
        }


        inline void swap(Vector3& other)
        {
            std::swap(x, other.x);
            std::swap(y, other.y);
            std::swap(z, other.z);
        }

        inline Real operator [] ( const size_t i ) const
        {
            assert( i < 3 );

            return *(&x+i);
        }

        inline Real& operator [] ( const size_t i )
        {
            assert( i < 3 );

            return *(&x+i);
        }
        inline Real* ptr()
        {
            return &x;
        }
        inline const Real* ptr() const
        {
            return &x;
        }

        inline Vector3& operator = ( const Vector3& rkVector )
        {
            x = rkVector.x;
            y = rkVector.y;
            z = rkVector.z;

            return *this;
        }

        inline Vector3& operator = ( const Real fScaler )
        {
            x = fScaler;
            y = fScaler;
            z = fScaler;

            return *this;
        }

        inline bool operator == ( const Vector3& rkVector ) const
        {
            return ( x == rkVector.x && y == rkVector.y && z == rkVector.z );
        }

        inline bool operator != ( const Vector3& rkVector ) const
        {
            return ( x != rkVector.x || y != rkVector.y || z != rkVector.z );
        }

        // arithmetic operations
        inline Vector3 operator + ( const Vector3& rkVector ) const
        {
            return Vector3(
                x + rkVector.x,
                y + rkVector.y,
                z + rkVector.z);
        }

        inline Vector3 operator - ( const Vector3& rkVector ) const
        {
            return Vector3(
                x - rkVector.x,
                y - rkVector.y,
                z - rkVector.z);
        }

        inline Vector3 operator * ( const Real fScalar ) const
        {
            return Vector3(
                x * fScalar,
                y * fScalar,
                z * fScalar);
        }

        inline Vector3 operator * ( const Vector3& rhs) const
        {
            return Vector3(
                x * rhs.x,
                y * rhs.y,
                z * rhs.z);
        }

        inline Vector3 operator / ( const Real fScalar ) const
        {
            assert( fScalar != 0.0 );

            Real fInv = 1.0f / fScalar;

            return Vector3(
                x * fInv,
                y * fInv,
                z * fInv);
        }

        inline Vector3 operator / ( const Vector3& rhs) const
        {
            return Vector3(
                x / rhs.x,
                y / rhs.y,
                z / rhs.z);
        }

        inline const Vector3& operator + () const
        {
            return *this;
        }

        inline Vector3 operator - () const
        {
            return Vector3(-x, -y, -z);
        }

        // overloaded operators to help Vector3
        inline friend Vector3 operator * ( const Real fScalar, const Vector3& rkVector )
        {
            return Vector3(
                fScalar * rkVector.x,
                fScalar * rkVector.y,
                fScalar * rkVector.z);
        }

        inline friend Vector3 operator / ( const Real fScalar, const Vector3& rkVector )
        {
            return Vector3(
                fScalar / rkVector.x,
                fScalar / rkVector.y,
                fScalar / rkVector.z);
        }

        inline friend Vector3 operator + (const Vector3& lhs, const Real rhs)
        {
            return Vector3(
                lhs.x + rhs,
                lhs.y + rhs,
                lhs.z + rhs);
        }

        inline friend Vector3 operator + (const Real lhs, const Vector3& rhs)
        {
            return Vector3(
                lhs + rhs.x,
                lhs + rhs.y,
                lhs + rhs.z);
        }

        inline friend Vector3 operator - (const Vector3& lhs, const Real rhs)
        {
            return Vector3(
                lhs.x - rhs,
                lhs.y - rhs,
                lhs.z - rhs);
        }

        inline friend Vector3 operator - (const Real lhs, const Vector3& rhs)
        {
            return Vector3(
                lhs - rhs.x,
                lhs - rhs.y,
                lhs - rhs.z);
        }

        // arithmetic updates
        inline Vector3& operator += ( const Vector3& rkVector )
        {
            x += rkVector.x;
            y += rkVector.y;
            z += rkVector.z;

            return *this;
        }

        inline Vector3& operator += ( const Real fScalar )
        {
            x += fScalar;
            y += fScalar;
            z += fScalar;
            return *this;
        }

        inline Vector3& operator -= ( const Vector3& rkVector )
        {
            x -= rkVector.x;
            y -= rkVector.y;
            z -= rkVector.z;

            return *this;
        }

        inline Vector3& operator -= ( const Real fScalar )
        {
            x -= fScalar;
            y -= fScalar;
            z -= fScalar;
            return *this;
        }

        inline Vector3& operator *= ( const Real fScalar )
        {
            x *= fScalar;
            y *= fScalar;
            z *= fScalar;
            return *this;
        }

        inline Vector3& operator *= ( const Vector3& rkVector )
        {
            x *= rkVector.x;
            y *= rkVector.y;
            z *= rkVector.z;

            return *this;
        }

        inline Vector3& operator /= ( const Real fScalar )
        {
            assert( fScalar != 0.0 );

            Real fInv = 1.0f / fScalar;

            x *= fInv;
            y *= fInv;
            z *= fInv;

            return *this;
        }

        inline Vector3& operator /= ( const Vector3& rkVector )
        {
            x /= rkVector.x;
            y /= rkVector.y;
            z /= rkVector.z;

            return *this;
        }


        inline Real length () const
        {
            return Math::Sqrt( x * x + y * y + z * z );
        }

        inline Real squaredLength () const
        {
            return x * x + y * y + z * z;
        }

        inline Real distance(const Vector3& rhs) const
        {
            return (*this - rhs).length();
        }

        inline Real squaredDistance(const Vector3& rhs) const
        {
            return (*this - rhs).squaredLength();
        }

        inline Real dotProduct(const Vector3& vec) const
        {
            return x * vec.x + y * vec.y + z * vec.z;
        }

        inline Real absDotProduct(const Vector3& vec) const
        {
            return Math::Abs(x * vec.x) + Math::Abs(y * vec.y) + Math::Abs(z * vec.z);
        }

        inline Real normalise()
        {
            Real fLength = Math::Sqrt( x * x + y * y + z * z );

            // Will also work for zero-sized vectors, but will change nothing
            // We're not using epsilons because we don't need to.
            // Read http://www.ogre3d.org/forums/viewtopic.php?f=4&t=61259
            if ( fLength > Real(0.0f) )
            {
                Real fInvLength = 1.0f / fLength;
                x *= fInvLength;
                y *= fInvLength;
                z *= fInvLength;
            }

            return fLength;
        }

        inline Vector3 crossProduct( const Vector3& rkVector ) const
        {
            return Vector3(
                y * rkVector.z - z * rkVector.y,
                z * rkVector.x - x * rkVector.z,
                x * rkVector.y - y * rkVector.x);
        }

        inline Vector3 midPoint( const Vector3& vec ) const
        {
            return Vector3(
                ( x + vec.x ) * 0.5f,
                ( y + vec.y ) * 0.5f,
                ( z + vec.z ) * 0.5f );
        }

        inline bool operator < ( const Vector3& rhs ) const
        {
            if( x < rhs.x && y < rhs.y && z < rhs.z )
                return true;
            return false;
        }

        inline bool operator > ( const Vector3& rhs ) const
        {
            if( x > rhs.x && y > rhs.y && z > rhs.z )
                return true;
            return false;
        }

        inline void makeFloor( const Vector3& cmp )
        {
            if( cmp.x < x ) x = cmp.x;
            if( cmp.y < y ) y = cmp.y;
            if( cmp.z < z ) z = cmp.z;
        }

        inline void makeCeil( const Vector3& cmp )
        {
            if( cmp.x > x ) x = cmp.x;
            if( cmp.y > y ) y = cmp.y;
            if( cmp.z > z ) z = cmp.z;
        }

        inline Vector3 perpendicular(void) const
        {
            static const Real fSquareZero = (Real)(1e-06 * 1e-06);

            Vector3 perp = this->crossProduct( Vector3::UNIT_X );

            // Check length
            if( perp.squaredLength() < fSquareZero )
            {
                /* This vector is the Y axis multiplied by a scalar, so we have
                   to use another axis.
                */
                perp = this->crossProduct( Vector3::UNIT_Y );
            }
            perp.normalise();

            return perp;
        }
        inline Vector3 randomDeviant(
            const Radian& angle,
            const Vector3& up = Vector3::ZERO ) const
        {
            Vector3 newUp;

            if (up == Vector3::ZERO)
            {
                // Generate an up vector
                newUp = this->perpendicular();
            }
            else
            {
                newUp = up;
            }

            // Rotate up vector by random amount around this
            Quaternion q;
            q.FromAngleAxis( Radian(Math::UnitRandom() * Math::TWO_PI), *this );
            newUp = q * newUp;

            // Finally rotate this by given angle around randomised up
            q.FromAngleAxis( angle, newUp );
            return q * (*this);
        }

        inline Radian angleBetween(const Vector3& dest) const
        {
            Real lenProduct = length() * dest.length();

            // Divide by zero check
            if(lenProduct < 1e-6f)
                lenProduct = 1e-6f;

            Real f = dotProduct(dest) / lenProduct;

            f = Math::Clamp(f, (Real)-1.0, (Real)1.0);
            return Math::ACos(f);

        }
        Quaternion getRotationTo(const Vector3& dest,
            const Vector3& fallbackAxis = Vector3::ZERO) const
        {
            // Based on Stan Melax's article in Game Programming Gems
            Quaternion q;
            // Copy, since cannot modify local
            Vector3 v0 = *this;
            Vector3 v1 = dest;
            v0.normalise();
            v1.normalise();

            Real d = v0.dotProduct(v1);
            // If dot == 1, vectors are the same
            if (d >= 1.0f)
            {
                return Quaternion::IDENTITY;
            }
            if (d < (1e-6f - 1.0f))
            {
                if (fallbackAxis != Vector3::ZERO)
                {
                    // rotate 180 degrees about the fallback axis
                    q.FromAngleAxis(Radian(Math::PI), fallbackAxis);
                }
                else
                {
                    // Generate an axis
                    Vector3 axis = Vector3::UNIT_X.crossProduct(*this);
                    if (axis.isZeroLength()) // pick another if colinear
                        axis = Vector3::UNIT_Y.crossProduct(*this);
                    axis.normalise();
                    q.FromAngleAxis(Radian(Math::PI), axis);
                }
            }
            else
            {
                Real s = Math::Sqrt( (1+d)*2 );
                Real invs = 1 / s;

                Vector3 c = v0.crossProduct(v1);

                q.x = c.x * invs;
                q.y = c.y * invs;
                q.z = c.z * invs;
                q.w = s * 0.5f;
                q.normalise();
            }
            return q;
        }

        inline bool isZeroLength(void) const
        {
            Real sqlen = (x * x) + (y * y) + (z * z);
            return (sqlen < (1e-06 * 1e-06));

        }

        inline Vector3 normalisedCopy(void) const
        {
            Vector3 ret = *this;
            ret.normalise();
            return ret;
        }

        inline Vector3 reflect(const Vector3& normal) const
        {
            return Vector3( *this - ( 2 * this->dotProduct(normal) * normal ) );
        }

        inline bool positionEquals(const Vector3& rhs, Real tolerance = 1e-03) const
        {
            return Math::RealEqual(x, rhs.x, tolerance) &&
                Math::RealEqual(y, rhs.y, tolerance) &&
                Math::RealEqual(z, rhs.z, tolerance);

        }

        inline bool positionCloses(const Vector3& rhs, Real tolerance = 1e-03f) const
        {
            return squaredDistance(rhs) <=
                (squaredLength() + rhs.squaredLength()) * tolerance;
        }

        inline bool directionEquals(const Vector3& rhs,
            const Radian& tolerance) const
        {
            Real dot = dotProduct(rhs);
            Radian angle = Math::ACos(dot);

            return Math::Abs(angle.valueRadians()) <= tolerance.valueRadians();

        }

        inline bool isNaN() const
        {
            return Math::isNaN(x) || Math::isNaN(y) || Math::isNaN(z);
        }

        inline Vector3 primaryAxis() const
        {
            Real absx = Math::Abs(x);
            Real absy = Math::Abs(y);
            Real absz = Math::Abs(z);
            if (absx > absy)
                if (absx > absz)
                    return x > 0 ? Vector3::UNIT_X : Vector3::NEGATIVE_UNIT_X;
                else
                    return z > 0 ? Vector3::UNIT_Z : Vector3::NEGATIVE_UNIT_Z;
            else // absx <= absy
                if (absy > absz)
                    return y > 0 ? Vector3::UNIT_Y : Vector3::NEGATIVE_UNIT_Y;
                else
                    return z > 0 ? Vector3::UNIT_Z : Vector3::NEGATIVE_UNIT_Z;


        }

        // special points
        static const Vector3 ZERO;
        static const Vector3 UNIT_X;
        static const Vector3 UNIT_Y;
        static const Vector3 UNIT_Z;
        static const Vector3 NEGATIVE_UNIT_X;
        static const Vector3 NEGATIVE_UNIT_Y;
        static const Vector3 NEGATIVE_UNIT_Z;
        static const Vector3 UNIT_SCALE;

        inline _OgreExport friend std::ostream& operator <<
            ( std::ostream& o, const Vector3& v )
        {
            o << "Vector3(" << v.x << ", " << v.y << ", " << v.z << ")";
            return o;
        }
    };
}
#endif