/*

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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/

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*/

// This file is based on material originally from:

// Geometric Tools, LLC

// Copyright (c) 1998-2010

// Distributed under the Boost Software License, Version 1.0.

// http://www.boost.org/LICENSE_1_0.txt

// http://www.geometrictools.com/License/Boost/LICENSE_1_0.txt

#ifndef __Plane_H__

#define __Plane_H__

#include "OgrePrerequisites.h"

#include "OgreVector.h"

#include "OgreAxisAlignedBox.h"

namespace Ogre {

    /** \addtogroup Core

    *  @{

    */

    /** \addtogroup Math

    *  @{

    */

    /** Defines a plane in 3D space.

        A plane is defined in 3D space by the equation

        ```

        Ax + By + Cz + D = 0

        ```

        @par

            This equates to a vector (the normal of the plane, whose x, y

            and z components equate to the coefficients A, B and C

            respectively), and a constant (D) which is the distance along

            the normal you have to go to move the plane back to the origin.

     */

    class _OgreExport Plane

    {

    public:

        Vector3 normal;

        Real d;

    public:

        /** Default constructor - sets everything to 0.

        */

        Plane() : normal(Vector3::ZERO), d(0.0f) {}

        /** Construct a plane through a normal, and a distance to move the plane along the normal.*/

        Plane(const Vector3& rkNormal, Real fConstant)

        {

            normal = rkNormal;

            d = -fConstant;

        }

        /** Construct a plane using the 4 constants directly **/

        Plane(Real a, Real b, Real c, Real _d) : normal(a, b, c), d(_d) {}

        /// @overload

        explicit Plane(const Vector4& v) : normal(v.xyz()), d(v.w) {}

        Plane(const Vector3& rkNormal, const Vector3& rkPoint)

        {

            redefine(rkNormal, rkPoint);

        }

        Plane(const Vector3& p0, const Vector3& p1, const Vector3& p2)

        {

            redefine(p0, p1, p2);

        }

        /** The "positive side" of the plane is the half space to which the

            plane normal points. The "negative side" is the other half

            space. The flag "no side" indicates the plane itself.

        */

        enum Side

        {

            NO_SIDE,

            POSITIVE_SIDE,

            NEGATIVE_SIDE,

            BOTH_SIDE

        };

        Side getSide(const Vector3& rkPoint) const

        {

            Real fDistance = getDistance(rkPoint);

            if (fDistance < 0.0)

                return Plane::NEGATIVE_SIDE;

            if (fDistance > 0.0)

                return Plane::POSITIVE_SIDE;

            return Plane::NO_SIDE;

        }

        /**

        Returns the side where the alignedBox is. The flag BOTH_SIDE indicates an intersecting box.

        One corner ON the plane is sufficient to consider the box and the plane intersecting.

        */

        Side getSide(const AxisAlignedBox& box) const

        {

            if (box.isNull())

                return NO_SIDE;

            if (box.isInfinite())

                return BOTH_SIDE;

            return getSide(box.getCenter(), box.getHalfSize());

        }

        /** Returns which side of the plane that the given box lies on.

            The box is defined as centre/half-size pairs for effectively.

        @param centre The centre of the box.

        @param halfSize The half-size of the box.

        @return

            POSITIVE_SIDE if the box complete lies on the "positive side" of the plane,

            NEGATIVE_SIDE if the box complete lies on the "negative side" of the plane,

            and BOTH_SIDE if the box intersects the plane.

        */

        Side getSide(const Vector3& centre, const Vector3& halfSize) const

        {

            // Calculate the distance between box centre and the plane

            Real dist = getDistance(centre);

            // Calculate the maximise allows absolute distance for

            // the distance between box centre and plane

            Real maxAbsDist = normal.absDotProduct(halfSize);

            if (dist < -maxAbsDist)

                return NEGATIVE_SIDE;

            if (dist > +maxAbsDist)

                return POSITIVE_SIDE;

            return BOTH_SIDE;

        }

        /** This is a pseudodistance. The sign of the return value is

            positive if the point is on the positive side of the plane,

            negative if the point is on the negative side, and zero if the

            point is on the plane.

            @par

            The absolute value of the return value is the true distance only

            when the plane normal is a unit length vector.

        */

        Real getDistance(const Vector3& rkPoint) const

        {

            return normal.dotProduct(rkPoint) + d;

        }

        /** Redefine this plane based on 3 points. */

        void redefine(const Vector3& p0, const Vector3& p1, const Vector3& p2)

        {

            normal = Math::calculateBasicFaceNormal(p0, p1, p2);

            d = -normal.dotProduct(p0);

        }

        /** Redefine this plane based on a normal and a point. */

        void redefine(const Vector3& rkNormal, const Vector3& rkPoint)

        {

            normal = rkNormal;

            d = -rkNormal.dotProduct(rkPoint);

        }

        /** Project a vector onto the plane. 

        @remarks This gives you the element of the input vector that is perpendicular 

            to the normal of the plane. You can get the element which is parallel

            to the normal of the plane by subtracting the result of this method

            from the original vector, since parallel + perpendicular = original.

        @param v The input vector

        */

        Vector3 projectVector(const Vector3& v) const

        {

            // We know plane normal is unit length, so use simple method

            Matrix3 xform;

            xform[0][0] = 1.0f - normal.x * normal.x;

            xform[0][1] = -normal.x * normal.y;

            xform[0][2] = -normal.x * normal.z;

            xform[1][0] = -normal.y * normal.x;

            xform[1][1] = 1.0f - normal.y * normal.y;

            xform[1][2] = -normal.y * normal.z;

            xform[2][0] = -normal.z * normal.x;

            xform[2][1] = -normal.z * normal.y;

            xform[2][2] = 1.0f - normal.z * normal.z;

            return xform * v;

        }

        /** Normalises the plane.

            This method normalises the plane's normal and the length scale of d

            is as well.

            @note

                This function will not crash for zero-sized vectors, but there

                will be no changes made to their components.

            @return The previous length of the plane's normal.

        */

        Real normalise(void)

        {

            Real fLength = normal.length();

            // 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;

                normal *= fInvLength;

                d *= fInvLength;

            }

            return fLength;

        }

        /// Get flipped plane, with same location but reverted orientation

        Plane operator - () const

        {

            return Plane(-(normal.x), -(normal.y), -(normal.z), -d); // not equal to Plane(-normal, -d)

        }

        /// Comparison operator

        bool operator==(const Plane& rhs) const

        {

            return (rhs.d == d && rhs.normal == normal);

        }

        bool operator!=(const Plane& rhs) const

        {

            return (rhs.d != d || rhs.normal != normal);

        }

        friend std::ostream& operator<<(std::ostream& o, const Plane& p)

        {

            o << "Plane(normal=" << p.normal << ", d=" << p.d << ")";

            return o;

        }

    };

    inline Plane operator * (const Matrix4& mat, const Plane& p)

    {

        Plane ret;

        Matrix4 invTrans = mat.inverse().transpose();

        Vector4 v4( p.normal.x, p.normal.y, p.normal.z, p.d );

        v4 = invTrans * v4;

        ret.normal.x = v4.x;

        ret.normal.y = v4.y;

        ret.normal.z = v4.z;

        ret.d = v4.w / ret.normal.normalise();

        return ret;

    }

    inline bool Math::intersects(const Plane& plane, const AxisAlignedBox& box)

    {

        return plane.getSide(box) == Plane::BOTH_SIDE;

    }

    typedef std::vector<Plane> PlaneList;

    /** @} */

    /** @} */

} // namespace Ogre

#endif