/* * All or portions of this file Copyright (c) Amazon.com, Inc. or its affiliates or * its licensors. * * For complete copyright and license terms please see the LICENSE at the root of this * distribution (the "License"). All use of this software is governed by the License, * or, if provided, by the license below or the license accompanying this file. Do not * remove or modify any license notices. This file is distributed on an "AS IS" BASIS, * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * */ #pragma once #include #include #include "StandardHeaders.h" namespace MCore { // forward declarations class AABB; /** * 3D Oriented Bounding Box (OBB) template. * This is basically a AABB with an arbitrary rotation. */ class MCORE_API OBB { public: /** * The constructor. * This automatically initializes the box. After initialization the box is invalid since it basically has no size yet. * The IsValid() method will return false. */ MCORE_INLINE OBB() { Init(); } /** * Construct the OBB from a given axis aligned bounding box and a transformation. * @param aabb The axis aligned bounding box. * @param transformation The transformation of the box. */ MCORE_INLINE OBB(const AABB& aabb, const AZ::Transform& transformation) { Create(aabb, transformation); } /** * Construct the OBB from a center, extends and a rotation. * @param center The center of the box. * @param extents The extents of the box, which start at the center of the box. * @param rot The matrix, representing the transformation of the box. */ MCORE_INLINE OBB(const AZ::Vector3& center, const AZ::Vector3& extents, const AZ::Transform& rot) : mRotation(rot) , mExtents(extents) , mCenter(center) {} /** * Reset the OBB with as center 0,0,0, infinite negative extents and no rotation. * This makes the box an invalid box as well, because the extents have not been set. */ MCORE_INLINE void Init(); /** * Initialize the box from a set of points. * This uses the covariant matrix and eigen vectors to fit the box to the set of points. * @param points The set of points to fit the box to. * @param numPoints The number of points inside array specified as first parameter. */ void InitFromPoints(const AZ::Vector3* points, uint32 numPoints); /** * Check if this box OBB contains a given point or not. * @param p The point to check. * @result Returns true when the point is inside this box, otherwise false is returned. */ bool Contains(const AZ::Vector3& p) const; /** * Check if this OBB is inside another specified box. * @param box The OBB to check. * @result Returns true when this OBB is inside the box specified as parameter. */ bool CheckIfIsInside(const OBB& box) const; /** * Create the OBB from a given AABB and a matrix. * @param aabb The axis aligned bounding box. * @param mat The matrix, which represents the orientation of the box. */ void Create(const AABB& aabb, const AZ::Transform& mat); /** * Transform this OBB with a given matrix. * This means the transformation specified as parameter will be applied to the current transformation of the OBB. * So the transformation specified is NOT an absolute rotation, but a relative transformation. * @param transMatrix The relative transformation matrix, to be applied to the current transformation. */ void Transform(const AZ::Transform& transMatrix); /** * Calculate the transformed version of this OBB. * @param rotMatrix The transformation matrix to be applied to the rotation of this OBB, so not an absolute rotation! * @param outOBB A pointer to the OBB to fill with the rotated version of this OBB. */ void Transformed(const AZ::Transform& rotMatrix, OBB* outOBB) const; /** * Check if this is a valid OBB or not. * The box is only valid if the extents are non-negative. * @result Returns true when the OBB is valid, otherwise false is returned. */ MCORE_INLINE bool CheckIfIsValid() const; /** * Set the center of the box. * @param center The new center of the box. */ MCORE_INLINE void SetCenter(const AZ::Vector3& center) { mCenter = center; } /** * Set the extents of the box. * @param extents The new extents of the box. */ MCORE_INLINE void SetExtents(const AZ::Vector3& extents) { mExtents = extents; } /** * Set the transformation of the box. * @param transform The new transformation of the box. */ MCORE_INLINE void SetTransformation(const AZ::Transform& transform) { mRotation = transform; } /** * Get the center of the box. * @result The center point of the box. */ MCORE_INLINE const AZ::Vector3& GetCenter() const { return mCenter; } /** * Get the extents of the box. * @result The extents of the box, which start at the center. */ MCORE_INLINE const AZ::Vector3& GetExtents() const { return mExtents; } /** * Get the transformation of the box. * @result The transformation of the box. */ MCORE_INLINE const AZ::Transform& GetTransformation() const { return mRotation; } /** * Calculate the 8 corner points of the box. * The layout is as follows: * 
         *
         *     7+------+6
         *     /|     /|
         *    / |    / |
         *   / 4+---/--+5
         * 3+------+2 /
         *  | /    | /
         *  |/     |/
         * 0+------+1
         *
         *
* @param outPoints the array of at least 8 vectors to write the points in. */ void CalcCornerPoints(AZ::Vector3* outPoints) const; /** * Calculate the rotated minimum and maximum points of the box. * After rotation it is possible that the min point is not really the min anymore though. The same goes for max. * But the main use for this method however is to quickly approximate an AABB from this OBB, without having to * calculate all 8 corner points. * 
         *
         *        +------+MAX
         *       /|     /|
         *      / |    / |
         *     /  +---/--+
         *    +------+  /
         *    | /    | /
         *    |/     |/
         * MIN+------+
         *
         *
* @param outMin The vector that we will write the minimum point to. * @param outMax The vector that we will write the maximum point to. */ void CalcMinMaxPoints(AZ::Vector3* outMin, AZ::Vector3* outMax) const; private: AZ::Transform mRotation; /**< The rotation of the box. */ // TODO: store the center inside the translation component and extents inside last column? AZ::Vector3 mExtents; /**< The extents of the box. */ AZ::Vector3 mCenter; /**< The center of the box. */ /** * Calculate the three eigen vectors for a symmetric matrix. * @param A The symmetric matrix values. * @param v1 The first output eigen vector. * @param v2 The second output eigen vector. * @param v3 The third output eigen vector. */ void GetRealSymmetricEigenvectors(const float A[6], AZ::Vector3& v1, AZ::Vector3& v2, AZ::Vector3& v3); /** * Calculate the eigen vector from a symmetric matrix. * This assumes that the specified eigenvalue is of order 1. * @param A The symmetric matrix values. * @param eigenValue The eigen value. * @param v1 The output eigen vector. */ void CalcSymmetricEigenVector(const float A[6], float eigenValue, AZ::Vector3& v1); /** * Calculate the pair of eigen vectors from a symmetric matrix. * This assumes that the specified eigen value is of order 2. * @param A The symmetric matrix values. * @param eigenValue The eigen value. * @param v1 The first output eigen vector. * @param v2 The second output eigen vector. */ void CalcSymmetricEigenPair(const float A[6], float eigenValue, AZ::Vector3& v1, AZ::Vector3& v2); /** * Calculate the covariance matrix from a set of points. * @param points The set of points to calculate the covariance matrix from. * @param numPoints The number of points inside the specified set of points. * @param mean The statistical mean will be output in this vector. * @param C The covariance matrix values that will be written to. Since the matrix is symmetric we only output one triangle of the 3x3 matrix. */ void CovarianceMatrix(const AZ::Vector3 * points, uint32 numPoints, AZ::Vector3 & mean, float C[6]); void InitFromPointsRange(const AZ::Vector3* points, uint32 numPoints, float xDegrees, float* outMinArea, AABB* outMinBox, AZ::Transform* outMinMatrix); }; // include the inline code #include "OBB.inl" } // namespace MCore