Quadric.h

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/*
 * Copyright (c) Meta Platforms, Inc. and affiliates.
 *
 * This source code is licensed under the MIT license found in the
 * LICENSE file in the root directory of this source tree.
 */
 
#ifndef META_OCEAN_GEOMETRY_CONE_H
#define META_OCEAN_GEOMETRY_CONE_H
 
#include "ocean/geometry/Geometry.h"
 
#include "ocean/math/HomogenousMatrix4.h"
#include "ocean/math/SquareMatrix4.h"
#include "ocean/math/Vector3.h"
 
namespace Ocean
{
 
namespace Geometry
{
 
/**
 * This class implements the base for all quadric object.
 * @ingroup geometry
 */
class OCEAN_GEOMETRY_EXPORT Quadric
{
    public:
 
        /**
         * Creates an invalid quadric.
         */
        Quadric();
 
        /**
         * Returns whether a given point lies inside or on the surface of the cone.
         * @param point Point to check
         * @return True, if so
         */
        bool isInside(const Vector3& point) const;
 
        /**
         * Returns whether a given point lies on the surface of the cone.
         * @param point Point to check
         * @return True, if so
         */
        bool isOnSurface(const Vector3& point) const;
 
        /**
         * Returns the quadric value for a given point.
         * @param point Point to check
         * @return Quadric value
         */
        Scalar value(const Vector3& point) const;
 
    protected:
 
        /**
         * Creates the combination of quadric and transformation matrix.
         * @param quadric Quadric matrix
         * @param transformation Transformation matrix to be combined with the quadric
         */
        void createCombinedQuadric(const SquareMatrix4& quadric, const HomogenousMatrix4 &transformation);
 
    protected:
 
        /// Holds the combined quadric and transformation matrix.
        SquareMatrix4 combinedQuadric;
};
 
/**
 * This class implements a cone quadric.
 * Quadric for cone Q:
 * Cone apex at: (m_x, m_y, m_z)
 * Cone angle: a
 *
 * [   1            0             0                      -m_x                 ]<br>
 * [   0            1             0                      -m_y                 ]<br>
 * [   0            0          -tan^2(a)              m_z tan^2               ]<br>
 * [  -m_x         -m_y        m_z tan^2(a)  (m_x^2 + m_y^2 - m_z^2 tan^2(a)) ]<br>
 *
 * Inside test: p^T * Q * p <= 0.0
 * @ingroup geometry
 */
class OCEAN_GEOMETRY_EXPORT Cone : public Quadric
{
    public:
 
        /**
         * Creates an invalid cone.
         */
        Cone();
 
        /**
         * Creates a cone by a given dihedral angle and a transformation.
         * @param angle Dihedral angle of the cone in radian, which is half of the aperture (aperture = 2 * angle)
         * @param transformation Transformation to transform the default cone defined about the z axis
         */
        Cone(const Scalar angle, const HomogenousMatrix4 &transformation);
};
 
/**
 * This class implements a sphere quadric.
 * Quadric for sphere Q:
 * Sphere midpoint at: (m_x, m_y, m_z)
 * Sphere radius: r
 *
 * [   1         0        0                 -m_x              ]<br>
 * [   0         1        0                 -m_y              ]<br>
 * [   0         0        1                 -m_z              ]<br>
 * [  -m_x     -m_y     -m_z    (m_x^2 + m_y^2 - m_z^2 - r^2) ]<br>
 *
 * Inside test: p^T * Q * p <= 0.0
 * @ingroup geometry
 */
class OCEAN_GEOMETRY_EXPORT Sphere : public Quadric
{
    public:
 
        /**
         * Creates an invalid sphere.
         */
        Sphere();
 
        /**
         * Creates a sphere by a given radius and a transformation.
         * @param radius Radius of the sphere
         * @param transformation Transformation to transform the default sphere defined with midpoint at (0, 0, 0)
         */
        Sphere(const Scalar radius, const HomogenousMatrix4 &transformation);
};
 
}
 
}
 
#endif // META_OCEAN_GEOMETRY_CONE_H