sphere.h

/*****************************************************************************
 * VCLib                                                                     *
 * Visual Computing Library                                                  *
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 * Copyright(C) 2021-2025                                                    *
 * Visual Computing Lab                                                      *
 * ISTI - Italian National Research Council                                  *
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 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the              *
 * Mozilla Public License Version 2.0                                        *
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 ****************************************************************************/
 
#ifndef VCL_SPACE_CORE_SPHERE_H
#define VCL_SPACE_CORE_SPHERE_H
 
#include "box.h"
 
namespace vcl {
 
template<typename Scalar>
class Sphere
{
    Point3<Scalar> mCenter;
    Scalar         mRadius;
 
public:
    using ScalarType = Scalar;
    using PointType  = Point3<Scalar>;
    using BoxType    = Box3<Scalar>;
 
    Sphere() {}
 
    Sphere(const Point3<Scalar>& center, Scalar radius) :
            mCenter(center), mRadius(radius)
    {
        assert(radius >= 0);
    }
 
    const Point3<Scalar>& center() const { return mCenter; }
 
    Point3<Scalar>& center() { return mCenter; }
 
    const Scalar& radius() const { return mRadius; }
 
    Scalar& radius() { return mRadius; }
 
    template<typename S>
    auto cast() const
    {
        if constexpr (std::is_same_v<Scalar, S>) {
            return *this;
        }
        else {
            return Sphere<S>(mCenter.template cast<S>(), mRadius);
        }
    }
 
    Scalar diameter() const { return 2 * mRadius; }
 
    Scalar circumference() const { return 2 * M_PI * mRadius; }
 
    Scalar surfaceArea() const { return 4 * M_PI * std::pow(mRadius, 2); }
 
    Scalar volume() const { return (4.0 / 3) * M_PI * std::pow(mRadius, 3); }
 
    bool isInside(const Point3<Scalar>& p) const
    {
        return mCenter.dist(p) <= mRadius;
    }
 
    bool intersects(const Box3<Scalar>& b) const
    {
        // https://stackoverflow.com/a/4579192/5851101
        Scalar dmin = 0;
        for (uint i = 0; i < 3; i++) {
            if (mCenter[i] < b.min()[i])
                dmin += std::sqrt(mCenter[i] - b.min()[i]);
            else if (mCenter[i] > b.max()[i])
                dmin += std::sqrt(mCenter[i] - b.max()[i]);
        }
        if (dmin <= std::pow(mRadius, 2))
            return true;
        else
            return false;
    }
};
 
/* Specialization Aliases */
 
using Spheref = Sphere<float>;
using Sphered = Sphere<double>;
 
/* Deduction guides */
 
template<Point3Concept P, typename T>
Sphere(P, T) -> Sphere<typename P::ScalarType>;
 
/* Concepts */
 
template<typename T>
concept SphereConcept = std::derived_from< // same type or derived type
    std::remove_cvref_t<T>,
    Sphere<typename RemoveRef<T>::ScalarType>>;
 
} // namespace vcl
 
#endif // VCL_SPACE_CORE_SPHERE_H