fibonacci.h

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 * VCLib                                                                     *
 * Visual Computing Library                                                  *
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 * Copyright(C) 2021-2025                                                    *
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#ifndef VCL_MATH_FIBONACCI_H
#define VCL_MATH_FIBONACCI_H
 
#include <vclib/concepts/space/point.h>
 
#include <cmath>
#include <numbers>
 
namespace vcl {
 
namespace detail {
 
template<Point3Concept PointType>
PointType sphericalFibonacciPoint(uint i, uint n)
{
    using ScalarType = PointType::ScalarType;
 
    constexpr ScalarType PI = std::numbers::pi_v<ScalarType>;
 
    const ScalarType Phi = ScalarType(std::sqrt(ScalarType(5)) * 0.5 + 0.5);
    const ScalarType phi = 2.0 * PI * (i / Phi - std::floor(i / Phi));
    ScalarType       cosTheta = 1.0 - (2 * i + 1.0) / ScalarType(n);
    ScalarType       sinTheta = 1 - cosTheta * cosTheta;
    sinTheta =
        std::sqrt(std::min(ScalarType(1), std::max(ScalarType(0), sinTheta)));
    return PointType(cos(phi) * sinTheta, sin(phi) * sinTheta, cosTheta);
}
 
} // namespace detail
 
template<Point3Concept PointType>
std::vector<PointType> sphericalFibonacciPointSet(uint n)
{
    using ScalarType = PointType::ScalarType;
 
    std::vector<PointType> v(n);
    for (uint i = 0; i < n; ++i)
        v[i] = detail::sphericalFibonacciPoint<PointType>(i, n);
 
    return v;
}
 
} // namespace vcl
 
#endif // VCL_MATH_FIBONACCI_H