Program Listing for File point.hpp

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/*-
 * SPDX-License-Identifier: BSD-2-Clause
 *
 * Copyright (c) 2020 NKI/AVL, Netherlands Cancer Institute
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions are met:
 *
 * 1. Redistributions of source code must retain the above copyright notice, this
 *    list of conditions and the following disclaimer
 * 2. Redistributions in binary form must reproduce the above copyright notice,
 *    this list of conditions and the following disclaimer in the documentation
 *    and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED
 * WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE
 * DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR
 * ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES
 * (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND
 * ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
 * (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS
 * SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
 */

#pragma once

#include <array>
#include <cmath>
#include <complex>
#include <cstdint>
#include <functional>
#include <valarray>

#if __has_include(<clipper/core/coords.h>)
#define HAVE_LIBCLIPPER 1
#pragma GCC diagnostic push
#pragma GCC diagnostic ignored "-Wignored-qualifiers"
#include <clipper/core/coords.h>
#pragma GCC diagnostic pop
#endif

namespace cif
{

// --------------------------------------------------------------------

const double
    kPI = 3.141592653589793238462643383279502884;

// --------------------------------------------------------------------
template <typename T>
class quaternion_type
{
  public:
    using value_type = T;

    constexpr explicit quaternion_type(value_type const &value_a = {}, value_type const &value_b = {}, value_type const &value_c = {}, value_type const &value_d = {})
        : a(value_a)
        , b(value_b)
        , c(value_c)
        , d(value_d)
    {
    }

    constexpr explicit quaternion_type(std::complex<value_type> const &z0, std::complex<value_type> const &z1 = std::complex<value_type>())
        : a(z0.real())
        , b(z0.imag())
        , c(z1.real())
        , d(z1.imag())
    {
    }

    constexpr quaternion_type(quaternion_type const &) = default;
    constexpr quaternion_type(quaternion_type &&) = default;

    template <typename X>
    constexpr explicit quaternion_type(quaternion_type<X> const &rhs)
        : a(static_cast<value_type>(rhs.a))
        , b(static_cast<value_type>(rhs.b))
        , c(static_cast<value_type>(rhs.c))
        , d(static_cast<value_type>(rhs.d))
    {
    }

    // accessors

    constexpr value_type real() const
    {
        return a;
    }

    constexpr quaternion_type unreal() const
    {
        return { 0, b, c, d };
    }

    constexpr void swap(quaternion_type &o)
    {
        std::swap(a, o.a);
        std::swap(b, o.b);
        std::swap(c, o.c);
        std::swap(d, o.d);
    }

    // assignment operators

    template <typename X>
    constexpr quaternion_type &operator=(quaternion_type<X> const &rhs)
    {
        a = static_cast<value_type>(rhs.a);
        b = static_cast<value_type>(rhs.b);
        c = static_cast<value_type>(rhs.c);
        d = static_cast<value_type>(rhs.d);

        return *this;
    }

    constexpr quaternion_type &operator=(quaternion_type const &rhs)
    {
        a = rhs.a;
        b = rhs.b;
        c = rhs.c;
        d = rhs.d;

        return *this;
    }

    constexpr quaternion_type &operator=(value_type const &rhs)
    {
        a = rhs;

        b = c = d = static_cast<value_type>(0);

        return *this;
    }

    // parts are set to zero.
    constexpr quaternion_type &operator=(std::complex<value_type> const &rhs)
    {
        a = rhs.real();
        b = rhs.imag();

        c = d = static_cast<value_type>(0);

        return *this;
    }

    // other assignment-related operators

    constexpr quaternion_type &operator+=(value_type const &rhs)
    {
        a += rhs;
        return *this;
    }

    constexpr quaternion_type &operator+=(std::complex<value_type> const &rhs)
    {
        a += std::real(rhs);
        b += std::imag(rhs);
        return *this;
    }

    template <class X>
    constexpr quaternion_type &operator+=(quaternion_type<X> const &rhs)
    {
        a += rhs.a;
        b += rhs.b;
        c += rhs.c;
        d += rhs.d;
        return *this;
    }

    constexpr quaternion_type &operator-=(value_type const &rhs)
    {
        a -= rhs;
        return *this;
    }

    constexpr quaternion_type &operator-=(std::complex<value_type> const &rhs)
    {
        a -= std::real(rhs);
        b -= std::imag(rhs);
        return *this;
    }

    template <class X>
    constexpr quaternion_type &operator-=(quaternion_type<X> const &rhs)
    {
        a -= rhs.a;
        b -= rhs.b;
        c -= rhs.c;
        d -= rhs.d;
        return *this;
    }

    constexpr quaternion_type &operator*=(value_type const &rhs)
    {
        a *= rhs;
        b *= rhs;
        c *= rhs;
        d *= rhs;
        return *this;
    }

    constexpr quaternion_type &operator*=(std::complex<value_type> const &rhs)
    {
        value_type ar = rhs.real();
        value_type br = rhs.imag();
        quaternion_type result(a * ar - b * br, a * br + b * ar, c * ar + d * br, -c * br + d * ar);
        swap(result);
        return *this;
    }

    friend constexpr quaternion_type operator*(const quaternion_type &a, const quaternion_type &b)
    {
        auto result = a;
        result *= b;
        return result;
    }

    template <typename X>
    constexpr quaternion_type &operator*=(quaternion_type<X> const &rhs)
    {
        value_type ar = static_cast<value_type>(rhs.a);
        value_type br = static_cast<value_type>(rhs.b);
        value_type cr = static_cast<value_type>(rhs.c);
        value_type dr = static_cast<value_type>(rhs.d);

        quaternion_type result(a * ar - b * br - c * cr - d * dr, a * br + b * ar + c * dr - d * cr, a * cr - b * dr + c * ar + d * br, a * dr + b * cr - c * br + d * ar);
        swap(result);
        return *this;
    }

    constexpr quaternion_type &operator/=(value_type const &rhs)
    {
        a /= rhs;
        b /= rhs;
        c /= rhs;
        d /= rhs;
        return *this;
    }

    constexpr quaternion_type &operator/=(std::complex<value_type> const &rhs)
    {
        value_type ar = rhs.real();
        value_type br = rhs.imag();
        value_type denominator = ar * ar + br * br;
        quaternion_type result((+a * ar + b * br) / denominator, (-a * br + b * ar) / denominator, (+c * ar - d * br) / denominator, (+c * br + d * ar) / denominator);
        swap(result);
        return *this;
    }

    template <typename X>
    constexpr quaternion_type &operator/=(quaternion_type<X> const &rhs)
    {
        value_type ar = static_cast<value_type>(rhs.a);
        value_type br = static_cast<value_type>(rhs.b);
        value_type cr = static_cast<value_type>(rhs.c);
        value_type dr = static_cast<value_type>(rhs.d);

        value_type denominator = ar * ar + br * br + cr * cr + dr * dr;
        quaternion_type result((+a * ar + b * br + c * cr + d * dr) / denominator, (-a * br + b * ar - c * dr + d * cr) / denominator, (-a * cr + b * dr + c * ar - d * br) / denominator, (-a * dr - b * cr + c * br + d * ar) / denominator);
        swap(result);
        return *this;
    }

    friend constexpr quaternion_type normalize(quaternion_type q)
    {
        std::valarray<value_type> t(4);

        t[0] = q.a;
        t[1] = q.b;
        t[2] = q.c;
        t[3] = q.d;

        t *= t;

        value_type length = std::sqrt(t.sum());

        if (length > 0.001)
            q /= static_cast<value_type>(length);
        else
            q = quaternion_type(1, 0, 0, 0);

        return q;
    }

    friend constexpr quaternion_type conj(quaternion_type q)
    {
        return quaternion_type{ +q.a, -q.b, -q.c, -q.d };
    }

    constexpr value_type get_a() const { return a; }
    constexpr value_type get_b() const { return b; }
    constexpr value_type get_c() const { return c; }
    constexpr value_type get_d() const { return d; }

    constexpr bool operator==(const quaternion_type &rhs) const
    {
        return a == rhs.a and b == rhs.b and c == rhs.c and d == rhs.d;
    }

    constexpr bool operator!=(const quaternion_type &rhs) const
    {
        return a != rhs.a or b != rhs.b or c != rhs.c or d != rhs.d;
    }

    constexpr operator bool() const
    {
        return a != 0 or b != 0 or c != 0 or d != 0;
    }

  private:
    value_type a, b, c, d;
};

template <typename T>
inline quaternion_type<T> spherical(T const &rho, T const &theta, T const &phi1, T const &phi2)
{
    T cos_phi1 = std::cos(phi1);
    T cos_phi2 = std::cos(phi2);

    T a = std::cos(theta) * cos_phi1 * cos_phi2;
    T b = std::sin(theta) * cos_phi1 * cos_phi2;
    T c = std::sin(phi1) * cos_phi2;
    T d = std::sin(phi2);

    quaternion_type result(a, b, c, d);
    result *= rho;

    return result;
}

using quaternion = quaternion_type<float>;

// --------------------------------------------------------------------

template <typename F>
struct point_type
{
    using value_type = F;

    value_type m_x,
        m_y,
        m_z;

    constexpr point_type()
        : m_x(0)
        , m_y(0)
        , m_z(0)
    {
    }

    constexpr point_type(value_type x, value_type y, value_type z)
        : m_x(x)
        , m_y(y)
        , m_z(z)
    {
    }

    template <typename PF>
    constexpr point_type(const point_type<PF> &pt)
        : m_x(static_cast<F>(pt.m_x))
        , m_y(static_cast<F>(pt.m_y))
        , m_z(static_cast<F>(pt.m_z))
    {
    }

    constexpr point_type(const std::tuple<value_type, value_type, value_type> &pt)
        : point_type(std::get<0>(pt), std::get<1>(pt), std::get<2>(pt))
    {
    }

#if HAVE_LIBCLIPPER
    constexpr point_type(const clipper::Coord_orth &pt)
        : m_x(pt[0])
        , m_y(pt[1])
        , m_z(pt[2])
    {
    }

    constexpr point_type &operator=(const clipper::Coord_orth &rhs)
    {
        m_x = rhs[0];
        m_y = rhs[1];
        m_z = rhs[2];
        return *this;
    }
#endif

    template <typename PF>
    constexpr point_type &operator=(const point_type<PF> &rhs)
    {
        m_x = static_cast<F>(rhs.m_x);
        m_y = static_cast<F>(rhs.m_y);
        m_z = static_cast<F>(rhs.m_z);
        return *this;
    }

    constexpr value_type &get_x() { return m_x; }
    constexpr value_type get_x() const { return m_x; }
    constexpr void set_x(value_type x) { m_x = x; }

    constexpr value_type &get_y() { return m_y; }
    constexpr value_type get_y() const { return m_y; }
    constexpr void set_y(value_type y) { m_y = y; }

    constexpr value_type &get_z() { return m_z; }
    constexpr value_type get_z() const { return m_z; }
    constexpr void set_z(value_type z) { m_z = z; }

    constexpr point_type &operator+=(const point_type &rhs)
    {
        m_x += rhs.m_x;
        m_y += rhs.m_y;
        m_z += rhs.m_z;

        return *this;
    }

    constexpr point_type &operator+=(value_type d)
    {
        m_x += d;
        m_y += d;
        m_z += d;

        return *this;
    }

    template <typename F2>
    friend constexpr auto operator+(const point_type &lhs, const point_type<F2> &rhs)
    {
        return point_type<std::common_type_t<value_type, F2>>(lhs.m_x + rhs.m_x, lhs.m_y + rhs.m_y, lhs.m_z + rhs.m_z);
    }

    constexpr point_type &operator-=(const point_type &rhs)
    {
        m_x -= rhs.m_x;
        m_y -= rhs.m_y;
        m_z -= rhs.m_z;

        return *this;
    }

    constexpr point_type &operator-=(value_type d)
    {
        m_x -= d;
        m_y -= d;
        m_z -= d;

        return *this;
    }

    template <typename F2>
    friend constexpr auto operator-(const point_type &lhs, const point_type<F2> &rhs)
    {
        return point_type<std::common_type_t<value_type, F2>>(lhs.m_x - rhs.m_x, lhs.m_y - rhs.m_y, lhs.m_z - rhs.m_z);
    }

    friend constexpr point_type operator-(const point_type &pt)
    {
        return point_type(-pt.m_x, -pt.m_y, -pt.m_z);
    }

    constexpr point_type &operator*=(value_type rhs)
    {
        m_x *= rhs;
        m_y *= rhs;
        m_z *= rhs;
        return *this;
    }

    template <typename F2>
    friend constexpr auto operator*(const point_type &pt, F2 f)
    {
        return point_type<std::common_type_t<value_type, F2>>(pt.m_x * f, pt.m_y * f, pt.m_z * f);
    }

    template <typename F2>
    friend constexpr auto operator*(F2 f, const point_type &pt)
    {
        return point_type<std::common_type_t<value_type, F2>>(pt.m_x * f, pt.m_y * f, pt.m_z * f);
    }

    constexpr point_type &operator/=(value_type rhs)
    {
        m_x /= rhs;
        m_y /= rhs;
        m_z /= rhs;
        return *this;
    }

    template <typename F2>
    friend constexpr auto operator/(const point_type &pt, F2 f)
    {
        return point_type<std::common_type_t<value_type, F2>>(pt.m_x / f, pt.m_y / f, pt.m_z / f);
    }

    constexpr value_type normalize()
    {
        auto length = m_x * m_x + m_y * m_y + m_z * m_z;
        if (length > 0)
        {
            length = std::sqrt(length);
            operator/=(length);
        }
        return length;
    }

    constexpr void rotate(const quaternion &q)
    {
        quaternion_type<value_type> p(0, m_x, m_y, m_z);

        p = q * p * conj(q);

        m_x = p.get_b();
        m_y = p.get_c();
        m_z = p.get_d();
    }

    constexpr void rotate(const quaternion &q, point_type pivot)
    {
        operator-=(pivot);
        rotate(q);
        operator+=(pivot);
    }

#if HAVE_LIBCLIPPER
    operator clipper::Coord_orth() const
    {
        return clipper::Coord_orth(m_x, m_y, m_z);
    }
#endif

    constexpr operator std::tuple<const value_type &, const value_type &, const value_type &>() const
    {
        return std::make_tuple(std::ref(m_x), std::ref(m_y), std::ref(m_z));
    }

    constexpr operator std::tuple<value_type &, value_type &, value_type &>()
    {
        return std::make_tuple(std::ref(m_x), std::ref(m_y), std::ref(m_z));
    }

    constexpr bool operator==(const point_type &rhs) const
    {
        return m_x == rhs.m_x and m_y == rhs.m_y and m_z == rhs.m_z;
    }

    // consider point as a vector... perhaps I should rename point?

    constexpr value_type length_sq() const
    {
        return m_x * m_x + m_y * m_y + m_z * m_z;
    }

    constexpr value_type length() const
    {
        return std::sqrt(length_sq());
    }

    friend std::ostream &operator<<(std::ostream &os, const point_type &pt)
    {
        os << '(' << pt.m_x << ',' << pt.m_y << ',' << pt.m_z << ')';
        return os;
    }
};

using point = point_type<float>;

// --------------------------------------------------------------------
// several standard 3d operations

template <typename F1, typename F2>
constexpr auto distance_squared(const point_type<F1> &a, const point_type<F2> &b)
{
    return (a.m_x - b.m_x) * (a.m_x - b.m_x) +
           (a.m_y - b.m_y) * (a.m_y - b.m_y) +
           (a.m_z - b.m_z) * (a.m_z - b.m_z);
}

template <typename F1, typename F2>
constexpr auto distance(const point_type<F1> &a, const point_type<F2> &b)
{
    return std::sqrt(
        (a.m_x - b.m_x) * (a.m_x - b.m_x) +
        (a.m_y - b.m_y) * (a.m_y - b.m_y) +
        (a.m_z - b.m_z) * (a.m_z - b.m_z));
}

template <typename F1, typename F2>
inline constexpr auto dot_product(const point_type<F1> &a, const point_type<F2> &b)
{
    return a.m_x * b.m_x + a.m_y * b.m_y + a.m_z * b.m_z;
}

template <typename F1, typename F2>
inline constexpr auto cross_product(const point_type<F1> &a, const point_type<F2> &b)
{
    return point_type<std::common_type_t<F1, F2>>(
        a.m_y * b.m_z - b.m_y * a.m_z,
        a.m_z * b.m_x - b.m_z * a.m_x,
        a.m_x * b.m_y - b.m_x * a.m_y);
}

template <typename F>
constexpr auto angle(const point_type<F> &p1, const point_type<F> &p2, const point_type<F> &p3)
{
    point_type<F> v1 = p1 - p2;
    point_type<F> v2 = p3 - p2;

    return std::acos(dot_product(v1, v2) / (v1.length() * v2.length())) * 180 / kPI;
}

template <typename F>
constexpr auto dihedral_angle(const point_type<F> &p1, const point_type<F> &p2, const point_type<F> &p3, const point_type<F> &p4)
{
    point_type<F> v12 = p1 - p2; // vector from p2 to p1
    point_type<F> v43 = p4 - p3; // vector from p3 to p4

    point_type<F> z = p2 - p3; // vector from p3 to p2

    point_type<F> p = cross_product(z, v12);
    point_type<F> x = cross_product(z, v43);
    point_type<F> y = cross_product(z, x);

    auto u = dot_product(x, x);
    auto v = dot_product(y, y);

    F result = 360;
    if (u > 0 and v > 0)
    {
        u = dot_product(p, x) / std::sqrt(u);
        v = dot_product(p, y) / std::sqrt(v);
        if (u != 0 or v != 0)
            result = std::atan2(v, u) * static_cast<F>(180 / kPI);
    }

    return result;
}

template <typename F>
constexpr auto cosinus_angle(const point_type<F> &p1, const point_type<F> &p2, const point_type<F> &p3, const point_type<F> &p4)
{
    point_type<F> v12 = p1 - p2;
    point_type<F> v34 = p3 - p4;

    auto x = dot_product(v12, v12) * dot_product(v34, v34);

    return x > 0 ? dot_product(v12, v34) / std::sqrt(x) : 0;
}

template <typename F>
constexpr auto distance_point_to_line(const point_type<F> &l1, const point_type<F> &l2, const point_type<F> &p)
{
    auto line = l2 - l1;
    auto p_to_l1 = p - l1;
    auto p_to_l2 = p - l2;
    auto cross = cross_product(p_to_l1, p_to_l2);
    return cross.length() / line.length();
}

// --------------------------------------------------------------------
point nudge(point p, float offset);

// --------------------------------------------------------------------

quaternion construct_from_angle_axis(float angle, point axis);

std::tuple<double, point> quaternion_to_angle_axis(quaternion q);

quaternion construct_for_dihedral_angle(point p1, point p2, point p3, point p4,
    float angle, float esd);

point centroid(const std::vector<point> &pts);

point center_points(std::vector<point> &pts);

quaternion align_points(const std::vector<point> &a, const std::vector<point> &b);

double RMSd(const std::vector<point> &a, const std::vector<point> &b);

// --------------------------------------------------------------------
template <int N>
class spherical_dots
{
  public:
    constexpr static int P = 2 * N * 1;

    constexpr static double W = (4 * kPI) / P;

    using array_type = typename std::array<point, P>;

    using iterator = typename array_type::const_iterator;

    static spherical_dots &instance()
    {
        static spherical_dots sInstance;
        return sInstance;
    }

    std::size_t size() const { return P; }

    const point operator[](uint32_t inIx) const { return m_points[inIx]; }

    iterator begin() const { return m_points.begin(); }

    iterator end() const { return m_points.end(); }

    double weight() const { return W; }

    spherical_dots()
    {
        const double
            kGoldenRatio = (1 + std::sqrt(5.0)) / 2;

        auto p = m_points.begin();

        for (int32_t i = -N; i <= N; ++i)
        {
            double lat = std::asin((2.0 * i) / P);
            double lon = std::fmod(i, kGoldenRatio) * 2 * kPI / kGoldenRatio;

            p->m_x = std::sin(lon) * std::cos(lat);
            p->m_y = std::cos(lon) * std::cos(lat);
            p->m_z = std::sin(lat);

            ++p;
        }
    }

  private:
    array_type m_points;
};

} // namespace cif