libcruft-util/geom/segment.hpp

/*
 * This Source Code Form is subject to the terms of the Mozilla Public
 * License, v. 2.0. If a copy of the MPL was not distributed with this
 * file, You can obtain one at http://mozilla.org/MPL/2.0/.
 *
 * Copyright 2018 Danny Robson <danny@nerdcruft.net>
 */

#pragma once

#include "../point.hpp"


namespace cruft::geom {
    /// Represents a line that has a start and an end.
    ///
    /// It is not valid to create an unbounded segment by fixing one of the
    /// points at infinity.
    template <size_t S, typename T>
    struct segment {
        cruft::point<S,T> a; /// The start of the segment.
        cruft::point<S,T> b; /// The end of the segment.

        /// Return a copy of this object with the underlying type casted to
        /// the specified type.
        template <typename CastT>
        segment<S,CastT>
        cast (void) const {
            return {
                .a = a.template cast<CastT> (),
                .b = b.template cast<CastT> ()
            };
        }
    };


    /// Return the squared distance from the closest point of the segment `s`
    /// to the point `p`.
    template <size_t S, typename T>
    T
    distance2 (segment<S,T> s, point<S,T> p)
    {
        const auto dir = s.b - s.a;
        const auto t1 = dot (p - s.a, dir);
        if (t1 < 0)
            return distance2 (p, s.a);

        const auto t2 = dot (dir, dir);
        if (t2 < t1)
            return distance2 (p, s.b);

        auto t = t1 / t2;
        return distance2 (p, s.a + t * dir);
    }


    /// Return the distance from a the closest point of the segment `s` to
    /// the point `p`.
    template <size_t S, typename T>
    T
    distance (segment<S,T> s, point<S,T> p)
    {
        return std::sqrt (distance2 (s, p));
    }


    /// Returns the un-normalised direction of the segment from its start to
    /// end components. ie, `a' to `b'.
    template <size_t S, typename T>
    cruft::vector<S,T>
    udirection (segment<S,T> const &val)
    {
        return val.b - val.a;
    }


    /// Returns the normalised direction of the segment.
    template <size_t S, typename T>
    cruft::vector<S,T>
    ndirection (segment<S,T> const &val)
    {
        return normalised (udirection (val));
    }


    using segment2i = segment<2,int>;
    using segment3i = segment<3,int>;

    using segment2f = segment<2,float>;
    using segment3f = segment<3,float>;


    template <size_t S, typename T>
    segment (point<S,T>, point<S,T>) -> segment<S,T>;
}