aabb_functions.h

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#pragma once
 
#include <liboscar/concepts/input_range_with_size_greater_than.h>
#include <liboscar/maths/aabb.h>
#include <liboscar/maths/common_functions.h>
#include <liboscar/maths/matrix4x4.h>
#include <liboscar/maths/rect.h>
#include <liboscar/maths/transform.h>
#include <liboscar/maths/vector.h>
 
#include <array>
#include <concepts>
#include <functional>
#include <optional>
#include <ranges>
 
namespace osc
{
    // returns the average centroid of `aabb`
    constexpr Vector3 centroid_of(const AABB& aabb)
    {
        return 0.5f * (aabb.min + aabb.max);
    }
 
    // returns the widths of the edges of `aabb`
    constexpr Vector3 dimensions_of(const AABB& aabb)
    {
        return aabb.max - aabb.min;
    }
 
    // returns the half-widths of the edges of `aabb`
    constexpr Vector3 half_widths_of(const AABB& aabb)
    {
        return 0.5f * dimensions_of(aabb);
    }
 
    // returns the volume of `aabb`
    constexpr float volume_of(const AABB& aabb)
    {
        Vector3 const dims = dimensions_of(aabb);
        return dims.x() * dims.y() * dims.z();
    }
 
    // tests if `aabb` has zero width along all of its edges
    constexpr bool is_point(const AABB& aabb)
    {
        return aabb.min == aabb.max;
    }
 
    // tests if `aabb` has zero width along any of its edges
    constexpr bool has_zero_volume(const AABB& aabb)
    {
        return volume_of(aabb) == 0.0f;
    }
 
    // returns the eight corner vertices of `aabb`
    std::array<Vector3, 8> corner_vertices_of(const AABB& aabb);
 
    // returns an `AABB` computed by transforming `aabb` with `m`
    AABB transform_aabb(const Matrix4x4& m, const AABB& aabb);
 
    // returns an `AABB` computed by transforming `aabb` with `t`
    AABB transform_aabb(const Transform& t, const AABB& aabb);
 
    // returns an `AABB` that tightly bounds `x`
    constexpr AABB bounding_aabb_of(const Vector3& x)
    {
        return AABB{.min = x, .max = x};
    }
 
    // returns an `AABB` that tightly bounds both `x` and `y`
    constexpr AABB bounding_aabb_of(const AABB& x, const Vector3& y)
    {
        return AABB{elementwise_min(x.min, y), elementwise_max(x.max, y)};
    }
 
    // returns an `AABB` that tightly bounds both `x` and `y`
    constexpr AABB bounding_aabb_of(const AABB& x, const AABB& y)
    {
        return AABB{elementwise_min(x.min, y.min), elementwise_max(x.max, y.max)};
    }
 
    // returns an `AABB` that tightly bounds the union of `x` and `y`, or only `y` if `x` is `std::nullopt`
    constexpr AABB bounding_aabb_of(const std::optional<AABB>& x, const AABB& y)
    {
        return x ? bounding_aabb_of(*x, y) : y;
    }
 
    // returns an `AABB` that tightly bounds any non-`std::nullopt` `AABB`s in `x` or `y`
    //
    // if both `x` and `y` are `std::nullopt`, returns `std::nullopt`
    constexpr std::optional<AABB> bounding_aabb_of(std::optional<AABB> x, std::optional<AABB> y)
    {
        if (x and y) {
            return bounding_aabb_of(*x, *y);
        }
        else if (x) {
            return *x;
        }
        else if (y) {
            return *y;
        }
        else {
            return std::nullopt;
        }
    }
 
    namespace detail
    {
        // returns an `AABB` that tightly bounds the `Vector3`s projected from `r`
        template<std::ranges::input_range R, class Proj = std::identity>
        requires std::convertible_to<typename std::projected<std::ranges::iterator_t<R>, Proj>::value_type, const Vector3&>
        constexpr AABB bounding_aabb_of_nonempty_range(R&& r, Proj proj = {})
        {
            auto it = std::ranges::begin(r);
            const auto last = std::ranges::end(r);
 
            AABB rv = bounding_aabb_of(std::invoke(proj, *it));
            while (++it != last) {
                rv = bounding_aabb_of(rv, std::invoke(proj, *it));
            }
            return rv;
        }
    }
 
    // returns an `AABB` that tightly bounds the `Vector3`s projected from `r`
    template<std::ranges::input_range R, class Proj = std::identity>
    requires std::convertible_to<typename std::projected<std::ranges::iterator_t<R>, Proj>::value_type, const Vector3&>
    constexpr std::optional<AABB> bounding_aabb_of(R&& r, Proj proj = {})
    {
        if (std::ranges::begin(r) != std::ranges::end(r)) {
            return detail::bounding_aabb_of_nonempty_range(std::forward<R>(r), std::move(proj));
        } else {
            return std::nullopt;
        }
    }
 
    // returns an `AABB` that tightly bounds the `Vector3`s projected from `r` (specialized for compile-time-non-empty ranges)
    template<InputRangeWithSizeGreaterThan<0> R, class Proj = std::identity>
    requires std::convertible_to<typename std::projected<std::ranges::iterator_t<R>, Proj>::value_type, const Vector3&>
    constexpr AABB bounding_aabb_of(R&& r, Proj proj = {})
    {
        return detail::bounding_aabb_of_nonempty_range(std::forward<R>(r), std::move(proj));
    }
 
    // returns an `AABB` that tightly bounds the `AABB`s projected from `r`
    template<std::ranges::input_range Range, class Proj = std::identity>
    requires std::convertible_to<typename std::projected<std::ranges::iterator_t<Range>, Proj>::value_type, const AABB&>
    constexpr std::optional<AABB> bounding_aabb_of(Range&& r, Proj proj = {})
    {
        auto it = std::ranges::begin(r);
        auto const last = std::ranges::end(r);
        if (it == last) {
            return std::nullopt;  // empty range
        }
 
        AABB rv = std::invoke(proj, *it);
        while (++it != last) {
            rv = bounding_aabb_of(rv, std::invoke(proj, *it));
        }
        return rv;
    }
 
    // returns an `AABB` that tightly bounds any non-`std::nullopt` `std::optional<AABB>`s projected from `r`
    //
    // if no element in `r` projects an `AABB`, returns `std::nullopt`
    template<std::ranges::input_range Range, class Proj = std::identity>
    requires
        std::convertible_to<typename std::projected<std::ranges::iterator_t<Range>, Proj>::value_type, const std::optional<AABB>&>
        and (not std::convertible_to<typename std::projected<std::ranges::iterator_t<Range>, Proj>::value_type, const AABB&>)
    constexpr std::optional<AABB> bounding_aabb_of(Range&& r, Proj proj = {})
    {
        auto it = std::ranges::begin(r);
        const auto last = std::ranges::end(r);
 
        // find first non-nullopt AABB (or the end)
        std::optional<AABB> rv;
        while (!rv && it != last) {
            rv = std::invoke(proj, *it++);
        }
        if (not rv) {
            return rv;
        }
 
        // combine with remainder of range
        for (; it != last; ++it) {
            rv = bounding_aabb_of(std::invoke(proj, *it), *rv);
        }
 
        return rv;
    }
 
    // returns a `Rect` in normalized device coordinate-like (NDC-like) space that loosely
    // bounds the world-space-located `aabb`
    //
    // if the AABB does not lie within the NDC clipping bounds (i.e. between (-1, -1)
    // and (1, 1)), returns `std::nullopt`
    std::optional<Rect> loosely_project_into_ndc(
        const AABB& aabb,
        const Matrix4x4& view_mat,
        const Matrix4x4& proj_mat,
        float znear,
        float zfar
    );
}