1#@!#!123s

: / usr / include / Imath /
Filename : ImathBoxAlgo.h
back
//
// SPDX-License-Identifier: BSD-3-Clause
// Copyright Contributors to the OpenEXR Project.
//

//
// Axis-aligned bounding box utility functions
//

#ifndef INCLUDED_IMATHBOXALGO_H
#define INCLUDED_IMATHBOXALGO_H

#include "ImathNamespace.h"

#include "ImathBox.h"
#include "ImathLineAlgo.h"
#include "ImathMatrix.h"
#include "ImathPlane.h"

IMATH_INTERNAL_NAMESPACE_HEADER_ENTER

///
/// Clip the coordinates of a point, `p`, against a `Box<T>`, `box`.
/// Return the closest point to `p` that is inside the box.
///

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 inline T
clip (const T& p, const Box<T>& box) IMATH_NOEXCEPT
{
    T q;

    for (int i = 0; i < int (box.min.dimensions()); i++)
    {
        if (p[i] < box.min[i])
            q[i] = box.min[i];
        else if (p[i] > box.max[i])
            q[i] = box.max[i];
        else
            q[i] = p[i];
    }

    return q;
}

///
/// Return the point in or on the `Box<T>`, `box`, that is closesest to
/// the point, `p`.
///

template <class T>
IMATH_HOSTDEVICE constexpr inline T
closestPointInBox (const T& p, const Box<T>& box) IMATH_NOEXCEPT
{
    return clip (p, box);
}

///
/// Return the point on the surface of the `Box<T>`, `box`, that is
/// closest to point `p`.
///
/// If the box is empty, return `p`.
///

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 Vec3<T>
closestPointOnBox (const Vec3<T>& p, const Box<Vec3<T>>& box) IMATH_NOEXCEPT
{
    if (box.isEmpty())
        return p;

    Vec3<T> q = closestPointInBox (p, box);

    if (q == p)
    {
        Vec3<T> d1 = p - box.min;
        Vec3<T> d2 = box.max - p;

        Vec3<T> d ((d1.x < d2.x) ? d1.x : d2.x,
                   (d1.y < d2.y) ? d1.y : d2.y,
                   (d1.z < d2.z) ? d1.z : d2.z);

        if (d.x < d.y && d.x < d.z)
        {
            q.x = (d1.x < d2.x) ? box.min.x : box.max.x;
        }
        else if (d.y < d.z)
        {
            q.y = (d1.y < d2.y) ? box.min.y : box.max.y;
        }
        else
        {
            q.z = (d1.z < d2.z) ? box.min.z : box.max.z;
        }
    }

    return q;
}

///
/// Transform a 3D box by a matrix, and compute a new box that
/// tightly encloses the transformed box. Return the transformed box.
///
/// If `m` is an affine transform, then we use James Arvo's fast
/// method as described in "Graphics Gems", Academic Press, 1990,
/// pp. 548-550.
///
/// A transformed empty box is still empty, and a transformed infinite box
/// is still infinite.
///

template <class S, class T>
IMATH_HOSTDEVICE Box<Vec3<S>>
transform (const Box<Vec3<S>>& box, const Matrix44<T>& m) IMATH_NOEXCEPT
{
    if (box.isEmpty() || box.isInfinite())
        return box;

    //
    // If the last column of m is (0 0 0 1) then m is an affine
    // transform, and we use the fast Graphics Gems trick.
    //

    if (m[0][3] == 0 && m[1][3] == 0 && m[2][3] == 0 && m[3][3] == 1)
    {
        Box<Vec3<S>> newBox;

        for (int i = 0; i < 3; i++)
        {
            newBox.min[i] = newBox.max[i] = (S) m[3][i];

            for (int j = 0; j < 3; j++)
            {
                S a, b;

                a = (S) m[j][i] * box.min[j];
                b = (S) m[j][i] * box.max[j];

                if (a < b)
                {
                    newBox.min[i] += a;
                    newBox.max[i] += b;
                }
                else
                {
                    newBox.min[i] += b;
                    newBox.max[i] += a;
                }
            }
        }

        return newBox;
    }

    //
    // M is a projection matrix.  Do things the naive way:
    // Transform the eight corners of the box, and find an
    // axis-parallel box that encloses the transformed corners.
    //

    Vec3<S> points[8];

    points[0][0] = points[1][0] = points[2][0] = points[3][0] = box.min[0];
    points[4][0] = points[5][0] = points[6][0] = points[7][0] = box.max[0];

    points[0][1] = points[1][1] = points[4][1] = points[5][1] = box.min[1];
    points[2][1] = points[3][1] = points[6][1] = points[7][1] = box.max[1];

    points[0][2] = points[2][2] = points[4][2] = points[6][2] = box.min[2];
    points[1][2] = points[3][2] = points[5][2] = points[7][2] = box.max[2];

    Box<Vec3<S>> newBox;

    for (int i = 0; i < 8; i++)
        newBox.extendBy (points[i] * m);

    return newBox;
}

///
/// Transform a 3D box by a matrix, and compute a new box that
/// tightly encloses the transformed box. The transformed box is
/// returned in the `result` argument.
///
/// If m is an affine transform, then we use James Arvo's fast
/// method as described in "Graphics Gems", Academic Press, 1990,
/// pp. 548-550.
///
/// A transformed empty box is still empty, and a transformed infinite
/// box is still infinite
///

template <class S, class T>
IMATH_HOSTDEVICE void
transform (const Box<Vec3<S>>& box, const Matrix44<T>& m, Box<Vec3<S>>& result) IMATH_NOEXCEPT
{
    if (box.isEmpty() || box.isInfinite())
    {
        return;
    }

    //
    // If the last column of m is (0 0 0 1) then m is an affine
    // transform, and we use the fast Graphics Gems trick.
    //

    if (m[0][3] == 0 && m[1][3] == 0 && m[2][3] == 0 && m[3][3] == 1)
    {
        for (int i = 0; i < 3; i++)
        {
            result.min[i] = result.max[i] = (S) m[3][i];

            for (int j = 0; j < 3; j++)
            {
                S a, b;

                a = (S) m[j][i] * box.min[j];
                b = (S) m[j][i] * box.max[j];

                if (a < b)
                {
                    result.min[i] += a;
                    result.max[i] += b;
                }
                else
                {
                    result.min[i] += b;
                    result.max[i] += a;
                }
            }
        }

        return;
    }

    //
    // M is a projection matrix.  Do things the naive way:
    // Transform the eight corners of the box, and find an
    // axis-parallel box that encloses the transformed corners.
    //

    Vec3<S> points[8];

    points[0][0] = points[1][0] = points[2][0] = points[3][0] = box.min[0];
    points[4][0] = points[5][0] = points[6][0] = points[7][0] = box.max[0];

    points[0][1] = points[1][1] = points[4][1] = points[5][1] = box.min[1];
    points[2][1] = points[3][1] = points[6][1] = points[7][1] = box.max[1];

    points[0][2] = points[2][2] = points[4][2] = points[6][2] = box.min[2];
    points[1][2] = points[3][2] = points[5][2] = points[7][2] = box.max[2];

    for (int i = 0; i < 8; i++)
        result.extendBy (points[i] * m);
}

///
/// Transform a 3D box by a matrix whose rightmost column `(0 0 0 1)`,
/// and compute a new box that tightly encloses the transformed
/// box. Return the transformed box.
///
/// As in the transform() function, use James Arvo's fast method if
/// possible.
///
/// A transformed empty or infinite box is still empty or infinite.
///

template <class S, class T>
IMATH_HOSTDEVICE Box<Vec3<S>>
affineTransform (const Box<Vec3<S>>& box, const Matrix44<T>& m) IMATH_NOEXCEPT
{
    if (box.isEmpty() || box.isInfinite())
        return box;

    Box<Vec3<S>> newBox;

    for (int i = 0; i < 3; i++)
    {
        newBox.min[i] = newBox.max[i] = (S) m[3][i];

        for (int j = 0; j < 3; j++)
        {
            S a, b;

            a = (S) m[j][i] * box.min[j];
            b = (S) m[j][i] * box.max[j];

            if (a < b)
            {
                newBox.min[i] += a;
                newBox.max[i] += b;
            }
            else
            {
                newBox.min[i] += b;
                newBox.max[i] += a;
            }
        }
    }

    return newBox;
}

///
/// Transform a 3D box by a matrix whose rightmost column is
/// `(0 0 0 1)`, and compute a new box that tightly encloses 
/// the transformed box. Return the transformed box in the `result`
/// argument.
///
/// As in the transform() function, use James Arvo's fast method if
/// possible.
///
/// A transformed empty or infinite box is still empty or infinite.
///

template <class S, class T>
IMATH_HOSTDEVICE void
affineTransform (const Box<Vec3<S>>& box, const Matrix44<T>& m, Box<Vec3<S>>& result) IMATH_NOEXCEPT
{
    if (box.isEmpty())
    {
        result.makeEmpty();
        return;
    }

    if (box.isInfinite())
    {
        result.makeInfinite();
        return;
    }

    for (int i = 0; i < 3; i++)
    {
        result.min[i] = result.max[i] = (S) m[3][i];

        for (int j = 0; j < 3; j++)
        {
            S a, b;

            a = (S) m[j][i] * box.min[j];
            b = (S) m[j][i] * box.max[j];

            if (a < b)
            {
                result.min[i] += a;
                result.max[i] += b;
            }
            else
            {
                result.min[i] += b;
                result.max[i] += a;
            }
        }
    }
}

///
/// Compute the points where a ray, `r`, enters and exits a 3D box, `b`:
///
/// Return true if the ray starts inside the box or if the ray starts
/// outside and intersects the box, or return false otherwise (that
/// is, if the ray does not intersect the box).
///
/// The entry and exit points are the points on two of the faces of
/// the box when the function returns true (the entry end exit points
/// may be on either side of the ray's origin), or undefined if the
/// the function returns false.
///

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
findEntryAndExitPoints (const Line3<T>& r, const Box<Vec3<T>>& b, Vec3<T>& entry, Vec3<T>& exit) IMATH_NOEXCEPT
{
    if (b.isEmpty())
    {
        //
        // No ray intersects an empty box
        //

        return false;
    }

    //
    // The following description assumes that the ray's origin is outside
    // the box, but the code below works even if the origin is inside the
    // box:
    //
    // Between one and three "frontfacing" sides of the box are oriented
    // towards the ray's origin, and between one and three "backfacing"
    // sides are oriented away from the ray's origin.
    // We intersect the ray with the planes that contain the sides of the
    // box, and compare the distances between the ray's origin and the
    // ray-plane intersections.  The ray intersects the box if the most
    // distant frontfacing intersection is nearer than the nearest
    // backfacing intersection.  If the ray does intersect the box, then
    // the most distant frontfacing ray-plane intersection is the entry
    // point and the nearest backfacing ray-plane intersection is the
    // exit point.
    //

    const T TMAX = std::numeric_limits<T>::max();

    T tFrontMax = -TMAX;
    T tBackMin  = TMAX;

    //
    // Minimum and maximum X sides.
    //

    if (r.dir.x >= 0)
    {
        T d1 = b.max.x - r.pos.x;
        T d2 = b.min.x - r.pos.x;

        if (r.dir.x > 1 || (abs (d1) < TMAX * r.dir.x && abs (d2) < TMAX * r.dir.x))
        {
            T t1 = d1 / r.dir.x;
            T t2 = d2 / r.dir.x;

            if (tBackMin > t1)
            {
                tBackMin = t1;

                exit.x = b.max.x;
                exit.y = clamp (r.pos.y + t1 * r.dir.y, b.min.y, b.max.y);
                exit.z = clamp (r.pos.z + t1 * r.dir.z, b.min.z, b.max.z);
            }

            if (tFrontMax < t2)
            {
                tFrontMax = t2;

                entry.x = b.min.x;
                entry.y = clamp (r.pos.y + t2 * r.dir.y, b.min.y, b.max.y);
                entry.z = clamp (r.pos.z + t2 * r.dir.z, b.min.z, b.max.z);
            }
        }
        else if (r.pos.x < b.min.x || r.pos.x > b.max.x)
        {
            return false;
        }
    }
    else // r.dir.x < 0
    {
        T d1 = b.min.x - r.pos.x;
        T d2 = b.max.x - r.pos.x;

        if (r.dir.x < -1 || (abs (d1) < -TMAX * r.dir.x && abs (d2) < -TMAX * r.dir.x))
        {
            T t1 = d1 / r.dir.x;
            T t2 = d2 / r.dir.x;

            if (tBackMin > t1)
            {
                tBackMin = t1;

                exit.x = b.min.x;
                exit.y = clamp (r.pos.y + t1 * r.dir.y, b.min.y, b.max.y);
                exit.z = clamp (r.pos.z + t1 * r.dir.z, b.min.z, b.max.z);
            }

            if (tFrontMax < t2)
            {
                tFrontMax = t2;

                entry.x = b.max.x;
                entry.y = clamp (r.pos.y + t2 * r.dir.y, b.min.y, b.max.y);
                entry.z = clamp (r.pos.z + t2 * r.dir.z, b.min.z, b.max.z);
            }
        }
        else if (r.pos.x < b.min.x || r.pos.x > b.max.x)
        {
            return false;
        }
    }

    //
    // Minimum and maximum Y sides.
    //

    if (r.dir.y >= 0)
    {
        T d1 = b.max.y - r.pos.y;
        T d2 = b.min.y - r.pos.y;

        if (r.dir.y > 1 || (abs (d1) < TMAX * r.dir.y && abs (d2) < TMAX * r.dir.y))
        {
            T t1 = d1 / r.dir.y;
            T t2 = d2 / r.dir.y;

            if (tBackMin > t1)
            {
                tBackMin = t1;

                exit.x = clamp (r.pos.x + t1 * r.dir.x, b.min.x, b.max.x);
                exit.y = b.max.y;
                exit.z = clamp (r.pos.z + t1 * r.dir.z, b.min.z, b.max.z);
            }

            if (tFrontMax < t2)
            {
                tFrontMax = t2;

                entry.x = clamp (r.pos.x + t2 * r.dir.x, b.min.x, b.max.x);
                entry.y = b.min.y;
                entry.z = clamp (r.pos.z + t2 * r.dir.z, b.min.z, b.max.z);
            }
        }
        else if (r.pos.y < b.min.y || r.pos.y > b.max.y)
        {
            return false;
        }
    }
    else // r.dir.y < 0
    {
        T d1 = b.min.y - r.pos.y;
        T d2 = b.max.y - r.pos.y;

        if (r.dir.y < -1 || (abs (d1) < -TMAX * r.dir.y && abs (d2) < -TMAX * r.dir.y))
        {
            T t1 = d1 / r.dir.y;
            T t2 = d2 / r.dir.y;

            if (tBackMin > t1)
            {
                tBackMin = t1;

                exit.x = clamp (r.pos.x + t1 * r.dir.x, b.min.x, b.max.x);
                exit.y = b.min.y;
                exit.z = clamp (r.pos.z + t1 * r.dir.z, b.min.z, b.max.z);
            }

            if (tFrontMax < t2)
            {
                tFrontMax = t2;

                entry.x = clamp (r.pos.x + t2 * r.dir.x, b.min.x, b.max.x);
                entry.y = b.max.y;
                entry.z = clamp (r.pos.z + t2 * r.dir.z, b.min.z, b.max.z);
            }
        }
        else if (r.pos.y < b.min.y || r.pos.y > b.max.y)
        {
            return false;
        }
    }

    //
    // Minimum and maximum Z sides.
    //

    if (r.dir.z >= 0)
    {
        T d1 = b.max.z - r.pos.z;
        T d2 = b.min.z - r.pos.z;

        if (r.dir.z > 1 || (abs (d1) < TMAX * r.dir.z && abs (d2) < TMAX * r.dir.z))
        {
            T t1 = d1 / r.dir.z;
            T t2 = d2 / r.dir.z;

            if (tBackMin > t1)
            {
                tBackMin = t1;

                exit.x = clamp (r.pos.x + t1 * r.dir.x, b.min.x, b.max.x);
                exit.y = clamp (r.pos.y + t1 * r.dir.y, b.min.y, b.max.y);
                exit.z = b.max.z;
            }

            if (tFrontMax < t2)
            {
                tFrontMax = t2;

                entry.x = clamp (r.pos.x + t2 * r.dir.x, b.min.x, b.max.x);
                entry.y = clamp (r.pos.y + t2 * r.dir.y, b.min.y, b.max.y);
                entry.z = b.min.z;
            }
        }
        else if (r.pos.z < b.min.z || r.pos.z > b.max.z)
        {
            return false;
        }
    }
    else // r.dir.z < 0
    {
        T d1 = b.min.z - r.pos.z;
        T d2 = b.max.z - r.pos.z;

        if (r.dir.z < -1 || (abs (d1) < -TMAX * r.dir.z && abs (d2) < -TMAX * r.dir.z))
        {
            T t1 = d1 / r.dir.z;
            T t2 = d2 / r.dir.z;

            if (tBackMin > t1)
            {
                tBackMin = t1;

                exit.x = clamp (r.pos.x + t1 * r.dir.x, b.min.x, b.max.x);
                exit.y = clamp (r.pos.y + t1 * r.dir.y, b.min.y, b.max.y);
                exit.z = b.min.z;
            }

            if (tFrontMax < t2)
            {
                tFrontMax = t2;

                entry.x = clamp (r.pos.x + t2 * r.dir.x, b.min.x, b.max.x);
                entry.y = clamp (r.pos.y + t2 * r.dir.y, b.min.y, b.max.y);
                entry.z = b.max.z;
            }
        }
        else if (r.pos.z < b.min.z || r.pos.z > b.max.z)
        {
            return false;
        }
    }

    return tFrontMax <= tBackMin;
}

///
/// Intersect a ray, `r`, with a 3D box, `b, and compute the intersection
/// point, returned in `ip`.
///
/// The intersection point is
/// - the ray's origin if the ray starts inside the box
/// - a point on one of the faces of the box if the ray
///   starts outside the box
/// - undefined when intersect() returns false
///
/// @return
/// - true if the ray starts inside the box or if the
///   ray starts outside and intersects the box
/// - false if the ray starts outside the box and intersects it,
///   but the intersection is behind the ray's origin.
/// - false if the ray starts outside and does not intersect it
///

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
intersects (const Box<Vec3<T>>& b, const Line3<T>& r, Vec3<T>& ip) IMATH_NOEXCEPT
{
    if (b.isEmpty())
    {
        //
        // No ray intersects an empty box
        //

        return false;
    }

    if (b.intersects (r.pos))
    {
        //
        // The ray starts inside the box
        //

        ip = r.pos;
        return true;
    }

    //
    // The ray starts outside the box.  Between one and three "frontfacing"
    // sides of the box are oriented towards the ray, and between one and
    // three "backfacing" sides are oriented away from the ray.
    // We intersect the ray with the planes that contain the sides of the
    // box, and compare the distances between ray's origin and the ray-plane
    // intersections.
    // The ray intersects the box if the most distant frontfacing intersection
    // is nearer than the nearest backfacing intersection.  If the ray does
    // intersect the box, then the most distant frontfacing ray-plane
    // intersection is the ray-box intersection.
    //

    const T TMAX = std::numeric_limits<T>::max();

    T tFrontMax = -1;
    T tBackMin  = TMAX;

    //
    // Minimum and maximum X sides.
    //

    if (r.dir.x > 0)
    {
        if (r.pos.x > b.max.x)
            return false;

        T d = b.max.x - r.pos.x;

        if (r.dir.x > 1 || d < TMAX * r.dir.x)
        {
            T t = d / r.dir.x;

            if (tBackMin > t)
                tBackMin = t;
        }

        if (r.pos.x <= b.min.x)
        {
            T d = b.min.x - r.pos.x;
            T t = (r.dir.x > 1 || d < TMAX * r.dir.x) ? d / r.dir.x : TMAX;

            if (tFrontMax < t)
            {
                tFrontMax = t;

                ip.x = b.min.x;
                ip.y = clamp (r.pos.y + t * r.dir.y, b.min.y, b.max.y);
                ip.z = clamp (r.pos.z + t * r.dir.z, b.min.z, b.max.z);
            }
        }
    }
    else if (r.dir.x < 0)
    {
        if (r.pos.x < b.min.x)
            return false;

        T d = b.min.x - r.pos.x;

        if (r.dir.x < -1 || d > TMAX * r.dir.x)
        {
            T t = d / r.dir.x;

            if (tBackMin > t)
                tBackMin = t;
        }

        if (r.pos.x >= b.max.x)
        {
            T d = b.max.x - r.pos.x;
            T t = (r.dir.x < -1 || d > TMAX * r.dir.x) ? d / r.dir.x : TMAX;

            if (tFrontMax < t)
            {
                tFrontMax = t;

                ip.x = b.max.x;
                ip.y = clamp (r.pos.y + t * r.dir.y, b.min.y, b.max.y);
                ip.z = clamp (r.pos.z + t * r.dir.z, b.min.z, b.max.z);
            }
        }
    }
    else // r.dir.x == 0
    {
        if (r.pos.x < b.min.x || r.pos.x > b.max.x)
            return false;
    }

    //
    // Minimum and maximum Y sides.
    //

    if (r.dir.y > 0)
    {
        if (r.pos.y > b.max.y)
            return false;

        T d = b.max.y - r.pos.y;

        if (r.dir.y > 1 || d < TMAX * r.dir.y)
        {
            T t = d / r.dir.y;

            if (tBackMin > t)
                tBackMin = t;
        }

        if (r.pos.y <= b.min.y)
        {
            T d = b.min.y - r.pos.y;
            T t = (r.dir.y > 1 || d < TMAX * r.dir.y) ? d / r.dir.y : TMAX;

            if (tFrontMax < t)
            {
                tFrontMax = t;

                ip.x = clamp (r.pos.x + t * r.dir.x, b.min.x, b.max.x);
                ip.y = b.min.y;
                ip.z = clamp (r.pos.z + t * r.dir.z, b.min.z, b.max.z);
            }
        }
    }
    else if (r.dir.y < 0)
    {
        if (r.pos.y < b.min.y)
            return false;

        T d = b.min.y - r.pos.y;

        if (r.dir.y < -1 || d > TMAX * r.dir.y)
        {
            T t = d / r.dir.y;

            if (tBackMin > t)
                tBackMin = t;
        }

        if (r.pos.y >= b.max.y)
        {
            T d = b.max.y - r.pos.y;
            T t = (r.dir.y < -1 || d > TMAX * r.dir.y) ? d / r.dir.y : TMAX;

            if (tFrontMax < t)
            {
                tFrontMax = t;

                ip.x = clamp (r.pos.x + t * r.dir.x, b.min.x, b.max.x);
                ip.y = b.max.y;
                ip.z = clamp (r.pos.z + t * r.dir.z, b.min.z, b.max.z);
            }
        }
    }
    else // r.dir.y == 0
    {
        if (r.pos.y < b.min.y || r.pos.y > b.max.y)
            return false;
    }

    //
    // Minimum and maximum Z sides.
    //

    if (r.dir.z > 0)
    {
        if (r.pos.z > b.max.z)
            return false;

        T d = b.max.z - r.pos.z;

        if (r.dir.z > 1 || d < TMAX * r.dir.z)
        {
            T t = d / r.dir.z;

            if (tBackMin > t)
                tBackMin = t;
        }

        if (r.pos.z <= b.min.z)
        {
            T d = b.min.z - r.pos.z;
            T t = (r.dir.z > 1 || d < TMAX * r.dir.z) ? d / r.dir.z : TMAX;

            if (tFrontMax < t)
            {
                tFrontMax = t;

                ip.x = clamp (r.pos.x + t * r.dir.x, b.min.x, b.max.x);
                ip.y = clamp (r.pos.y + t * r.dir.y, b.min.y, b.max.y);
                ip.z = b.min.z;
            }
        }
    }
    else if (r.dir.z < 0)
    {
        if (r.pos.z < b.min.z)
            return false;

        T d = b.min.z - r.pos.z;

        if (r.dir.z < -1 || d > TMAX * r.dir.z)
        {
            T t = d / r.dir.z;

            if (tBackMin > t)
                tBackMin = t;
        }

        if (r.pos.z >= b.max.z)
        {
            T d = b.max.z - r.pos.z;
            T t = (r.dir.z < -1 || d > TMAX * r.dir.z) ? d / r.dir.z : TMAX;

            if (tFrontMax < t)
            {
                tFrontMax = t;

                ip.x = clamp (r.pos.x + t * r.dir.x, b.min.x, b.max.x);
                ip.y = clamp (r.pos.y + t * r.dir.y, b.min.y, b.max.y);
                ip.z = b.max.z;
            }
        }
    }
    else // r.dir.z == 0
    {
        if (r.pos.z < b.min.z || r.pos.z > b.max.z)
            return false;
    }

    return tFrontMax <= tBackMin;
}

///
/// Return whether the the ray `ray` interects the 3D box `box`.
///

template <class T>
IMATH_HOSTDEVICE IMATH_CONSTEXPR14 bool
intersects (const Box<Vec3<T>>& box, const Line3<T>& ray) IMATH_NOEXCEPT
{
    Vec3<T> ignored;
    return intersects (box, ray, ignored);
}

IMATH_INTERNAL_NAMESPACE_HEADER_EXIT

#endif // INCLUDED_IMATHBOXALGO_H