Source/OpenEXR/Imath/ImathBoxAlgo.h

///////////////////////////////////////////////////////////////////////////
//
// Copyright (c) 2002, Industrial Light & Magic, a division of Lucas
// Digital Ltd. LLC
// 
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///////////////////////////////////////////////////////////////////////////



#ifndef INCLUDED_IMATHBOXALGO_H
#define INCLUDED_IMATHBOXALGO_H


//---------------------------------------------------------------------------
//
//	This file contains algorithms applied to or in conjunction
//	with bounding boxes (Imath::Box). These algorithms require
//	more headers to compile. The assumption made is that these
//	functions are called much less often than the basic box
//	functions or these functions require more support classes.
//
//	Contains:
//
//	T clip<T>(const T& in, const Box<T>& box)
//
//	Vec3<T> closestPointOnBox(const Vec3<T>&, const Box<Vec3<T>>& )
//
//	Vec3<T> closestPointInBox(const Vec3<T>&, const Box<Vec3<T>>& )
//
//	void transform(Box<Vec3<T>>&, const Matrix44<T>&)
//
//	bool findEntryAndExitPoints(const Line<T> &line,
//				    const Box< Vec3<T> > &box,
//				    Vec3<T> &enterPoint,
//				    Vec3<T> &exitPoint)
//
//	bool intersects(const Box<Vec3<T>> &box, 
//			const Line3<T> &ray, 
//			Vec3<T> intersectionPoint)
//
//	bool intersects(const Box<Vec3<T>> &box, const Line3<T> &ray)
//
//---------------------------------------------------------------------------

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

namespace Imath {


template <class T>
inline T clip(const T& in, const Box<T>& box)
{
    //
    //	Clip a point so that it lies inside the given bbox
    //

    T out;

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

    return out;
}


//
// Return p if p is inside the box.
//
 
template <class T>
Vec3<T> 
closestPointInBox(const Vec3<T>& p, const Box< Vec3<T> >& box )
{
    Imath::V3f b;

    if (p.x < box.min.x)
	b.x = box.min.x;
    else if (p.x > box.max.x)
	b.x = box.max.x;
    else
	b.x = p.x;

    if (p.y < box.min.y)
	b.y = box.min.y;
    else if (p.y > box.max.y)
	b.y = box.max.y;
    else
	b.y = p.y;

    if (p.z < box.min.z)
	b.z = box.min.z;
    else if (p.z > box.max.z)
	b.z = box.max.z;
    else
	b.z = p.z;

    return b;
}

template <class T>
Vec3<T> closestPointOnBox(const Vec3<T>& pt, const Box< Vec3<T> >& box )
{
    //
    //	This sucker is specialized to work with a Vec3f and a box
    //	made of Vec3fs. 
    //

    Vec3<T> result;
    
    // trivial cases first
    if (box.isEmpty())
	return pt;
    else if (pt == box.center()) 
    {
	// middle of z side
	result[0] = (box.max[0] + box.min[0])/2.0;
	result[1] = (box.max[1] + box.min[1])/2.0;
	result[2] = box.max[2];
    }
    else 
    {
	// Find the closest point on a unit box (from -1 to 1),
	// then scale up.

	// Find the vector from center to the point, then scale
	// to a unit box.
	Vec3<T> vec = pt - box.center();
	T sizeX = box.max[0]-box.min[0];
	T sizeY = box.max[1]-box.min[1];
	T sizeZ = box.max[2]-box.min[2];

	T halfX = sizeX/2.0;
	T halfY = sizeY/2.0;
	T halfZ = sizeZ/2.0;
	if (halfX > 0.0)
	    vec[0] /= halfX;
	if (halfY > 0.0)
	    vec[1] /= halfY;
	if (halfZ > 0.0)
	    vec[2] /= halfZ;

	// Side to snap side that has greatest magnitude in the vector.
	Vec3<T> mag;
	mag[0] = fabs(vec[0]);
	mag[1] = fabs(vec[1]);
	mag[2] = fabs(vec[2]);

	result = mag;

	// Check if beyond corners
	if (result[0] > 1.0)
	    result[0] = 1.0;
	if (result[1] > 1.0)
	    result[1] = 1.0;
	if (result[2] > 1.0)
	    result[2] = 1.0;

	// snap to appropriate side	    
	if ((mag[0] > mag[1]) && (mag[0] >  mag[2])) 
        {
	    result[0] = 1.0;
	}
	else if ((mag[1] > mag[0]) && (mag[1] >  mag[2])) 
        {
	    result[1] = 1.0;
	}
	else if ((mag[2] > mag[0]) && (mag[2] >  mag[1])) 
        {
	    result[2] = 1.0;
	}
	else if ((mag[0] == mag[1]) && (mag[0] == mag[2])) 
        {
	    // corner
	    result = Vec3<T>(1,1,1);
	}
	else if (mag[0] == mag[1]) 
        {
	    // edge parallel with z
	    result[0] = 1.0;
	    result[1] = 1.0;
	}
	else if (mag[0] == mag[2]) 
        {
	    // edge parallel with y
	    result[0] = 1.0;
	    result[2] = 1.0;
	}
	else if (mag[1] == mag[2]) 
        {
	    // edge parallel with x
	    result[1] = 1.0;
	    result[2] = 1.0;
	}

	// Now make everything point the right way
	for (int i=0; i < 3; i++)
        {
	    if (vec[i] < 0.0)
		result[i] = -result[i];
        }

	// scale back up and move to center
	result[0] *= halfX;
	result[1] *= halfY;
	result[2] *= halfZ;

	result += box.center();
    }
    return result;
}

template <class S, class T>
Box< Vec3<S> >
transform(const Box< Vec3<S> >& box, const Matrix44<T>& m)
{
    //
    // Transform a 3D box by a matrix, and compute a new box that
    // tightly encloses 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
    //

    if (box.isEmpty())
	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++) 
            {
		float 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;
}

template <class T>
Box< Vec3<T> >
affineTransform(const Box< Vec3<T> > &bbox, const Matrix44<T> &M)
{
    float       min0, max0, min1, max1, min2, max2, a, b;
    float       min0new, max0new, min1new, max1new, min2new, max2new;

    min0 = bbox.min[0];
    max0 = bbox.max[0];
    min1 = bbox.min[1];
    max1 = bbox.max[1];
    min2 = bbox.min[2];
    max2 = bbox.max[2];

    min0new = max0new = M[3][0];
    a = M[0][0] * min0;
    b = M[0][0] * max0;
    if (a < b) {
        min0new += a;
        max0new += b;
    } else {
        min0new += b;
        max0new += a;
    }
    a = M[1][0] * min1;
    b = M[1][0] * max1;
    if (a < b) {
        min0new += a;
        max0new += b;
    } else {
        min0new += b;
        max0new += a;
    }
    a = M[2][0] * min2;
    b = M[2][0] * max2;
    if (a < b) {
        min0new += a;
        max0new += b;
    } else {
        min0new += b;
        max0new += a;
    }

    min1new = max1new = M[3][1];
    a = M[0][1] * min0;
    b = M[0][1] * max0;
    if (a < b) {
        min1new += a;
        max1new += b;
    } else {
        min1new += b;
        max1new += a;
    }
    a = M[1][1] * min1;
    b = M[1][1] * max1;
    if (a < b) {
        min1new += a;
        max1new += b;
    } else {
        min1new += b;
        max1new += a;
    }
    a = M[2][1] * min2;
    b = M[2][1] * max2;
    if (a < b) {
        min1new += a;
        max1new += b;
    } else {
        min1new += b;
        max1new += a;
    }

    min2new = max2new = M[3][2];
    a = M[0][2] * min0;
    b = M[0][2] * max0;
    if (a < b) {
        min2new += a;
        max2new += b;
    } else {
        min2new += b;
        max2new += a;
    }
    a = M[1][2] * min1;
    b = M[1][2] * max1;
    if (a < b) {
        min2new += a;
        max2new += b;
    } else {
        min2new += b;
        max2new += a;
    }
    a = M[2][2] * min2;
    b = M[2][2] * max2;
    if (a < b) {
        min2new += a;
        max2new += b;
    } else {
        min2new += b;
        max2new += a;
    }

    Box< Vec3<T> > xbbox;

    xbbox.min[0] = min0new;
    xbbox.max[0] = max0new;
    xbbox.min[1] = min1new;
    xbbox.max[1] = max1new;
    xbbox.min[2] = min2new;
    xbbox.max[2] = max2new;

    return xbbox;
}


template <class T>
bool findEntryAndExitPoints(const Line3<T>& line,
			    const Box<Vec3<T> >& box,
			    Vec3<T> &enterPoint,
			    Vec3<T> &exitPoint)
{
    if ( box.isEmpty() ) return false;
    if ( line.distanceTo(box.center()) > box.size().length()/2. ) return false;

    Vec3<T>	points[8], inter, bary;
    Plane3<T>	plane;
    int		i, v0, v1, v2;
    bool	front = false, valid, validIntersection = false;

    // set up the eight coords of the corners of the box
    for(i = 0; i < 8; i++) 
    {
	points[i].setValue( i & 01 ? box.min[0] : box.max[0],
			    i & 02 ? box.min[1] : box.max[1],
			    i & 04 ? box.min[2] : box.max[2]);
    }

    // intersect the 12 triangles.
    for(i = 0; i < 12; i++) 
    {
	switch(i) 
        {
	case  0: v0 = 2; v1 = 1; v2 = 0; break;		// +z
	case  1: v0 = 2; v1 = 3; v2 = 1; break;

	case  2: v0 = 4; v1 = 5; v2 = 6; break;		// -z
	case  3: v0 = 6; v1 = 5; v2 = 7; break;

	case  4: v0 = 0; v1 = 6; v2 = 2; break;		// -x
	case  5: v0 = 0; v1 = 4; v2 = 6; break;

	case  6: v0 = 1; v1 = 3; v2 = 7; break;		// +x
	case  7: v0 = 1; v1 = 7; v2 = 5; break;

	case  8: v0 = 1; v1 = 4; v2 = 0; break;		// -y
	case  9: v0 = 1; v1 = 5; v2 = 4; break;

	case 10: v0 = 2; v1 = 7; v2 = 3; break;		// +y
	case 11: v0 = 2; v1 = 6; v2 = 7; break;
	}
	if((valid=intersect (line, points[v0], points[v1], points[v2],
                             inter, bary, front)) == true) 
        {
	    if(front == true) 
            {
		enterPoint = inter;
		validIntersection = valid;
	    }
	    else 
            {
		exitPoint = inter;
		validIntersection = valid;
	    }
	}
    }
    return validIntersection;
}


template<class T>
bool
intersects (const Box< Vec3<T> > &b, const Line3<T> &r, Vec3<T> &ip)
{
    //
    // Intersect a ray, r, with a box, b, and compute the intersection
    // point, ip:
    //
    // intersect() returns
    //
    //     - 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
    //
    // 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
    //

    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 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 = 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;
}


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


} // namespace Imath

#endif