llsphere.cpp

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#include "llsphere.h"

LLSphere::LLSphere()
:       mCenter(0.f, 0.f, 0.f),
        mRadius(0.f)
{ }

LLSphere::LLSphere( const LLVector3& center, F32 radius)
{
        set(center, radius);
}

void LLSphere::set( const LLVector3& center, F32 radius )
{
        mCenter = center;
        setRadius(radius);
}

void LLSphere::setCenter( const LLVector3& center)
{
        mCenter = center;
}

void LLSphere::setRadius( F32 radius)
{
        if (radius < 0.f)
        {
                radius = -radius;
        }
        mRadius = radius;
}
        
const LLVector3& LLSphere::getCenter() const
{
        return mCenter;
}

F32 LLSphere::getRadius() const
{
        return mRadius;
}

// returns 'TRUE' if this sphere completely contains other_sphere
BOOL LLSphere::contains(const LLSphere& other_sphere) const
{
        F32 separation = (mCenter - other_sphere.mCenter).length();
        return (mRadius >= separation + other_sphere.mRadius) ? TRUE : FALSE;
}

// returns 'TRUE' if this sphere completely contains other_sphere
BOOL LLSphere::overlaps(const LLSphere& other_sphere) const
{
        F32 separation = (mCenter - other_sphere.mCenter).length();
        return (separation <= mRadius + other_sphere.mRadius) ? TRUE : FALSE;
}

// returns overlap
// negative overlap is closest approach
F32 LLSphere::getOverlap(const LLSphere& other_sphere) const
{
        // separation is distance from other_sphere's edge and this center
        return (mCenter - other_sphere.mCenter).length() - mRadius - other_sphere.mRadius;
}

bool LLSphere::operator==(const LLSphere& rhs) const
{
        // TODO? -- use approximate equality for centers?
        return (mRadius == rhs.mRadius
                        && mCenter == rhs.mCenter);
}

std::ostream& operator<<( std::ostream& output_stream, const LLSphere& sphere)
{
        output_stream << "{center=" << sphere.mCenter << "," << "radius=" << sphere.mRadius << "}";
        return output_stream;
}

// static 
// removes any spheres that are contained in others
void LLSphere::collapse(std::vector<LLSphere>& sphere_list)
{
        std::vector<LLSphere>::iterator first_itr = sphere_list.begin();
        while (first_itr != sphere_list.end())
        {
                bool delete_from_front = false;

                std::vector<LLSphere>::iterator second_itr = first_itr;
                ++second_itr;
                while (second_itr != sphere_list.end())
                {
                        if (second_itr->contains(*first_itr))
                        {
                                delete_from_front = true;
                                break;
                        }
                        else if (first_itr->contains(*second_itr))
                        {
                                sphere_list.erase(second_itr++);
                        }
                        else
                        {
                                ++second_itr;
                        }
                }

                if (delete_from_front)
                {
                        sphere_list.erase(first_itr++);
                }
                else
                {
                        ++first_itr;
                }
        }
}

// static
// returns the bounding sphere that contains both spheres
LLSphere LLSphere::getBoundingSphere(const LLSphere& first_sphere, const LLSphere& second_sphere)
{
        LLVector3 direction = second_sphere.mCenter - first_sphere.mCenter;

        // HACK -- it is possible to get enough floating point error in the 
        // other getBoundingSphere() method that we have to add some slop
        // at the end.  Unfortunately, this breaks the link-order invarience
        // for the linkability tests... unless we also apply the same slop
        // here.
        F32 half_milimeter = 0.0005f;

        F32 distance = direction.length();
        if (0.f == distance)
        {
                direction.setVec(1.f, 0.f, 0.f);
        }
        else
        {
                direction.normVec();
        }
        // the 'edge' is measured from the first_sphere's center
        F32 max_edge = 0.f;
        F32 min_edge = 0.f;

        max_edge = llmax(max_edge + first_sphere.getRadius(), max_edge + distance + second_sphere.getRadius() + half_milimeter);
        min_edge = llmin(min_edge - first_sphere.getRadius(), min_edge + distance - second_sphere.getRadius() - half_milimeter);
        F32 radius = 0.5f * (max_edge - min_edge);
        LLVector3 center = first_sphere.mCenter + (0.5f * (max_edge + min_edge)) * direction;
        return LLSphere(center, radius);
}

// static
// returns the bounding sphere that contains an arbitrary set of spheres
LLSphere LLSphere::getBoundingSphere(const std::vector<LLSphere>& sphere_list)
{
        // this algorithm can get relatively inaccurate when the sphere 
        // collection is 'small' (contained within a bounding sphere of about 
        // 2 meters or less)
        // TODO -- improve the accuracy for small collections of spheres

        LLSphere bounding_sphere( LLVector3(0.f, 0.f, 0.f), 0.f );
        S32 sphere_count = sphere_list.size();
        if (1 == sphere_count)
        {
                // trivial case -- single sphere
                std::vector<LLSphere>::const_iterator sphere_itr = sphere_list.begin();
                bounding_sphere = *sphere_itr;
        }
        else if (2 == sphere_count)
        {
                // trivial case -- two spheres
                std::vector<LLSphere>::const_iterator first_sphere = sphere_list.begin();
                std::vector<LLSphere>::const_iterator second_sphere = first_sphere;
                ++second_sphere;
                bounding_sphere = LLSphere::getBoundingSphere(*first_sphere, *second_sphere);
        }
        else if (sphere_count > 0)
        {
                // non-trivial case -- we will approximate the solution
                //
                // NOTE -- there is a fancy/fast way to do this for large 
                // numbers of arbirary N-dimensional spheres -- you can look it
                // up on the net.  We're dealing with 3D spheres at collection
                // sizes of 256 spheres or smaller, so we just use this
                // brute force method.

                // TODO -- perhaps would be worthwile to test for the solution where
                // the largest spanning radius just happens to work.  That is, where
                // there are really two spheres that determine the bounding sphere,
                // and all others are contained therein.

                // compute the AABB
                std::vector<LLSphere>::const_iterator first_itr = sphere_list.begin();
                LLVector3 max_corner = first_itr->getCenter() + first_itr->getRadius() * LLVector3(1.f, 1.f, 1.f);
                LLVector3 min_corner = first_itr->getCenter() - first_itr->getRadius() * LLVector3(1.f, 1.f, 1.f);
                {
                        std::vector<LLSphere>::const_iterator sphere_itr = sphere_list.begin();
                        for (++sphere_itr; sphere_itr != sphere_list.end(); ++sphere_itr)
                        {
                                LLVector3 center = sphere_itr->getCenter();
                                F32 radius = sphere_itr->getRadius();
                                for (S32 i=0; i<3; ++i)
                                {
                                        if (center.mV[i] + radius > max_corner.mV[i])
                                        {
                                                max_corner.mV[i] = center.mV[i] + radius;
                                        }
                                        if (center.mV[i] - radius < min_corner.mV[i])
                                        {
                                                min_corner.mV[i] = center.mV[i] - radius;
                                        }
                                }
                        }
                }

                // get the starting center and radius from the AABB
                LLVector3 diagonal = max_corner - min_corner;
                F32 bounding_radius = 0.5f * diagonal.length();
                LLVector3 bounding_center = 0.5f * (max_corner + min_corner);

                // compute the starting step-size
                F32 minimum_radius = 0.5f * llmin(diagonal.mV[VX], llmin(diagonal.mV[VY], diagonal.mV[VZ]));
                F32 step_length = bounding_radius - minimum_radius;
                S32 step_count = 0;
                S32 max_step_count = 12;
                F32 half_milimeter = 0.0005f;

                // wander the center around in search of tighter solutions
                S32 last_dx = 2;        // 2 is out of bounds --> no match
                S32 last_dy = 2;
                S32 last_dz = 2;

                while (step_length > half_milimeter
                                && step_count < max_step_count)
                {
                        // the algorithm for testing the maximum radius could be expensive enough
                        // that it makes sense to NOT duplicate testing when possible, so we keep
                        // track of where we last tested, and only test the new points

                        S32 best_dx = 0;
                        S32 best_dy = 0;
                        S32 best_dz = 0;

                        // sample near the center of the box
                        bool found_better_center = false;
                        for (S32 dx = -1; dx < 2; ++dx)
                        {
                                for (S32 dy = -1; dy < 2; ++dy)
                                {
                                        for (S32 dz = -1; dz < 2; ++dz)
                                        {
                                                if (dx == 0 && dy == 0 && dz == 0)
                                                {
                                                        continue;
                                                }

                                                // count the number of indecies that match the last_*'s
                                                S32 match_count = 0;
                                                if (last_dx == dx) ++match_count;
                                                if (last_dy == dy) ++match_count;
                                                if (last_dz == dz) ++match_count;
                                                if (match_count == 2)
                                                {
                                                        // we've already tested this point
                                                        continue;
                                                }

                                                LLVector3 center = bounding_center;
                                                center.mV[VX] += (F32) dx * step_length;
                                                center.mV[VY] += (F32) dy * step_length;
                                                center.mV[VZ] += (F32) dz * step_length;

                                                // compute the radius of the bounding sphere
                                                F32 max_radius = 0.f;
                                                std::vector<LLSphere>::const_iterator sphere_itr;
                                                for (sphere_itr = sphere_list.begin(); sphere_itr != sphere_list.end(); ++sphere_itr)
                                                {
                                                        F32 radius = (sphere_itr->getCenter() - center).length() + sphere_itr->getRadius();
                                                        if (radius > max_radius)
                                                        {
                                                                max_radius = radius;
                                                        }
                                                }
                                                if (max_radius < bounding_radius)
                                                {
                                                        best_dx = dx;
                                                        best_dy = dy;
                                                        best_dz = dz;
                                                        bounding_center = center;
                                                        bounding_radius = max_radius;
                                                        found_better_center = true;
                                                }
                                        }
                                }
                        }
                        if (found_better_center)
                        {
                                // remember where we came from so we can avoid retesting
                                last_dx = -best_dx;
                                last_dy = -best_dy;
                                last_dz = -best_dz;
                        }
                        else
                        {
                                // reduce the step size
                                step_length *= 0.5f;
                                //++step_count;
                                // reset the last_*'s
                                last_dx = 2;    // 2 is out of bounds --> no match
                                last_dy = 2;
                                last_dz = 2;
                        }
                }

                // HACK -- it is possible to get enough floating point error for the
                // bounding sphere to too small on the order of 10e-6, but we only need
                // it to be accurate to within about half a millimeter
                bounding_radius += half_milimeter;

                // this algorithm can get relatively inaccurate when the sphere 
                // collection is 'small' (contained within a bounding sphere of about 
                // 2 meters or less)
                // TODO -- fix this
                /* debug code
                {
                        std::vector<LLSphere>::const_iterator sphere_itr;
                        for (sphere_itr = sphere_list.begin(); sphere_itr != sphere_list.end(); ++sphere_itr)
                        {
                                F32 radius = (sphere_itr->getCenter() - bounding_center).length() + sphere_itr->getRadius();
                                if (radius + 0.1f > bounding_radius)
                                {
                                        std::cout << " rad = " << radius << "  bounding - rad = " << (bounding_radius - radius) << std::endl;
                                }
                        }
                        std::cout << "\n" << std::endl;
                }
                */ 

                bounding_sphere.set(bounding_center, bounding_radius);
        }
        return bounding_sphere;
}

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