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llsphere.cpp 10.74 KiB
/**
* @file llsphere.cpp
* @author Andrew Meadows
* @brief Simple line class that can compute nearest approach between two lines
*
* $LicenseInfo:firstyear=2007&license=viewerlgpl$
* Second Life Viewer Source Code
* Copyright (C) 2010, Linden Research, Inc.
*
* This library is free software; you can redistribute it and/or
* modify it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation;
* version 2.1 of the License only.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
*
* Linden Research, Inc., 945 Battery Street, San Francisco, CA 94111 USA
* $/LicenseInfo$
*/
#include "linden_common.h"
#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;
}