boundingSphere.cxx

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/**
 * PANDA 3D SOFTWARE
 * Copyright (c) Carnegie Mellon University.  All rights reserved.
 *
 * All use of this software is subject to the terms of the revised BSD
 * license.  You should have received a copy of this license along
 * with this source code in a file named "LICENSE."
 *
 * @file boundingSphere.cxx
 * @author drose
 * @date 1999-10-01
 */

#include "boundingSphere.h"
#include "boundingBox.h"
#include "boundingHexahedron.h"
#include "boundingLine.h"
#include "boundingPlane.h"
#include "config_mathutil.h"
#include "dcast.h"
#include "cmath.h"

#include <algorithm>

using std::max;
using std::min;

TypeHandle BoundingSphere::_type_handle;

/**
 *
 */
BoundingVolume *BoundingSphere::
make_copy() const {
  return new BoundingSphere(*this);
}

/**
 *
 */
LPoint3 BoundingSphere::
get_min() const {
  nassertr(!is_empty(), LPoint3::zero());
  nassertr(!is_infinite(), LPoint3::zero());
  return LPoint3(_center[0] - _radius,
                  _center[1] - _radius,
                  _center[2] - _radius);
}

/**
 *
 */
LPoint3 BoundingSphere::
get_max() const {
  nassertr(!is_empty(), LPoint3::zero());
  nassertr(!is_infinite(), LPoint3::zero());
  return LPoint3(_center[0] + _radius,
                  _center[1] + _radius,
                  _center[2] + _radius);
}

/**
 *
 */
PN_stdfloat BoundingSphere::
get_volume() const {
  nassertr(!is_infinite(), 0.0f);
  if (is_empty()) {
    return 0.0f;
  }

  // Volume of a sphere: four-thirds pi r cubed.
  return 4.0f / 3.0f * MathNumbers::pi_f * _radius * _radius * _radius;
}

/**
 *
 */
LPoint3 BoundingSphere::
get_approx_center() const {
  nassertr(!is_empty(), LPoint3::zero());
  nassertr(!is_infinite(), LPoint3::zero());
  return get_center();
}

/**
 *
 */
void BoundingSphere::
xform(const LMatrix4 &mat) {
  nassertv(!mat.is_nan());

  if (!is_empty() && !is_infinite()) {
    // First, determine the longest axis of the matrix, in case it contains a
    // non-uniform scale.

    LVecBase3 x, y, z;
    mat.get_row3(x, 0);
    mat.get_row3(y, 1);
    mat.get_row3(z, 2);

    PN_stdfloat xd = dot(x, x);
    PN_stdfloat yd = dot(y, y);
    PN_stdfloat zd = dot(z, z);

    PN_stdfloat scale = max(xd, yd);
    scale = max(scale, zd);
    scale = csqrt(scale);

    // Transform the radius
    _radius *= scale;

    // Transform the center
    _center = _center * mat;
  }
}

/**
 *
 */
void BoundingSphere::
output(std::ostream &out) const {
  if (is_empty()) {
    out << "bsphere, empty";
  } else if (is_infinite()) {
    out << "bsphere, infinite";
  } else {
    out << "bsphere, c (" << _center << "), r " << _radius;
  }
}

/**
 * Virtual downcast method.  Returns this object as a pointer of the indicated
 * type, if it is in fact that type.  Returns NULL if it is not that type.
 */
const BoundingSphere *BoundingSphere::
as_bounding_sphere() const {
  return this;
}

/**
 *
 */
bool BoundingSphere::
extend_other(BoundingVolume *other) const {
  return other->extend_by_sphere(this);
}

/**
 *
 */
bool BoundingSphere::
around_other(BoundingVolume *other,
             const BoundingVolume **first,
             const BoundingVolume **last) const {
  return other->around_spheres(first, last);
}

/**
 *
 */
int BoundingSphere::
contains_other(const BoundingVolume *other) const {
  return other->contains_sphere(this);
}


/**
 *
 */
bool BoundingSphere::
extend_by_point(const LPoint3 &point) {
  nassertr(!point.is_nan(), false);

  if (is_empty()) {
    _center = point;
    _radius = 0.0f;
    _flags = 0;
  } else if (!is_infinite()) {
    LVector3 v = point - _center;
    PN_stdfloat dist2 = dot(v, v);
    if (dist2 > _radius * _radius) {
      _radius = csqrt(dist2);
    }
  }
  return true;
}

/**
 *
 */
bool BoundingSphere::
extend_by_sphere(const BoundingSphere *sphere) {
  nassertr(!sphere->is_empty() && !sphere->is_infinite(), false);
  nassertr(!is_infinite(), false);

  if (is_empty()) {
    _center = sphere->_center;
    _radius = sphere->_radius;
    _flags = 0;
  } else {
    PN_stdfloat dist = length(sphere->_center - _center);

    _radius = max(_radius, dist + sphere->_radius);
  }
  return true;
}

/**
 *
 */
bool BoundingSphere::
extend_by_box(const BoundingBox *box) {
  const LVector3 &min1 = box->get_minq();
  const LVector3 &max1 = box->get_maxq();

  if (is_empty()) {
    _center = (min1 + max1) * 0.5f;
    _radius = length(LVector3(max1 - _center));
    _flags = 0;

  } else {
    // Find the minimum radius necessary to reach the corner.
    PN_stdfloat max_dist2 = -1.0;
    for (int i = 0; i < 8; ++i) {
      PN_stdfloat dist2 = (box->get_point(i) - _center).length_squared();
      if (dist2 > max_dist2) {
        max_dist2 = dist2;
      }
    }
    if (max_dist2 > _radius * _radius) {
      _radius = csqrt(max_dist2);
    }
  }

  return true;
}

/**
 *
 */
bool BoundingSphere::
extend_by_hexahedron(const BoundingHexahedron *hexahedron) {
  nassertr(!hexahedron->is_empty(), false);

  BoundingBox box(hexahedron->get_min(), hexahedron->get_max());
  box.local_object();
  return extend_by_box(&box);
}

/**
 *
 */
bool BoundingSphere::
extend_by_finite(const FiniteBoundingVolume *volume) {
  nassertr(!volume->is_empty(), false);

  BoundingBox box(volume->get_min(), volume->get_max());
  box.local_object();
  return extend_by_box(&box);
}

/**
 *
 */
bool BoundingSphere::
around_points(const LPoint3 *first, const LPoint3 *last) {
  nassertr(first != last, false);

  // First, get the box of all the points to construct a bounding box.
  const LPoint3 *p = first;

#ifndef NDEBUG
  // Skip any NaN points.
  int skipped_nan = 0;
  while (p != last && (*p).is_nan()) {
    ++p;
    ++skipped_nan;
  }
  if (p == last) {
    mathutil_cat.warning()
      << "BoundingSphere around NaN\n";
    return false;
  }
#endif

  LPoint3 min_box(*p);
  LPoint3 max_box(*p);
  ++p;

#ifndef NDEBUG
  // Skip more NaN points.
  while (p != last && (*p).is_nan()) {
    ++p;
    ++skipped_nan;
  }
#endif

  if (p == last) {
    // Only one point; we have a radius of zero.  This is not the same thing
    // as an empty sphere, because our volume contains one point; an empty
    // sphere contains no points.
    _center = min_box;
    _radius = 0.0f;

  } else {
    // More than one point; we have a nonzero radius.
    while (p != last) {
#ifndef NDEBUG
      // Skip more NaN points.
      if ((*p).is_nan()) {
        ++skipped_nan;
      } else
#endif
        {
          min_box.set(min(min_box[0], (*p)[0]),
                      min(min_box[1], (*p)[1]),
                      min(min_box[2], (*p)[2]));
          max_box.set(max(max_box[0], (*p)[0]),
                      max(max_box[1], (*p)[1]),
                      max(max_box[2], (*p)[2]));
        }
      ++p;
    }

    // Now take the center of the bounding box as the center of the sphere.
    _center = (min_box + max_box) * 0.5f;

    // Now walk back through to get the max distance from center.
    PN_stdfloat max_dist2 = 0.0f;
    for (p = first; p != last; ++p) {
      LVector3 v = (*p) - _center;
      PN_stdfloat dist2 = dot(v, v);
      max_dist2 = max(max_dist2, dist2);
    }

    _radius = csqrt(max_dist2);
  }

#ifndef NDEBUG
  if (skipped_nan != 0) {
    mathutil_cat.warning()
      << "BoundingSphere ignored " << skipped_nan << " NaN points of "
      << (last - first) << " total.\n";
  }
#endif

  _flags = 0;

  return true;
}

/**
 *
 */
bool BoundingSphere::
around_finite(const BoundingVolume **first,
              const BoundingVolume **last) {
  nassertr(first != last, false);

  // We're given a set of bounding volumes, all of which are finite, and at
  // least the first one of which is guaranteed to be nonempty.  Some others
  // may not be.

  // First, get the box of all the points to construct a bounding box.
  const BoundingVolume **p = first;
  nassertr(!(*p)->is_empty() && !(*p)->is_infinite(), false);
  const FiniteBoundingVolume *vol = (*p)->as_finite_bounding_volume();
  nassertr(vol != nullptr, false);
  LPoint3 min_box = vol->get_min();
  LPoint3 max_box = vol->get_max();

  bool any_spheres = (vol->as_bounding_sphere() != nullptr);

  for (++p; p != last; ++p) {
    nassertr(!(*p)->is_infinite(), false);
    if (!(*p)->is_empty()) {
      vol = (*p)->as_finite_bounding_volume();
      if (vol == nullptr) {
        set_infinite();
        return true;
      }
      LPoint3 min1 = vol->get_min();
      LPoint3 max1 = vol->get_max();
      min_box.set(min(min_box[0], min1[0]),
                  min(min_box[1], min1[1]),
                  min(min_box[2], min1[2]));
      max_box.set(max(max_box[0], max1[0]),
                  max(max_box[1], max1[1]),
                  max(max_box[2], max1[2]));

      if (vol->as_bounding_sphere() != nullptr) {
        any_spheres = true;
      }
    }
  }

  // Now take the center of the bounding box as the center of the sphere.
  _center = (min_box + max_box) * 0.5f;

  if (!any_spheres) {
    // Since there are no spheres in the list, we have to make this sphere
    // fully enclose all of the bounding boxes.
    _radius = length(max_box - _center);

  } else {
    // We might be able to go tighter, by lopping off the corners of the
    // spheres.
    _radius = 0.0f;
    for (p = first; p != last; ++p) {
      if (!(*p)->is_empty()) {
        const BoundingSphere *sphere = (*p)->as_bounding_sphere();
        if (sphere != nullptr) {
          // This is a sphere; consider its corner.
          PN_stdfloat dist = length(sphere->_center - _center);
          _radius = max(_radius, dist + sphere->_radius);

        } else {
          // This is a nonsphere.  We fit around it.
          const FiniteBoundingVolume *vol = (*p)->as_finite_bounding_volume();
          nassertr(vol != nullptr, false);

          BoundingBox box(vol->get_min(), vol->get_max());
          box.local_object();

          // Find the minimum radius necessary to reach the corner.
          PN_stdfloat max_dist2 = -1.0;
          for (int i = 0; i < 8; ++i) {
            PN_stdfloat dist2 = (box.get_point(i) - _center).length_squared();
            if (dist2 > max_dist2) {
              max_dist2 = dist2;
            }
          }
          _radius = max(_radius, csqrt(max_dist2));
        }
      }
    }
  }

  _flags = 0;
  return true;
}

/**
 *
 */
int BoundingSphere::
contains_point(const LPoint3 &point) const {
  nassertr(!point.is_nan(), IF_no_intersection);

  if (is_empty()) {
    return IF_no_intersection;

  } else if (is_infinite()) {
    return IF_possible | IF_some | IF_all;

  } else {
    LVector3 v = point - _center;
    PN_stdfloat dist2 = dot(v, v);
    return (dist2 <= _radius * _radius) ?
      IF_possible | IF_some | IF_all : IF_no_intersection;
  }
}

/**
 *
 */
int BoundingSphere::
contains_lineseg(const LPoint3 &a, const LPoint3 &b) const {
  nassertr(!a.is_nan() && !b.is_nan(), IF_no_intersection);

  if (a == b) {
    return contains_point(a);
  }
  if (is_empty()) {
    return IF_no_intersection;

  } else if (is_infinite()) {
    return IF_possible | IF_some | IF_all;

  } else {
    LPoint3 from = a;
    LVector3 delta = b - a;
    PN_stdfloat t1, t2;

    // Solve the equation for the intersection of a line with a sphere using
    // the quadratic equation.
    PN_stdfloat A = dot(delta, delta);

    nassertr(A != 0.0f, 0);    // Trivial line segment.

    LVector3 fc = from - _center;
    PN_stdfloat B = 2.0f * dot(delta, fc);
    PN_stdfloat C = dot(fc, fc) - _radius * _radius;

    PN_stdfloat radical = B*B - 4.0f*A*C;

    if (IS_NEARLY_ZERO(radical)) {
      // Tangent.
      t1 = t2 = -B / (2.0f*A);
      return (t1 >= 0.0f && t1 <= 1.0f) ?
                 IF_possible | IF_some : IF_no_intersection;
    }

    if (radical < 0.0f) {
      // No real roots: no intersection with the line.
      return IF_no_intersection;
    }

    PN_stdfloat reciprocal_2A = 1.0f/(2.0f*A);
    PN_stdfloat sqrt_radical = csqrt(radical);

    t1 = ( -B - sqrt_radical ) * reciprocal_2A;
    t2 = ( -B + sqrt_radical ) * reciprocal_2A;

    if (t1 >= 0.0f && t2 <= 1.0f) {
      return IF_possible | IF_some | IF_all;
    } else if (t1 <= 1.0f && t2 >= 0.0f) {
      return IF_possible | IF_some;
    } else {
      return IF_no_intersection;
    }
  }
}

/**
 * Double-dispatch support: called by contains_other() when the type we're
 * testing for intersection is known to be a sphere.
 */
int BoundingSphere::
contains_sphere(const BoundingSphere *sphere) const {
  nassertr(!is_empty() && !is_infinite(), 0);
  nassertr(!sphere->is_empty() && !sphere->is_infinite(), 0);

  LVector3 v = sphere->_center - _center;
  PN_stdfloat dist2 = dot(v, v);

  if (_radius >= sphere->_radius &&
      dist2 <= (_radius - sphere->_radius) * (_radius - sphere->_radius)) {
    // The other sphere is completely within this sphere.
    return IF_possible | IF_some | IF_all;

  } else if (dist2 > (_radius + sphere->_radius) * (_radius + sphere->_radius)) {
    // The other sphere is completely outside this sphere.
    return IF_no_intersection;

  } else {
    // The other sphere is partially within this sphere.
    return IF_possible | IF_some;
  }
}

/**
 * Double-dispatch support: called by contains_other() when the type we're
 * testing for intersection is known to be a box.
 */
int BoundingSphere::
contains_box(const BoundingBox *box) const {
  return box->contains_sphere(this) & ~IF_all;
}

/**
 * Double-dispatch support: called by contains_other() when the type we're
 * testing for intersection is known to be a hexahedron.
 */
int BoundingSphere::
contains_hexahedron(const BoundingHexahedron *hexahedron) const {
  return hexahedron->contains_sphere(this) & ~IF_all;
}

/**
 * Double-dispatch support: called by contains_other() when the type we're
 * testing for intersection is known to be a line.
 */
int BoundingSphere::
contains_line(const BoundingLine *line) const {
  return line->contains_sphere(this) & ~IF_all;
}

/**
 * Double-dispatch support: called by contains_other() when the type we're
 * testing for intersection is known to be a plane.
 */
int BoundingSphere::
contains_plane(const BoundingPlane *plane) const {
  return plane->contains_sphere(this) & ~IF_all;
}