float3
OpenSteer::SteerLibrary::
steerForSeparation (const AbstractVehicle& v,
const float maxDistance,
const float cosMaxAngle,
const AVGroup& flock)
{
// steering accumulator and count of neighbors, both initially zero
float3 steering = float3_zero();
int neighbors = 0;
// for each of the other vehicles...
for (AVIterator other = flock.begin(); other != flock.end(); other++)
{
if (inBoidNeighborhood (v, **other, v.radius() * 3, maxDistance, cosMaxAngle))
{
// add in steering contribution
// (opposite of the offset direction, divided once by distance
// to normalize, divided another time to get 1/d falloff)
const float3 offset = float3_subtract(make_float3((**other).position()), make_float3(v.position()));
const float distanceSquared = float3_dot(offset, offset);
steering = float3_add(steering, float3_scalar_divide(offset, -distanceSquared));
// count neighbors
neighbors++;
}
}
// divide by neighbors, then normalize to pure direction
if (neighbors > 0)
steering = float3_normalize(float3_scalar_divide(steering, (float)neighbors));
return steering;
}
float3
OpenSteer::SteerLibrary::
steerForCohesion (const AbstractVehicle& v,
const float maxDistance,
const float cosMaxAngle,
const AVGroup& flock)
{
// steering accumulator and count of neighbors, both initially zero
float3 steering = float3_zero();
int neighbors = 0;
// for each of the other vehicles...
for (AVIterator other = flock.begin(); other != flock.end(); other++)
{
if (inBoidNeighborhood (v, **other, v.radius() * 3, maxDistance, cosMaxAngle))
{
// accumulate sum of neighbor's positions
steering = float3_add(steering, make_float3((**other).position()));
// count neighbors
neighbors++;
}
}
// divide by neighbors, subtract off current position to get error-
// correcting direction, then normalize to pure direction
if (neighbors > 0)
steering = float3_normalize(float3_subtract(float3_scalar_divide(steering, (float)neighbors), make_float3(v.position())));
return steering;
}
float3
OpenSteer::SteerLibrary::
steerToAvoidCloseNeighbors (const AbstractVehicle& v,
const float minSeparationDistance,
const AVGroup& others)
{
// for each of the other vehicles...
for (AVIterator i = others.begin(); i != others.end(); i++)
{
AbstractVehicle& other = **i;
if (&other != &v)
{
const float sumOfRadii = v.radius() + other.radius();
const float minCenterToCenter = minSeparationDistance + sumOfRadii;
const float3 offset = float3_subtract(make_float3(other.position()), make_float3(v.position()));
const float currentDistance = float3_length(offset);
if (currentDistance < minCenterToCenter)
{
annotateAvoidCloseNeighbor (other, minSeparationDistance);
return float3_perpendicularComponent(float3_minus(offset), make_float3(v.forward()));
}
}
}
// otherwise return zero
return float3_zero();
}
void
OpenSteer::OpenSteerDemo::circleHighlightVehicleUtility (const AbstractVehicle& vehicle)
{
if (&vehicle != NULL) drawXZCircle (vehicle.radius () * 1.1f,
vehicle.position(),
gGray60,
20);
}
void
OpenSteer::OpenSteerDemo::drawBoxHighlightOnVehicle (const AbstractVehicle& v,
const Color& color)
{
if (&v)
{
const float diameter = v.radius() * 2;
const Vec3 size (diameter, diameter, diameter);
drawBoxOutline (v, size, color);
}
}
void
OpenSteer::SteerLibrary::
findNextIntersectionWithSphere (const AbstractVehicle& v,
SphericalObstacleData& obs,
PathIntersection& intersection)
{
// xxx"SphericalObstacle& obs" should be "const SphericalObstacle&
// obs" but then it won't let me store a pointer to in inside the
// PathIntersection
// This routine is based on the Paul Bourke's derivation in:
// Intersection of a Line and a Sphere (or circle)
// http://www.swin.edu.au/astronomy/pbourke/geometry/sphereline/
float b, c, d, p, q, s;
float3 lc;
// initialize pathIntersection object
intersection.intersect = false;
intersection.obstacle = &obs;
// find "local center" (lc) of sphere in boid's coordinate space
lc = v.localizePosition (obs.center);
// computer line-sphere intersection parameters
b = -2 * lc.z;
c = square (lc.x) + square (lc.y) + square (lc.z) -
square (obs.radius + v.radius());
d = (b * b) - (4 * c);
// when the path does not intersect the sphere
if (d < 0) return;
// otherwise, the path intersects the sphere in two points with
// parametric coordinates of "p" and "q".
// (If "d" is zero the two points are coincident, the path is tangent)
s = sqrtXXX (d);
p = (-b + s) / 2;
q = (-b - s) / 2;
// both intersections are behind us, so no potential collisions
if ((p < 0) && (q < 0)) return;
// at least one intersection is in front of us
intersection.intersect = true;
intersection.distance =
((p > 0) && (q > 0)) ?
// both intersections are in front of us, find nearest one
((p < q) ? p : q) :
// otherwise only one intersections is in front, select it
((p > 0) ? p : q);
return;
}
void
OpenSteer::OpenSteerDemo::drawCircleHighlightOnVehicle (const AbstractVehicle& v,
const float radiusMultiplier,
const Color& color)
{
if (&v)
{
const Vec3& cPosition = camera.position();
draw3dCircle (v.radius() * radiusMultiplier, // adjusted radius
v.position(), // center
v.position() - cPosition, // view axis
color, // drawing color
20); // circle segments
}
}
void
OpenSteer::OpenSteerDemo::drawCircleHighlightOnVehicle (const AbstractVehicle& v,
const float radiusMultiplier,
const float3 color)
{
if (&v)
{
const float3& cPosition = make_float3(camera.position());
draw3dCircle (v.radius() * radiusMultiplier, // adjusted radius
make_float3(v.position()), // center
float3_subtract(make_float3(v.position()), cPosition), // view axis
color, // drawing color
20); // circle segments
}
}
void
OpenSteer::
PlaneObstacle::
findIntersectionWithVehiclePath (const AbstractVehicle& vehicle,
PathIntersection& pi) const
{
// initialize pathIntersection object to "no intersection found"
pi.intersect = false;
const Vec3 lp = localizePosition (vehicle.position ());
const Vec3 ld = localizeDirection (vehicle.forward ());
// no obstacle intersection if path is parallel to XY (side/up) plane
if (ld.dot (Vec3::forward) == 0.0f) return;
// no obstacle intersection if vehicle is heading away from the XY plane
if ((lp.z > 0.0f) && (ld.z > 0.0f)) return;
if ((lp.z < 0.0f) && (ld.z < 0.0f)) return;
// no obstacle intersection if obstacle "not seen" from vehicle's side
if ((seenFrom () == outside) && (lp.z < 0.0f)) return;
if ((seenFrom () == inside) && (lp.z > 0.0f)) return;
// find intersection of path with rectangle's plane (XY plane)
const float ix = lp.x - (ld.x * lp.z / ld.z);
const float iy = lp.y - (ld.y * lp.z / ld.z);
const Vec3 planeIntersection (ix, iy, 0.0f);
// no obstacle intersection if plane intersection is outside 2d shape
if (!xyPointInsideShape (planeIntersection, vehicle.radius ())) return;
// otherwise, the vehicle path DOES intersect this rectangle
const Vec3 localXYradial = planeIntersection.normalize ();
const Vec3 radial = globalizeDirection (localXYradial);
const float sideSign = (lp.z > 0.0f) ? +1.0f : -1.0f;
const Vec3 opposingNormal = forward () * sideSign;
pi.intersect = true;
pi.obstacle = this;
pi.distance = (lp - planeIntersection).length ();
pi.steerHint = opposingNormal + radial; // should have "toward edge" term?
pi.surfacePoint = globalizePosition (planeIntersection);
pi.surfaceNormal = opposingNormal;
pi.vehicleOutside = lp.z > 0.0f;
}
void
OpenSteer::OpenSteerDemo::highlightVehicleUtility (const AbstractVehicle& vehicle)
{
if (&vehicle != NULL)
drawXZDisk (vehicle.radius(), vehicle.position(), gGray60, 20);
}
float3
OpenSteer::SteerLibrary::
steerToAvoidNeighbors (const AbstractVehicle& v,
const float minTimeToCollision,
const AVGroup& others)
{
// first priority is to prevent immediate interpenetration
const float3 separation = steerToAvoidCloseNeighbors (v, 0, others);
if (!float3_equals(separation, float3_zero()))
return separation;
// otherwise, go on to consider potential future collisions
float steer = 0;
AbstractVehicle* threat = NULL;
// Time (in seconds) until the most immediate collision threat found
// so far. Initial value is a threshold: don't look more than this
// many frames into the future.
float minTime = minTimeToCollision;
// xxx solely for annotation
float3 xxxThreatPositionAtNearestApproach;
float3 xxxOurPositionAtNearestApproach;
// for each of the other vehicles, determine which (if any)
// pose the most immediate threat of collision.
for (AVIterator i = others.begin(); i != others.end(); i++)
{
AbstractVehicle& other = **i;
if (&other != &v)
{
// avoid when future positions are this close (or less)
const float collisionDangerThreshold = v.radius() * 2;
// predicted time until nearest approach of "this" and "other"
const float time = predictNearestApproachTime (v, other);
// If the time is in the future, sooner than any other
// threatened collision...
if ((time >= 0) && (time < minTime))
{
// if the two will be close enough to collide,
// make a note of it
if (computeNearestApproachPositions (v, other, time)
< collisionDangerThreshold)
{
minTime = time;
threat = &other;
xxxThreatPositionAtNearestApproach
= hisPositionAtNearestApproach;
xxxOurPositionAtNearestApproach
= ourPositionAtNearestApproach;
}
}
}
}
// if a potential collision was found, compute steering to avoid
if (threat != NULL)
{
// parallel: +1, perpendicular: 0, anti-parallel: -1
float parallelness = float3_dot(make_float3(v.forward()), make_float3(threat->forward()));
float angle = 0.707f;
if (parallelness < -angle)
{
// anti-parallel "head on" paths:
// steer away from future threat position
float3 offset = float3_subtract(xxxThreatPositionAtNearestApproach, make_float3(v.position()));
float sideDot = float3_dot(offset, v.side());
steer = (sideDot > 0) ? -1.0f : 1.0f;
}
else
{
if (parallelness > angle)
{
// parallel paths: steer away from threat
float3 offset = float3_subtract(make_float3(threat->position()), make_float3(v.position()));
float sideDot = float3_dot(offset, v.side());
steer = (sideDot > 0) ? -1.0f : 1.0f;
}
else
{
// perpendicular paths: steer behind threat
// (only the slower of the two does this)
if (threat->speed() <= v.speed())
{
float sideDot = float3_dot(v.side(), threat->velocity());
steer = (sideDot > 0) ? -1.0f : 1.0f;
}
}
}
annotateAvoidNeighbor (*threat,
steer,
xxxOurPositionAtNearestApproach,
xxxThreatPositionAtNearestApproach);
}
return float3_scalar_multiply(v.side(), steer);
}
void
OpenSteer::
SphereObstacle::
findIntersectionWithVehiclePath (const AbstractVehicle& vehicle,
PathIntersection& pi) const
{
// This routine is based on the Paul Bourke's derivation in:
// Intersection of a Line and a Sphere (or circle)
// http://www.swin.edu.au/astronomy/pbourke/geometry/sphereline/
// But the computation is done in the vehicle's local space, so
// the line in question is the Z (Forward) axis of the space which
// simplifies some of the calculations.
float b, c, d, p, q, s;
Vec3 lc;
// initialize pathIntersection object to "no intersection found"
pi.intersect = false;
// find sphere's "local center" (lc) in the vehicle's coordinate space
lc = vehicle.localizePosition (center);
pi.vehicleOutside = lc.length () > radius;
// if obstacle is seen from inside, but vehicle is outside, must avoid
// (noticed once a vehicle got outside it ignored the obstacle 2008-5-20)
if (pi.vehicleOutside && (seenFrom () == inside))
{
pi.intersect = true;
pi.distance = 0.0f;
pi.steerHint = (center - vehicle.position()).normalize();
return;
}
// compute line-sphere intersection parameters
const float r = radius + vehicle.radius();
b = -2 * lc.z;
c = square (lc.x) + square (lc.y) + square (lc.z) - square (r);
d = (b * b) - (4 * c);
// when the path does not intersect the sphere
if (d < 0) return;
// otherwise, the path intersects the sphere in two points with
// parametric coordinates of "p" and "q". (If "d" is zero the two
// points are coincident, the path is tangent)
s = sqrtXXX (d);
p = (-b + s) / 2;
q = (-b - s) / 2;
// both intersections are behind us, so no potential collisions
if ((p < 0) && (q < 0)) return;
// at least one intersection is in front, so intersects our forward
// path
pi.intersect = true;
pi.obstacle = this;
pi.distance =
((p > 0) && (q > 0)) ?
// both intersections are in front of us, find nearest one
((p < q) ? p : q) :
// otherwise one is ahead and one is behind: we are INSIDE obstacle
(seenFrom () == outside ?
// inside a solid obstacle, so distance to obstacle is zero
0.0f :
// hollow obstacle (or "both"), pick point that is in front
((p > 0) ? p : q));
pi.surfacePoint =
vehicle.position() + (vehicle.forward() * pi.distance);
pi.surfaceNormal = (pi.surfacePoint-center).normalize();
switch (seenFrom ())
{
case outside:
pi.steerHint = pi.surfaceNormal;
break;
case inside:
pi.steerHint = -pi.surfaceNormal;
break;
case both:
pi.steerHint = pi.surfaceNormal * (pi.vehicleOutside ? 1.0f : -1.0f);
break;
}
}