// Intersect AABBs ‘a’ and ‘b’ moving with constant velocities va and vb.
// On intersection, return time of first and last contact in tfirst and tlast
public static bool IntersectMovingAABBAABB(AABB a, AABB b, LVector3 va, LVector3 vb,
out LFloat tfirst, out LFloat tlast)
{
// Exit early if ‘a’ and ‘b’ initially overlapping
if (TestAABBAABB(a, b))
{
tfirst = tlast = LFloat.zero;
return(true);
}
// Use relative velocity; effectively treating 'a' as stationary
LVector3 v = vb - va;
// Initialize times of first and last contact
tfirst = LFloat.zero;
tlast = LFloat.one;
// For each axis, determine times of first and last contact, if any
for (int i = 0; i < 3; i++)
{
if (v[i] < LFloat.zero)
{
if (b.max[i] < a.min[i])
{
return(false); // Nonintersecting and moving apart
}
if (a.max[i] < b.min[i])
{
tfirst = Max((a.max[i] - b.min[i]) / v[i], tfirst);
}
if (b.max[i] > a.min[i])
{
tlast = Min((a.min[i] - b.max[i]) / v[i], tlast);
}
}
if (v
[i] > LFloat.zero)
{
if (b.min[i] > a.max[i])
{
return(false); // Nonintersecting and moving apart
}
if (b.max[i] < a.min[i])
{
tfirst = Max((a.min[i] - b.max[i]) / v[i], tfirst);
}
if (a.max[i] > b.min[i])
{
tlast = Min((a.max[i] - b.min[i]) / v[i], tlast);
}
}
// No overlap possible if time of first contact occurs after time of last contact
if (tfirst > tlast)
{
return(false);
}
}
return(true);
}
public static bool IntersectMovingSphereAABB(Sphere s, LVector3 d, AABB b, out LFloat t)
{
// Compute the AABB resulting from expanding b by sphere radius r
AABB e = b;
int _val = s.r._val;
e.min._x -= _val;
e.min._y -= _val;
e.min._z -= _val;
e.max._x += _val;
e.max._y += _val;
e.max._z += _val;
// Intersect ray against expanded AABB e. Exit with no intersection if ray
// misses e, else get intersection point p and time t as result
LVector3 p;
if (!IntersectRayAABB(s.c, d, e, out t, out p) || t > LFloat.one)
{
return(false);
}
// Compute which min and max faces of b the intersection point p lies
// outside of. Note, u and v cannot have the same bits set and
// they must have at least one bit set amongst them
int u = 0, v = 0;
if (p.x < b.min.x)
{
u |= 1;
}
if (p.x > b.max.x)
{
v |= 1;
}
if (p.y < b.min.y)
{
u |= 2;
}
if (p.y > b.max.y)
{
v |= 2;
}
if (p.z < b.min.z)
{
u |= 4;
}
if (p.z > b.max.z)
{
v |= 4;
}
// ‘Or’ all set bits together into a bit mask (note: here u + v == u | v)
int m = u + v;
// Define line segment [c, c+d] specified by the sphere movement
Segment seg = new Segment(s.c, s.c + d);
// If all 3 bits set (m == 7) then p is in a vertex region
if (m == 7)
{
// Must now intersect segment [c, c+d] against the capsules of the three
// edges meeting at the vertex and return the best time, if one or more hit
LFloat tmin = LFloat.FLT_MAX;
if (IntersectSegmentCapsule(seg, Corner(b, v), Corner(b, v ^ 1), s.r, out t))
{
tmin = Min(t, tmin);
}
if (IntersectSegmentCapsule(seg, Corner(b, v), Corner(b, v ^ 2), s.r, out t))
{
tmin = Min(t, tmin);
}
if (IntersectSegmentCapsule(seg, Corner(b, v), Corner(b, v ^ 4), s.r, out t))
{
tmin = Min(t, tmin);
}
if (tmin == LFloat.FLT_MAX)
{
return(false); // No intersection
}
t = tmin;
return(true); // Intersection at time t == tmin
}
// If only one bit set in m, then p is in a face region
if ((m & (m - 1)) == 0)
{
// Do nothing. Time t from intersection with
// expanded box is correct intersection time
return(true);
}
// p is in an edge region. Intersect against the capsule at the edge
return(IntersectSegmentCapsule(seg, Corner(b, u ^ 7), Corner(b, v), s.r, out t));
}