colDet_unstested.lua

function overlapsOBB_OBB(c1, x1, y1, z1, c2, x2, y2, z2)
  local cc = c1 - c2
  local d11, d12, d13 = abs(x1:dot(x2)), abs(x1:dot(y2)), abs(x1:dot(z2))
  local d21, d22, d23 = abs(y1:dot(x2)), abs(y1:dot(y2)), abs(y1:dot(z2))
  local d31, d32, d33 = abs(z1:dot(x2)), abs(z1:dot(y2)), abs(z1:dot(z2))

  return abs(cc:dot(x1))-d11-d12-d13<=x1:squaredLength() and abs(cc:dot(y1))-d21-d22-d23<=y1:squaredLength() and abs(cc:dot(z1))-d31-d32-d33<=z1:squaredLength()
        and abs(cc:dot(x2))-d11-d21-d31<=x2:squaredLength() and abs(cc:dot(y2))-d12-d22-d32<=y2:squaredLength() and abs(cc:dot(z2))-d13-d23-d33<=z2:squaredLength()
end

function containsOBB_OBB(c1, x1, y1, z1, c2, x2, y2, z2)
  local cc = c1 - c2
  return abs(cc:dot(x1))+abs(x1:dot(x2))+abs(x1:dot(y2))+abs(x1:dot(z2))<=x1:squaredLength() and abs(cc:dot(y1))+abs(y1:dot(x2))+abs(y1:dot(y2))+abs(y1:dot(z2))<=y1:squaredLength() and abs(cc:dot(z1))+abs(z1:dot(x2))+abs(z1:dot(y2))+abs(z1:dot(z2))<=z1:squaredLength()
end

function overlapsOBB_Sphere(c1, x1, y1, z1, c2, r2)
  local cc = c1 - c2
  local x1len, y1len, z1len = x1:length(), y1:length(), z1:length()
  local ccx, ccy, ccz = abs(cc:dot(x1)), abs(cc:dot(y1)), abs(cc:dot(z1))

  return ccx<=x1len*(x1len+r2) and ccy<=y1len*(y1len+r2) and ccz<=z1len*(z1len+r2)
    and (ccx<=x1len*x1len or ccy<=y1len*y1len or ccz<=z1len*z1len or
      square(ccx/(x1len+1e-30)-x1len) + square(ccy/(y1len+1e-30)-y1len) + square(ccz/(z1len+1e-30)-z1len)<=r2 * r2)
end

function containsOBB_Sphere(c1, x1, y1, z1, c2, r2)
  local cc = c1 - c2
  local x1len, y1len, z1len = x1:length(), y1:length(), z1:length()
  return abs(cc:dot(x1))<=x1len*(x1len-r2) and abs(cc:dot(y1))<=y1len*(y1len-r2) and abs(cc:dot(z1))<=z1len*(z1len-r2)
end

function containsSphere_OBB(c1, r1, c2, x2, y2, z2)
  local cc = c1 - c2
  local ccx1, cc_x1, y1z1, y1_z1 = cc+x2, cc-x2, y2+z2, y2-z2
  return max((ccx1+y1z1):squaredLength(), (ccx1+y1_z1):squaredLength(), (ccx1-y1_z1):squaredLength(), (ccx1-y1z1):squaredLength(),
      (cc_x1+y1z1):squaredLength(), (cc_x1+y1_z1):squaredLength(), (cc_x1-y1_z1):squaredLength(), (cc_x1-y1z1):squaredLength())<=r1*r1
end