static VALUE
m_sqrt(VALUE x)
{
if (f_real_p(x)) {
if (f_positive_p(x))
return m_sqrt_bang(x);
return f_complex_new2(rb_cComplex, ZERO, m_sqrt_bang(f_negate(x)));
}
else {
get_dat1(x);
if (f_negative_p(dat->imag))
return f_conj(m_sqrt(f_conj(x)));
else {
VALUE a = f_abs(x);
return f_complex_new2(rb_cComplex,
m_sqrt_bang(f_div(f_add(a, dat->real), TWO)),
m_sqrt_bang(f_div(f_sub(a, dat->real), TWO)));
}
}
}
// R1 and R2 hold the projection of edge endpoints onto cross-section of tube centered on origin
// t1 and t2 hold projections of edge onto axis of tube (tube goes from 0 to tubeLen)
// we assume t1<t2
// on return hit point is offset from center line but not projected along the line
bool edgeInTube(Point3F & R1,Point3F & R2,float t1,float t2, float radius, float invRadius2, float invTubeLen,
float & hitTime,Point3F & hitPoint)
{
// range of edge that could still be in tube and close enough: (0,1) is whole edge
float rangeA=0.0f;
float rangeB=1.0f;
// shrink down range based on time:
if (t1<0.0f)
{
if (t2<0.0f)
return false;
rangeA = -t1/(t2-t1);
}
if (invTubeLen * t2 > hitTime)
{
if (invTubeLen * t1 > hitTime)
return false;
rangeB = (hitTime - t1 * invTubeLen) / (invTubeLen * (t2-t1));
}
// now shrink down range based on distance of projection from origin
Point3F R12 = R2;
R12 -= R1;
float edgeLen2= m_dot(R12,R12);
if (edgeLen2==0.0f)
{
// R1=R2. Are they in the circle?
if (R1.x*R1.x + R1.y*R1.y + R1.z*R1.z >= radius*radius)
return false;
// o.w., don't restrict range based on projection
}
else
{
// signed dist from R1 of point on edge line (not edge) closest to origin
// actually R12 times above dist. (optimization)
float edgePointDist = - m_dot(R1,R12);
// dist squared of projected edge line (not edge) from origin
float edgeDistSquared = edgeLen2 * m_dot(R1,R1) - edgePointDist*edgePointDist;
if (edgeDistSquared>=edgeLen2 * radius * radius)
return false;
// put off adjusting edgePointDist and edgeDistSquared till now for speed...
float invEdgeLen = 1.0f/m_sqrt(edgeLen2);
edgePointDist *= invEdgeLen;
edgeDistSquared *= invEdgeLen;
edgeDistSquared *= invEdgeLen;
// projected edge intersects circle iff (0,edgeLen) intersects
// edgePointDist +/- sqrt(rad^2-edgeDist^2)
// use an approximation to sqrt:
float x = 1.0f-invRadius2*edgeDistSquared;
float bound = -.699 * radius * (x+.07978539f)*(x-2.277210289f);
float loRange = invEdgeLen * (edgePointDist-bound);
float hiRange = invEdgeLen * (edgePointDist+bound);
if (hiRange<rangeA || loRange>rangeB)
return false;
if (loRange > rangeA)
rangeA=loRange;
}
hitTime = (t1 + rangeA * (t2-t1)) * invTubeLen;
hitPoint.x = R1.x + (R2.x-R1.x) * rangeA;
hitPoint.y = R1.y + (R2.y-R1.y) * rangeA;
hitPoint.z = R1.z + (R2.z-R1.z) * rangeA;
return true;
}
