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Hi, I'm trying to intersect ray with "renderman hyperboloid" defined by two points P1(x1,y1,z1) and P2(x2,y2,z2). Hyperboloid equation from MathWorld is: (x/a)^2 + (y/a)^2 - (z/c)^2 = 1. (1) Plugging P1 & P2 into (1) I get: c2 = [(x2^2 + y2^2)*z1^2 - (x1^2 + y1^2)*z2^2]/[x1^2 + y1^2 - x2^2 - y2^2]. a2 = [z1^2*(x2^2+y2^2) - z2^2*(x1^2+y1^2)]/[z1^2-z2^2] Denominator of c2 is simply difference between distance of P1 and P2 to Z axis. If these distances are equal I cannot compute c2.Similarly if z1^2 == z2^2 there is no solution to a2. However it seems to me that there exists a2 & c2 for such points.(for example P1(1,1,1) P2(1,1,-1) a2=1, c2=1) Where is the mistake and what is the correct way to compute those coefficients ? Thanks for any help Regards Tom