[SciPy-user] Help with a 3D problem

[Nuttall, Brandon C]

Folks,

I need some help figuring out how to plot the trajectory of a path through 3D space. I know the trajectory passes through several points with (x, y, z) cooreinates:

Point 1: (0,0,0)
Point 2: (0,0,-z2) -- the 2 is a subscript for the variable "z", not
                                the square of z
Point 3: (A,B,-z3)
Point 4: (x4,y4,-C)
Point 5: (D,E,-C)

A, B, C, D, and E are constants (given)

I need to determine the variables z2, z3, x4, and y4 such that:
1) The path of the trajectory from Point 1 to Point 2 is a straight line
2) Points 2, 3, and 4 are on a circular path of constant radius
3) The path of the trajectory from Point 4 to Point 5 is a straight line
4) The straight line paths between points 1 and 2 and points 4 and 5 are tangents to the circular path described by points 2, 3, and 4
5) The straight line paths between points 1 and 2 and points 4 and 5 are perpendicular to each other.

Now, what I want to be able to do is once the trajectory is determined, I want to be able to either:

Given a distance, L, along the path of the trajectory from (0,0,0), determine the (x,y,z) coordinates of that point, or

Given an (x,y,z) location on the trajectory, determine L (inverse of above)

Thanks for any help or references.

Brandon Nuttall