My Second Chalice Lathe Customizer

thingiverse

A very specific input. This input appears to be a list of lathe objects, each represented as a string in a specific format. The first line defines the axes, which are 4-dimensional ( x,y,z,t ) and use an elliptical rotation along axis z ( i.e. , rotation matrix has elements sin and cos instead of -sin for z rotations ). Each line of the input specifies points on one "ring" with lathe parameter θ _{n} defining angle, s ^{0}_{ n }= t in which a particular ring should start rotating, h being height from equator.