Freesteel Blog » Two whole days to intersect a line with a cylinder

Two whole days to intersect a line with a cylinder

Tuesday, November 7th, 2006 at 2:13 pm Written by:


Baaaa! Brain’s in very bad thinking shape. Bug after bug after bug after bug in about 2 pages of code. This is a pencil fillet surface, used for protecting corners on high speed machining, and as the basis for rest machining, I think. Who knows, since no one else has ever told me about how they do rest machining, so the good old method I’ve used for 10 years has had to stand while no better ideas come along.

This is only for ball-nosed cutters, so it’s made up of pieces of cylinder. Now I got to extend it to flat bottom cutters, and then — horror — toroidal cutters. For them I’d need to find the root of a quartic polynomial. I have published some preparatory work on that score.

My quartic solver will go down into the groundsteel level of the code, so it should be released as public domain, along with my line-offset-ellipse 6th order polynomial solver. Eventually we’ll work out who’s interested enough to publish it, so we can show people how it is done. Or even better, they will take one look at it, decide it’s crap, and show us how it’s done.

There are already solvers on the net, like this one, but copyright some random person 1994 who hasn’t left any contact details in his code, so not a lot of good to beast nor man. I suppose we could always look and read it like a work of literature, but the purpose of code is to be used. If you write it and it doesn’t get used, what’s the point of that?


  • 1. Jeff replies at 11th November 2006, 6:06 am :

    Your solver is really a nice utility for toroidal cutters toolpath, it reminds me of my first project for projecting bull nose tool when I just began to work 10 years ago. I just wonder if you use the solver for waterline slicing?

  • 2. Julian replies at 13th November 2006, 12:03 pm :

    I’ve got some notes to add soon once I’ve had some time to make diagrams. My opinion has recently become divided on the use of the quartic solver now.

    Short summary: for the two problems of cutting a vertical line against the sweep of a toroidal cutter, and of dropping a toroidal cutter until it is in contact with an arbitrary line, the equation is fourth order — quartic.

    For waterline slicing, sliding a torus sideways until it is in contact with a line, the equation becomes sixth order, so you have to solve it numerically.

    The numeric solutions are not bad because you can predict where the solutions will be using geometry. For example, whether or not the torus moving sideways will hit or miss the line is decided by a quadratic equation.

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