This is about my third rewrite of this fairly simple cam-algorithm where the cutter is dropped from above until it touches a triangle. It's now in C++ with Boost-python bindings and with visualization using vtk. The cutter-location points are calculated by bringing the cutter into contact with the vertices of the triangle (green cl-points), the [...]
First test with drop-cutter aided by the kd-tree. The output toolpath looks very much like the one without kd-tree, which is good. Less great is that I expected a speed-up of the algorithm - but in fact when I use kd-tree the program slows down! Something to investigate over the next few days.
Drop-cutter requires a fast way of searching for triangles under the tool. A kd-tree (4-dimensional in this case) is suggested by Yau et al. I've tried to implement one here (look in trunk/Project2). Just ran some timing tests using Stopwatch() on it, and indeed the build_kdtree() function which takes a pile of triangles as input [...]
Wednesday, August 8, 2007
I think I've found the problems with my C# drop-cutter algorithm. The first bug was a trivial one where in the edge-test the rotation of the segment-under-test was messed up. The second one was not the facet-test itself but incorrect surface normal data. There's something going on that makes pre-calculated surface normal data not 'stick' [...]
I've now ported my Matlab work on Drop-Cutter to C#. It can load an ASCII STL file and then run the drop cutter algorithm. Not trying to take too much on in the beginning, here's an example of the output with only two triangles as input not quite there yet! (who can spot what's wrong?) [...]
Here's the first indication that my drop cutter algorithms(vertex, facet, edge) might work! I'm dropping down a toroidal cutter C(0.5, 0.125) towards a model consisting of a half-sphere sitting on a plane. The CL points are in magenta with cyan lines between them. 382 triangles in total. The code has no optimizations, so at each [...]
The third and final test in the drop cutter algorithm is to drop the cutter down so it touches an edge. The vertex and facet tests were quite easy, but this one requires a bit of calculations. I'm following Chuang2002. To simplify things we first translate the tool in the (x, y) plane to (0, [...]
The facet test I wrote about yesterday needs a 'point in triangle' test to determine if the found CC point lies within the given triangle and we should thus care about the ze value the algorithm determined, or if the CC point is outside, and we can skip to the next test/triangle. I wrote a [...]
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Now the problem of contacting a toroidal cutter with the facet of a triangle. We need to find the equation of the plane which contains the triangle. If the triangle is defined by three points p1 = (x1, y1, z1), p2 = (x2, y2, z2), p3 = (x3, y3, z3) then a surface normal will [...]
Based on a 2002 paper by Chuang et al., I'm trying to understand the math for calculating 'drop-cutter' toolpaths (Julian Todd also has a lot to say about the drop-cutter approach). The basic idea is that the x,y position of the cutter is known, and it is dropped down along the z-axis until it touches [...]