If you calculate toolpaths around a very narrow and 'pointy' triangle you will get toolpaths in the shape of the inverse cutter - the "Inverse Tool Offset". Here I've plotted the basic operations, in red/blue drop-cutter which drops the cutter down along the z-axis until it contacts the triangle, and in cyan waterlines which are [...]
Inspired by this post on the pycam forum and by this 1993 paper by Luiz Henrique de Figueiredo (or try another version) I did some work with adaptive sampling and drop-cutter today. The point based CAM approach in drop-cutter, or axial tool-projection, or z-projection machining (whatever you want to call it) is really quite similar [...]
Wednesday, April 21, 2010
I've experimented with using OpenMP to calculate drop-cutter toolpaths on a quad-core machine. These now run reasonably fast. There are obvious lurking bugs with BallCutter and BullCutter still... Code is here: code.google.com/p/opencamlib/ (if you know C++, computational geometry, and cnc-machining, or are willing to learn, this project needs your help!) See also: styrofoam spider
A one-triangle test of drop-cutter for toroidal tools (a.k.a. filleted-endmills, or bull-nose). The blue points are contacts with the facet, and the green points are contacts with the vertices. These are easy. The edges-contacts (red-points) are a bit more involved, and are done with the offset-ellipse solver presented earlier here(the initial geometry) and here(offset-ellipse construction) [...]
More on the offset-ellipse calculation, which is related to contacting toroidal cutters against edges(lines). An ellipse aligned with the x- and y-axes, with axes a and b can be given in parametric form as (a*cos(theta) , b*sin(theta) ). The ellipse is shown as the dotted oval, in four different colours. Now the sin() and cos() are [...]
Contacting a toroidal cutter (not shown) against an edge (cyan line), is equivalent to dropping down a cylindrical cutter (lower edge shown as yellow circle) against a cylinder (yellow tube) around the edge, with a radius equal to the tube-radius of the original toroidal cutter. The plane of the tip of the cylindrical cutter slices [...]
For spherical cutters (a.k.a. ball-nose), the vertex-test (green dots), and the facet-test (blue dots), are fairly trivial. The edge-test (red-dots) is slightly more involved. Here, unlike before, I tried doing it without too many calls to "expensive" functions like sin(), cos() and sqrt(). The final result of taking the maximum of all tests is shown [...]
After the kd-tree search is done, I've added an overlap-check which leaves only triangles with a bounding box intersecting the cutter's bounding box for the drop-cutter algorithm. It's seems like a band-aid kind of hack to get it working, I think if the tree-search would be bug free the overlap check would not be needed... [...]
Wednesday, March 17, 2010
When vimeo has had time to process the video, this will show a visualization of the kd-tree search: http://vimeo.com/10241672 the code is probably still a bit buggy...
I've continued to translate into C++ the old cam-experiments I wrote in C#. The kd-tree search for which triangles lie under the cutter seems to work, and the best way to visualize what is going on is through a video. Trying Vimeo for a change, to see if it's any better than youtube for these [...]