Here’s an initial test of octree-based cutting simulation: If you turn up the resolution to eleven, where it starts to be useful and not so grainy, the calculation of the tool-swept volume, which we subtract from the stock at each move, becomes too slow. See also octree operations. Download a short clip with a depth=10 [...]

When generating toolpaths with drop-cutter (“axial tool-projection”, if you like fancy words) the path ends up being composed of lots of short linear segments. It makes sense to filter this list of points and take out any middle points that lie on a straight line between neighboring points. Here’s a first attempt at such a [...]

People who, unlike me, actually know something about programming often talk about design patterns. One common idea is to compose objects out of other objects. I was able to add four new APT-tool like cutter classes to ocl with about 5-lines of code for each cutter (sans the bugfixing, taking much longer, that also took [...]

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

If you number the octants in an octree using a 1982 scheme called Gargantini-code, and store the codes for only the black nodes in the tree in a list then that’s called a linear octree. For quadtrees, there is a 1985 paper by Bauer with an algorithm for computing set-operations (intersection, union, difference) between two [...]

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) [...]

explanation(s) to follow at some point…

Recursion and ‘divide-and-conquer‘ must be two of the greatest ideas ever in computer science. Threw together some code in python today for building an octree, given a function isInside() which the tree-builder evaluates to see if a node is inside or outside of the object. Nodes completely outside the interesting volume(here a sphere, for simplicity) [...]

In colours and numbers, the number of iterations in the offset-ellipse solver required to reach an arbitrary 8-digit precision. A smart choice of initial value can save almost half of the computation.