Drawing in PDF: chamber_holder
Drawing in DXF: plate_v2.dxf

For the most part truetypetracer produces valid and nice input data for testing openvoronoi. But sometimes I see wiggles, and now this:

It is frustrating to try to track down bugs in downstream algorithms that take this as input, and assume all line-segments are non-intersecting when in fact the are not!

I seem to have only 13 .ttf files in my /usr/share/fonts/truetype/freefont folder, but maybe there are more elsewhere. I should find a font that is properly designed without wiggles and without overlaps. The other approach is to write a pre-processor that looks at input data and either rejects or cleans it. Looking for all pair-wise intersections of N line-segments is a slow N^2 algorithm - at least for a naive implementation (without bounding-boxes or binning or other tricks).

Unlike the wiggles, this overlap doesn't happen in Inkscape:

Here is G-code generated with ttt-4.0 and drawn in LinuxCNC:

Here is a screenshot from LibreOffice 3:

and GIMP:

A first try at v-carving, with toolpaths produced by the ttt2medial python script.

The medial axis on the right does not look correct. If we zoom in it's clear that there's an "S-curve" in the input geometry, which causes a LINELINE edge (drawn in darker blue), which the medial-axis filter doesn't think should be removed:

For the letters "EMC" it looks mostly OK, but there's a similar wiggle in "E"

Increasing the number of line-segments further causes even stranger things. Here's a zoom-in at the top of "P" that shows both the wiggle that was visible before, but also a strange inward bulge:

Hopefully this is a bug in how conics/cubics are converted to line-segments in ttt, and not an issue with how FreeType fonts are represented.

The first one is ttt2ngc which simply demonstrates my C++ port of Chris Radek's truetype-tracer. The original code is a rather monolithic C-program while my C++ port is divided into smaller files and offers python-bindings and more options (for example arc, cubic, conic output can be turned on/off independently).

The seconds script is ttt2offset which takes ttt-geometry, builds a VD, and produces offsets. By reversing the list of points from ttt either inwards or outwards offsets can be produced. Currently the toolpaths are machined in the order they are produced, i.e. in order of increasing offset value. An improvement would be to order the loops so that for e.g. pocketing the innermost loop is machined first, and rapid-traverses are minimized.

The third script is ttt2medial. Here the VD is filtered down to an (approximate) medial-axis, and the edges of the medial axis are chained together into a toolpath. The chaining-algorithm could probably be improved much, again to minimize rapid-traverses.

If this is run with a V-shaped cutter with a 90-degree angle we can push the cutter into the material by an amount equal to the clearance-disk radius of the edge. This is a "V-carving" toolpath which should produce a cut-out very similar to the outline of the font. For added effect choose a material with  contrasting surface and interior colors.

It would be interesting to know if this v-carving g-code is anywhere near to correct. If someone has a cutting-simulator, or is adventurous enough to run this on an actual machine, I'd be very interested in the results! (here is the g-code: emc2_vcarve.ngc)

Here is a metric version. The max depth is around -3mm, so a 10mm diameter 90-degree V-cutter should be OK. The text should be roughly 100mm long: emc2_vcarve_mm_ver2.ngc

Disclaimer: This is experimental code. Warnings, Errors, and Segfaults are common.

The first one detects the interior or exterior of a polygon. When the VD is constructed the polygon boundary must be input in CW order, and any islands inside the polygon in CCW order (or vice versa). This allows running other downstream algorithms only on the parts of the VD that pass the filter. Like these exterior and interior offsets:

The other filter looks at the interior VD and tries to produce an approximate medial axis. We can start with the complete interior VD, such as this "J":

By definition the medial axis consists of "the set of all points having more than one closest point on the object's boundary". The separator edges shown in purple above can clearly be eliminated, since their adjacent/defining sites are an open line-segment and the segment's endpoint. Removing separators gives us this:

Now we can either finish here, or try to filter out some more edges to make it look better. Since we approximated smooth curves with line-segments we should try to detect which parts of the boundary are really distinct curves, and which are merely many consecutive line-segments approximating a single smooth curve. I've compared the dot-product (angle) between two consecutive segments, and applied an arbitrary threshold:

For the whole alphabet it looks like this.

The choice of threshold value for the angle-filtering is arbitrary. In many cases such as "x" and "m" it results in small or large left-over branches. This could probably be avoided by (1) tuning the angle-threshold, (2) approximating smooth curves with a larger number of line-segments, (3) eliminating branches below a certain length, or (4) choosing a font that's made for v-carving (are there any?).

Although it's probably not right to call it a "medial axis" , the same filter applied to the exterior VD also looks interesting. It divides the plane into organic looking shapes around each letter. It could probably be used for a lot of shape analysis. For example in a smart pocketing routine to find large areas that can be cleared with a large cutter, before a smaller cutter is required for the details. Note that in addition to the geometric shape of all the blue-ish edges the diagram also holds distance-information at each point of an edge. The distance stored is a clearance-disk radius, i.e. we can draw a circle at any point of an edge with this radius, and no input geometry (in yellow) will intersect the circle.

Here is a larger example where VD takes 1.3 seconds, and all offsets shown take 99 milliseconds in total to produce. It would be interesting to benchmark this against libarea or other open-source 2D offset solutions. (here all line/arc offsets in one green color, for simplicity)

Here is a third picture with offsets for a single offset-distance:

Over here: http://www.anderswallin.net/loppiaisrogaining2012/

OpenLayers has a nice set of examples online. Browsing and copy/pasting from examples is much better than trying to read & understand formal documentation.

There was an issue with handling collinear line-segments, which is hopefully now fixed. OpenVoronoi seems to deal OK with most characters from ttt now.

I am still getting some Warnings about numerical instability from LLLSolver, possibly related to these high-degree vertices which don't look quite right (this is a zoom-in inside the circular dot of "j" in the picture above):

I should write a class for extracting offsets next. Then perhaps medial axis (if anyone is interested in v-carving toolpaths).