Find subcurves with normals between certain angles

I would like to use grasshopper to shatter curves into pieces, based on the relationship of the normals of the curve the unit X vector.

In my application, I want to separate out four different types of curve:

  1. Normals from 45-135 degrees of unit x
  2. from 135-225
  3. from 225-315
  4. greater than 315 and less than 45

Input curve with manually drawn normals and points on the left,
Manual representation of desired outcome on the right:

I have no idea where to start when it comes to achieving this. Could I use this definition, plus Galapagos? Or would that be painfully slow? Is there a simple mathy solution?

(definition: Find 15 135 225 315 (8.4 KB) )

Why do I need this? It’s for CNC routing hardwoods. When routing along the grain, you get less tearout by doing a climb cut, when routing across the grain, you get less tearout by doing a conventional cut. (climb vs. conventional is about the direction of rotation of the bit relative to it’s path of movement). Being able to automatically separate a curve into portions that get one type of cut vs. the other would save a lot of time when programing cuts in hardwood. I currently do it by eyeballing the angle in Rhino and using the perpendicular curve tool. Tedious.

Thank you.

I don’t know c# and have never used scripting components myself.

Would you mind uploading the definition?

No problem- (10.1 KB)
The script is just that one line shown in the screenshot.

I just realised as well that it looks like there is a built in Gh component for this - the “X-tremez” component under curve analysis

It looks like the built in component only gives the outer tangent points though: (4.9 KB)

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Yup. That’s why it didn’t occur to me to use it.

Haven’t had a chance to open your definition with the script yet because I’m doing child care, but it looks like plugging in all the combinations of .5 and -.5 x and y values will get me where I want to go.

OK. It works. Almost*.

Thanks again for your help.

Definition:Find 45 135 225 315 (13.8 KB)

*Dividing up closed curves works. Not quite ready to use for CNC toolpaths yet, because concave polyline vertices will need some special treatment.

Do you actually machine the profiles as 2 sets of curves? One set for climb and another conventional?
Do you get marks on the wood where the curves meet?
Have you tried using spiral cutters with a down spiral?

So far I’ve only done this when cutting circles.

I do a roughing pass all the way around, leaving 1/16", and then climb cut the side grain and conventional cut the end grain. Upcut rougher, compression spiral for finishing. The rougher has a larger diameter than the finisher, so I just plunge the finisher into the void left by the rougher and do a radial entry to the cut. I overlap the spots where the curves meet by a little.

Wouldn’t a downcut give me tearout on the bottom of the workpiece?

Here’s an updated definition, still not complete. It has some Human plugin components in clusters for baking. Other than that I think it’s all native.

It bakes to two different layers, but I think I’m going to change it to bake to one layer with two different colors.

It also has a setting for overlapping the curves. And there’s setting for a minimum cut length so that situations where the output includes tiny cuts on pointy objects can be tamed if you want. (look close at the pic labeled “almost works” above. There’s a teeny spot of yellow in one place. I didn’t like it so I created an option to extend it to a given length, say 1 inch minimum.

The overlaps are hard to see with basic custom preview, but they’re there.

It works perfectly with closed curves that have no convex vertices.

Convex vertices are a problem because splitting up a profile will give you curves that create toolpaths that cut into the part. That will take some headscratchy geometry to fix. It also has a relatively easy bug to fix with open curves: the overlap setting shouldn’t affect the outer ends of the original curve, only the interior ends of the new curve.

Lastly, I would like to figure out how to vary the angle at which the curves are split up. I’m pretty sure spitting them at 45-135-225-315 will work in most cases, but it’d be nice to have options. There’s a group in the definition I’m posting below that is my failed attempt to create a variable division point. @DanielPiker do you have suggestions on this one?

Here’s the definition. The cluster at the beginning just places the output in a bounding box at zero. If you draw input to the left of the y axis you can see input and result at the same time.

Find 45 135 225 315 (47.5 KB)

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You can set any angles you like in the v input of the script

I use up/down spiral cutters sometimes where the bottom few millimeters have an up spiral and the rest is down spiral. They’re good for finishing pass on hardwood plywood.
I need to cut 4 oak staircase stringers with 42 degree steps so might experiment with conventional vs climb. Probably make no difference at 42 degrees tho.