Technical question regarding "print and cut" funcion

How can it be that only 2 reference points are needed to get the amazingly precise results that this function gives us and not 3 reference points as “normally” are needed for “geocoding”. (I am aware that we are not working with 3 dimensions in plane drawings)

The features in print and cut only require 3 data points to function:

  1. position - LightBurn needs to know where on material the laser is positioned. This could actually be provided by a single reference point if you had an independent way of getting orientation. However, it’s easy to get orientation using a second reference point.
  2. orientation - The second reference point is used to determine the orientation of the material and the required rotation required of the design to match the material. This would technically only need to be a relative direction like degrees on a compass relative to the first reference point. But because we have an exact position for the second reference point we can determine scaling.
  3. scale - Since the distance of the 2 points can tell us about the scale of the design vs what’s on material, LightBurn can use that information to scale the design as necessary to match.

@bLouChip’s recent post about using 2-point rotate and scale essentially duplicates print and cut by using the first 2 required components above.

Thanks for your explanation. I’ve seen what you’re referring to and understand it. But is it more accurate as a 3-point reference or simpler, that’s what interests me about this method.

3 point would actually complicate the issue as you’d now have a potential situation where the shape created by the 3 points could differ in design vs what you align to on material. Imagine that when after you completed the identification of the 3-target reference points on material that the relative angles between the 3 points is different than what is in LightBurn. This is eliminated entirely if you limit yourself to 2 points as that gives you the position, orientation, and scale required.

You could potentially use 3 points to do some level of distortion correction but that would start to get really weird. At that point it would probably be easier to print a similar pattern to the lens calibration pattern onto the print and cut material and have LightBurn auto orient and correct.

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Thank you for this elaboration.

You’d need 3 reference IF this were in 3 dimensional space. But it’s not- it’s a flat plane.

In GPS, we’re not using reference points, but 3 dimensional distance measurements. The receiver only gets a range to a satellite. So a single range measurement- even if its accuracy is “perfect”- only “narrows it down” to a sphere tens of thousands of km in radius. Two readings adds a second sphere, which narrows it down to the intersection of two- a huge circle. Any point on that circle is solution that is possible for both range measurements. A third sphere narrows it down to 2 possible intersection points.

We’re not taking spherical range measurements, but defining a know XY reference point. Two points are all that is needed to orient and scale.

It is important for accuracy that the 2 points be as far apart as possible. It does not matter if they aren’t diagonal, either. We’re not triangulating. They can be aligned with the X or Y axis, that won’t matter- all that matters is that they be far apart with the content in between the points.

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Danny is right.
A vector and a single point isn’t enough and two points aren’t enough for 3D. With the plane known or a 2D system defined the solution resolves.

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