Precision ratio between Stepper axes when the main loop timestep is too coarse

[MLM]

How can I keep a precision ratio between two axes when the main loop timestep is too big?

Say the main loop timestep is 0.1 seconds. If the stepper pulse width is 0.01 for x and 0.05 for y. Then with my current code, on each tick they both step(because 0.1 > (0.01 || 0.05)) and you end up with a uniform diagonal line instead of a line with 1/5 slope.


I can't just use a fixed timestep and run through/catch-up on the frames because my actual application, driving stepper motors, there needs to be real-world time between each movement. Each step moves a certain linear distance.

I tried using the overflow/error time but it doesn't correct it.

The problem isn't calculating a linear path, it is translating that into pulse steps.

I am going to be running on a Teensy 3.0/3.1. I am using the elapsedMicros type to write non-blocking code.

Demos:

Here is a barebones JavaScript simulation demo: http://jsfiddle.net/MadLittleMods/6n3s3p1d/6/

I am going to port over this code once it is working correctly. I am using JavaScript for easy prototyping and debugging.

[Andy Watson]

Bresenham's algorithm works very well, but you have to tailor the code for each octant that you work in.

[MLM]

I was able to get my barebones demo working somewhat accurately with some help from Luggage over in the SO JavaScript chat room.

Fixed demo: http://jsfiddle.net/MadLittleMods/6n3s3p1d/20/

The key was to remove any the same amount of extra time(whichever axis had more time one was more) from both axes.

While this fix helps a lot, I am not totally happy with the result the line is far from perfect.

Bresenham's algorithm works very well...

I am working on a demo now that uses Bresenham's line algorithm to see how it works and compare.


Here are some later iterations: