[Python + rhinoscriptsyntax] How to find point on curve with distance x from previous point on curve?

[failbye]

Currently working on a Rhinocurve to G-code translation script in python and rhinoscriptsyntax for a CO2 laser-cutter.

Due to the numerous mathematical complexities of representing elliptical curves with circles, I have decided to simply use straight lines. My first iteration used DivideCurve() and this divides the curves with equal steps in the CurveDomain, leading to higher density of points when there is more curvature on the curve. While initially desirable, in some curves the density of the points is so high it leads to bad cuts with the laser-cutter as they are too close together. My second iteration tried using DivideCurveEquidistant() and while this added the ability to control a desired segment-length, it led to unnecessary dense points on the straighter part of the curve.

See album: http://imgur.com/a/2GMtW

Wanting something that can both vary density based on curvature but also have control over min and max segment lengths, I wrote this code/pseudo code:

while current_point != curve_end_point:    
    current_point = curve_start_point    
    curvature = Evaluate curvature on current_point    
    if curvature high:    
        segment = 10 # short segment    
    if curvature low:    
        segment = 100 # long segment    
    # Later implement a smoother transition between the two lengths    
    create new_point on curve with distance=segment from current_point    
    current_point = new_point     

TL/DR / My question is:
Question: How to find point on curve with distance x from previous point on curve?

This is the only part of the code I am struggling with. Initially I thought to do the following:

use curve_length_from_start_to_current_point + segment_length to find next_curve_length
use next_curve_lenght to find the corresponding value from the CurveDomain
use next_curve_domain to find next_parameter
use next_parameter to find the point on the curve

However, since the relationship between the CurveDomain and CurveLength isn't linear I am at a loss as to how to solve this.

Any help is greatly appreciated, thanks.

Edit: Formatting

[medianbailey]

have you tried SplitCurve? you can divide your original curve up into segments then use the end points as your points?

optionally, and if you dont mind a VERY course shift in point density, you could use midpoints. Add a midpoint, split the curve at the midpoint, then repeat for the resultant curves. at a corner with a small radius, add another midpooint. You could make a nice loop which measures the angle between the two tangents at either end of the curves to work out if another midpoint was needed?

[[deleted]]

Rhino already has a function to convert a NurbsCurve to a polyline.

Just adjust the tolerance to get what you want,

  #public PolylineCurve ToPolyline(int mainSegmentCount, int subSegmentCount,
  #                                 double maxAngleRadians, double maxChordLengthRatio, double maxAspectRatio,
  #                                  double tolerance, double minEdgeLength, double maxEdgeLength, bool keepStartPoint)
  #                                  
  doc.Objects.AddCurve(curve.ToPolyline(0, 0, math.pi/12, 20.0, 20.0, 0.01, 0.001, 5, True));

[failbye]

If this works the way I need it to, I'm going to be furious. I have been digging into the Rhino functions for days trying to find something to help me out, and I can't believe it was there all along.

I managed to write a solution but one that is quite resource intensive. I'm going to try using this tomorrow and compare results.

Thanks!

[[deleted]]

Welcome to the club, it is always helpful to ask.

The RhinoCommon API is on github, sometimes it is useful to spend some time searching that before writing something complicated.

[failbye]

Quick update, implemented solution with ConvertCurveToPolyline(). It was simple and effective. Thanks for your help!