Challenge: converting python (or Javascript) code to Livecode

[David Bovill]

Thanks Craig - I dug around but no joy. I hate it when you loose code as I had a function somewhere… The javascript and python code is not that long, so it will be an interesting challenge to translate:

Python code:

• https://github.com/volkerp/fitCurves/blob/master/fitCurves.py

Javascript code:

• https://github.com/soswow/fit-curve/blob/master/src/fit-curve.js

Here is the core python function:
> quote_type
> def fitCubic(points, leftTangent, rightTangent, error):
>  # Use heuristic if region only has two points in it
>  if (len(points) == 2):
>  dist = linalg.norm(points[0] - points[1]) / 3.0
>  bezCurve = [points[0], points[0] + leftTangent * dist, points[1] + rightTangent * dist, points[1]]
>  return [bezCurve]
>
>  # Parameterize points, and attempt to fit curve
>  u = chordLengthParameterize(points)
>  bezCurve = generateBezier(points, u, leftTangent, rightTangent)
>  # Find max deviation of points to fitted curve
>  maxError, splitPoint = computeMaxError(points, bezCurve, u)
>  if maxError < error:
>  return [bezCurve]
>
>  # If error not too large, try some reparameterization and iteration
>  if maxError < error**2:
>  for i in range(20):
>  uPrime = reparameterize(bezCurve, points, u)
>  bezCurve = generateBezier(points, uPrime, leftTangent, rightTangent)
>  maxError, splitPoint = computeMaxError(points, bezCurve, uPrime)
>  if maxError < error:
>  return [bezCurve]
>  u = uPrime
>
>  # Fitting failed -- split at max error point and fit recursively
>  beziers = []
>  centerTangent = normalize(points[splitPoint-1] - points[splitPoint+1])
>  beziers += fitCubic(points[:splitPoint+1], leftTangent, centerTangent, error)
>  beziers += fitCubic(points[splitPoint:], -centerTangent, rightTangent, error)
>
>  return beziers
>
The maths code for the Newton Raphson method is:
> quote_type
> def newtonRaphsonRootFind(bez, point, u):
>  """
>  Newton's root finding algorithm calculates f(x)=0 by reiterating
>  x_n+1 = x_n - f(x_n)/f'(x_n)
>
>  We are trying to find curve parameter u for some point p that minimizes
>  the distance from that point to the curve. Distance point to curve is d=q(u)-p.
>  At minimum distance the point is perpendicular to the curve.
>  We are solving
>  f = q(u)-p * q'(u) = 0
>  with
>  f' = q'(u) * q'(u) + q(u)-p * q''(u)
>
>  gives
>  u_n+1 = u_n - |q(u_n)-p * q'(u_n)| / |q'(u_n)**2 + q(u_n)-p * q''(u_n)|
>  """
>  d = bezier.q(bez, u)-point
>  numerator = (d * bezier.qprime(bez, u)).sum()
>  denominator = (bezier.qprime(bez, u)**2 + d * bezier.qprimeprime(bez, u)).sum()
>
>
>  if denominator == 0.0:
>  return u
>  else:
>  return u - numerator/denominator
>
Seems a useful little challenge for the list?

📆    Schedule a call with me
On 14 Jun 2022, 14:43 +0100, Craig Newman via use-livecode <use-livecode at lists.runrev.com>, wrote:
> There is a similar thread on the forum:
>
> https://forums.livecode.com/viewtopic.php?f=8&t=34550 <https://forums.livecode.com/viewtopic.php?f=8&t=34550>
>
> Craig
>
> > On Jun 14, 2022, at 8:54 AM, David Bovill via use-livecode <use-livecode at lists.runrev.com> wrote:
> >
> > I found some well documented python code:
> >
> > • https://github.com/volkerp/fitCurves/blob/master/fitCurves.py
> >
> > And some Javascript code:
> >
> > • https://github.com/soswow/fit-curve/blob/master/src/fit-curve.js
> >
> > The javascript code could be called from Livecode. To see the demo of how this would work in the browser:
> >
> > • http://soswow.github.io/fit-curve/demo/
> > • https://codepen.io/Sphinxxxx/pen/jrLxvQ
> >
> > Would seem to be a useful library to have available in native LC?
> >
> > 📆 Schedule a call with me
> > On 14 Jun 2022, 12:30 +0100, David Bovill <david.bovill at gmail.com>, wrote:
> > > Searching around for a function in LC. It should take the points of a graphic and return a smoothed the points of a smoothed line. I’ve found lots of bezier style experiments but no “curve fitting” code. Anyone have a function?
> > >
> > > 📆 Schedule a call with me
> > > On 6 Dec 2015, 12:10 +0000, Michael Kristensen <michael-kristensen at dsa-net.dk>, wrote:
> > > > Pointlist to Bezier
> > > >
> > > > Hi there
> > > >
> > > > I wonder if any have code to take a point-list and turn it into a smooth-lined bezier.
> > > >
> > > > There are explanations around the net for C-code but it is very hard to understand.
> > > >
> > > > (one here said to be good but misses the graphics:)
> > > > http://www.benknowscode.com/2012/09/path-interpolation-using-cubic-bezier_9742.html
> > > >
> > > > What could this code be used for.
> > > >
> > > > — Tracing an image
> > > >
> > > > — Smoothing the lines drawn by a user
> > > >
> > > > plus a lot more Im sure
> > > >
> > > > Thanks
> > > > Michael
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