Function for finding a point along curve that is a linear distance from start point

[nhfoley]

I built* this function months ago and use it pretty frequently - for example, when packing things of various known sizes along a curve, or when translating a design to meatspace (where the subtleties of varying arc lengths along a curve are just unnecessary complications). There are probably better ways of writing this code, but I think it's useful enough that something like it should be included by default in rhino.python.

Python Code:

def LinearDistAlongCurve(pathCurve, startPt, distance, tolerance = 0.1):
    """
    Uses a binary search to find a point at a given linear distance
    along a curve.
    """
   
    tmin = rs.CurveClosestPoint(pathCurve, startPt)
    tmax = rs.CurveDomain(pathCurve)[1]
    t0 = tmin
    t1 = tmax
    endPt = rs.EvaluateCurve(pathCurve, tmax)
    maxDist = rs.Distance(startPt,endPt)
    if distance > maxDist: return
   
    while True:
        t = 0.5 * (t0 + t1)
        tempPt = rs.EvaluateCurve(pathCurve,t)
        tempDist = rs.Distance(startPt, tempPt)
        if abs(tempDist - distance) < tolerance: break
        if tempDist > distance: t1 = t
        else: t0 = t
       
    return tempPt

Or maybe there's already a way to do this that I've missed?


*Copied and modified the code from a nearly identical but functionally different tutorial example on binary searches

[stjackin]

| CurveArcLengthPoint(curve_id, length, from_start=True) | Returns the point on the curve that is a specified arc length
| from the start of the curve.

try this method. maybe this is what you are looking for.

[nhfoley]

| CurveArcLengthPoint(curve_id, length, from_start=True) | Returns the point on the curve that is a specified arc length
| from the start of the curve.

try this method. maybe this is what you are looking for.

Unfortunately, there are many instances in which arc length is mostly irrelevant - the code I presented finds points based on an absolute (linear) distance.

[Conrad]

I would check out the Intersection methods to get rid of the iteration part of your code.

If you have a planar curve construct a circle around the startpoint of the curve. Then find the Intersection-Points of pathCurve and circle. You might have to convert from Circle to NurbsCurve:

events = Rhino.Geometry.Intersect.Intersection.CurveCurve(pathCurve, circle.ToNurbsCurve(), intersection_tolerance, overlap_tolerance)
for e in events:
    print e.PointA

For non-planar curves go with a sphere around the startpoint of the basecurve.

[Mitch]

Check out rs.DivideCurveEquidistant in the Rhinoscript syntax methods as well.

DivideCurveEquidistant
Divides a curve such that the linear distance between the points is equal.
Unlike the DivideCurve and DivideCurveLength, which divides a curve based on arc length, or the distance along the curve between two points, this function divides a curve based on the linear distance between points.

I use the circle/sphere methods fairly often as well, especially where the 'from' point is not the start point of the curve.
--Mitch

[nhfoley]

I had built a circle-based intersection version previously... it seemed slower, though that may have just been the the application I was using it for at the time. Sphere-based intersection methods definitely seem slower. Maybe some testing is in order...

[Mitch]

I just briefly tested your algorithm, rs.DivideCurveEquidistant, and a circle-curve intersection with rs.CurveCurveIntersection. They all seem to run about equally fast - as long as you exclude adding the time it takes to add the circle to the document in the third method. This takes a huge amount of time, it's like 100x slower if you include that. If you avoid this by using RhinoCommon methods so you don't have to add the circle to the document, the run time is much better but the first two methods are still better by a factor of about 2...

--Mitch