find the point on a curve with a specific tangent

Hi, This is my problem:
I have a curve and a line on the same plane, the line has a specific direction, I'd like to find the points on that curve where the tangent has the same direction of the starting line.

Replies to This Discussion

Permalink Reply by David Rutten on April 13, 2016 at 4:47am

Divide the curve into N samples (I used 1000, higher numbers give more accurate results).
Measure the angle between the tangent at each sample and the target direction.
Graph all these angles (and lower them by 0.5*pi).
Find all the places where the graph hits zero using Line|Curve intersection.
Map the intersection points [x] coordinate back onto curve space.

Attachments:

tanfinder.gh, 9 KB

Permalink Reply by Balazs Furton on April 1, 2017 at 3:31pm

Hi David,

Could you explain a bit more why you lowered the whole graph by pi/2? Wouldn't 0, pi, and 2*pi angles be sufficient solutions? Or due to the interpolation we wouldn't have intersections at the two limits? I'm confused here.

Thanks for your help!

Permalink Reply by riccardo foschi on April 13, 2016 at 5:07am

Thak you very much, I hoped in a much accurate and less cumbersome solution, but I guess it's an iteration problem wich is hard to calculate without a certain grade of complexity, I'm just worried about the division in 1000 (or more) wich could de a problem in a much complex algoritm, there is not a solution wich wouldn't need to divide the whole curve in equal parts to raise the tolerance?
Anyway thank you very much!!!

Permalink Reply by Romain Mesnil on April 13, 2016 at 5:29am

Hi,

you can use a divide and conquer algorithm similar to what I used here and here.

1. You can use David's method up to Step 3. for a moderate number of points (say 20-100 following the complexity of your curve) and work on each subcurve separately.

2. Each time you identify a possible candidate (at Step 4. in David's post, that would mean that at one end you have a positive angle, and at the other you have a negative angle, zero must be somewhere between these values) you can split the curve in half and look for the half where the point is the most likely to be and apply this process iteratively.

The advantage of this kind of method is that you can set arbitrarely a precision, and you explore less dead ends. With a uniform subdivision, if you need N steps to reach a certain precision, you will need here log(N), which is the best you can do.

Off course this method depends on the initial number of subcurves, and you have to give enough input points in the first place.

Best,

Romain

Permalink Reply by Juan Stefani on April 28, 2016 at 5:53am