# How to parametrize with arc length a curve on a surface?

antoni.parellada shared this question 8 months ago

I want to calculate the unit tangent vector to a parametrized curve in space on a surface along an interval and to do so I believe I need to integrate along the parameter t to get a secondary parameter s that allows me to normalize the tangent vectors. This is explain at the beginning of this video.

I am attaching the beginning of the non-functioning ggb code.

The ultimate goal is to get the tangent vector at each point, as well as the normal vector to the curve as in this question. See the GGB for tangent vector at each point, as well as the normal vector to the curve. 2

See the GGB for tangent vector at each point, as well as the normal vector to the curve. 1

Thank you very much! I am doing this to try an understand how the partial derivatives involved are obtained, as in the question linked in my original post. Do you know, or can you provide me with some leads, as to where to find the actual equations implemented in the functions CurvatureVector() and Direction()? 1

Eventually, I'd also like to calculate the binormal vector... The problem I have is getting the second derivative (i.e. the derivative of the tangent vector).  1 1

My file or Seror's? Let me try attaching both of them... 1

All file 1

To calculate the binormal vector of vectors u and v, you can use the command : u ⊗ v 