From circumference to arc parametric equation (2D in 3D)

Question

I have to parametrize a 2D arc in 3D space.

In the beggining, I had the center of the arc, starting and ending points.

This thread here was very helpful, I was able to calculate radius and the vectors indicated, and to parametrize the circumference containing my arc (I plotted it and it is correctly done).

Now the problem is to get just the arc. I founded this thread where it is done in 2D space, but I don't know how to go translate my 3D case.

Do you know from which values should the angle in the circumference parametric equation go to create my arc?

My exact situation is the same described here, but I just want the arc between p1 and p2.

set $\theta$ from the begin angle to the end instead of $\theta\in[0,2\pi]$ — Raffaele, Oct 30 '17 at 13:50
The exact situation is the same described here, I want the angle between p1 and p2. https://math.stackexchange.com/questions/2375102/parametric-equation-of-a-circle-in-3d-given-center-and-two-points-on-the-circle?noredirect=1&lq=1 — Daniel Viaño, Oct 31 '17 at 12:40

score 0 · Accepted Answer · answered Nov 02 '17 at 11:41

0

Finally I found a solution here.

Using the equations in that link, starting angle is = 0 and ending angle = angle between center and starting point and center and ending point.

answered Nov 02 '17 at 11:41

Daniel Viaño

113
4

From circumference to arc parametric equation (2D in 3D)

1 Answers1