3D arc passing through 3 points

Compute the center, radii, angle and the reference frame of the arc passing through 3 points

Compute the center, radii, angle and the reference frame of the arc passing through 3 points

Input:

• p1, p2, p3: row 3-vectors representing 3d space points, the arc starts at p1 goes trough p2 and finishes at p3

Output:

• r: calculated radii
• p: raw 3-vector representing the center of the arc
• al3: the final angle of the arc
• X, Y: row unit 3-vectors representing the reference frame of the plane where the arc lies, X vector is pointing to the p1 so the starting angle is always 0

Examples:

Plot random arc:

• arc3(rand(1, 3), rand(1, 3), rand(1, 3));

Calculate without plotting:

• [r, p, al, X, Y] = arc3(rand(1, 3), rand(1, 3), rand(1, 3));

Reference: https://en.wikipedia.org/wiki/Circumcircle#Higher_dimensions