Calculate circle center (3D) from 2 point, arc angle and plane normal-CodePudding

I need to calculate a 3D circle center point from 2 points(3D) and arc angle (plane normal is also known).

I searched it with Google but I think my English is not good enough to search properly. Anyone know the calculations to do this?

CodePudding user response：

We have points A, B, normal N, angle Fi.

Calculate difference vector (arc chord) and middle point

AB = B - A
M = (A   B) / 2

Calculate vector F perpendicular to AB and N using vector product and normalize it

F = AB x N
uF = F / len(F)

We know that circle center C lies on the ray from point M with direction F (with parameter t equal to apothem CM length (center-chord distance))

C = M   t * uF

What should be t value? We can express t through right triangle AMC parameters

 tan(Fi/2) = 0.5*len(AB) / t

So finally center is

C = M   uF * 0.5*len(AB) / tan(Fi/2)

Note that center C is not unique because we don't know arc direction (just change sign before uF in the last formula and get mirror point C' against chord)