### math

#### Find any point on arc given center, start point, end point, total angle, normal, and radius

I have an 3D arc with coordinates such as: start = (-3,6,12) end = (-13,11,12) center = (-9,6,14) norm = (0.3204,0.6304,0.7071) radius = 7 Along with angle information: start angle = 216 total angle = 108 end angle = 324 Using the given information, I want to interpolate the arc at a specified distance. To do this, I perform the same operation in a loop and increment or decremented the angle depending on the direction I choose (start to end or vice-versa). I figured out how to do so in 2D with the algorithm: X = r * cosine(angle) Y = r * sine(angle) X = Cx + (r * cosine(angle)) Y = Cy + (r * sine(angle)) But once I add the Z axis it gets very confusing. I have been looking at multiple methods that use operations such as the cross product but these make me even more confused. How should I proceed with this?

If center is center of circle, than you have almost all information needed for SLERP - spherical linear interpolation p0 = start - circlecenter p1 = end - circlecenter p(t) = p0 * Sin(W*(1-t)) / Sin(W) + p1 * Sin(W*t) / Sin(W) point(t) = circlecenter + p(t) where p0 and p1 are starting and ending radius-vectors, W is total angle, t is parameter in range 0..1 (so W*t lies in range 0..total angle) If your center is middle of arc, you can find circle center: chord = end - start uchord = chord.normalize //(unit vector) perp = VectorProduct(normal, uchord) //unit vector in circle plane circlecenter = middle + perp * radius

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