Finding centre of the Arc

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I Have arc start point, end point, radius and normal direction.
With this data how to find arc centre point in 3D coordinates.
Thank You.

Posted 29-Jun-14 18:14pm

Madhan Mohan Reddy P

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YvesDaoust · Accepted Answer · 2014-07-03T06:22:00

Solution 1

The start-end vector together with the normal direction allow you to compute the direction of the line perpendicular to the chord in the circle plane.

r = SE/||SE|| /\ n

Make it pass through the midpoint.

M = 1/2(S + E).

By Pythagoras, you will find the altitude of the triangle formed with the center.

H^2 = R^2 - d^2(S, E)/4.

Compute the vector from the midpoint to the center.

C = M + H.r

(Beware that there are two solutions, with +/- H.)

Posted 3-Jul-14 6:22am

YvesDaoust

Updated 3-Jul-14 6:40am

v4

Comments

Madhan Mohan Reddy P 3-Jul-14 23:30pm

Hey,
Its working.
Thanks a lot.

YvesDaoust 4-Jul-14 2:45am

Glad to know :)

Madhan Mohan Reddy P 4-Jul-14 4:44am

Hi,
If you don't mind, One more question.
I have got Arc centre, radius, start point and end point.
With this, I need to collect all the points on the arc. Is there a way ? Am I clear in my question ?

YvesDaoust 8-Jul-14 16:28pm

"all" the points is a lot, as there are infinitely many of them :)
To compute a single point along the arc, consider the unit vectors s = SE/||SE|| and r (as above), and form the sum C + s.cos(t) + r.sin(t), where t is some angle in the allowed range. (You can compute this range from the chord length and the radius.)