CODEWITHSUNDEEP
c#algorithmgeometrycomputational-geometry
michaelbr92
michaelbr92

Reputation: 105

Algorithm - Find the midpoint of an arc

In the diagram below, I need to find the midpoint M of the arc from A to B:

midpoint

I want to find M in terms of the following information:

How do I compute the coordinates of M?

Upvotes: 5

Views: 5661

Answers (1)

Sebastian Negraszus
Sebastian Negraszus

Reputation: 12195

Assuming A, B, M and Center are objects of some vector type with the usual operations:

var a = A-C;
var b = B-C;
var m = a+b;

m is a vector that goes from Center towards M. Therefore:

m = m.Normalize() * Radius;
M = Center + m;

Please note: This algorithm does not assume an order of A and B, and always interprets the arc as the smaller of the two possible ones. Without adding special cases, it can only handle arcs with an angle smaller than 180°.

To handle order: First calculate the angle from a to b using atan2:

var angle = Math.Atan2(b.y, b.x) - Math.Atan2(a.y, a.x);
if (angle < 0)
{
    angle = 2*Math.PI + angle;
}

Then rotate a by half that angle:

angle /= 2;
var m = a.Rotate(angle);
M = Center + m;

Upvotes: 7

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