[Math] Distance from a point to a line in 2D.

Unity Engine
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1

I have 3 points for example:

Vector2 M = new Vector2(1, 2);
Vector2 B = new Vector2(5, 6);
Vector2 C = new Vector2(3, 4);
//BC - vector:
Vector2 BC  = B - C;

I want to compute the distance from M to BC. I came up with two methods that I think are too expensive:

float slopeBC = BC.y / BC.x;
float distance = Mathf.abs(slopeBC * M.x - M.y + slopeBC * B.x + B.y)/Mathf.sqrt(1 + slopeBC * slopeBC);

or

Vector3 MB = M - B;
Vector3 MC = M - C;
float p = (MB.magnitude + MC.magnitude + BC.magnitude)/2
float distance = 2 * Mathf.sqrt(p*(p - MB.magnitude)*(p - MC.magnitude)*(p - BC.magnitude)) / BC.magnitude;

They seem to work, but they also seem to use heavy-weight calculations.

2

Check out this thread of mine for the most optimal 2D intersector I’ve come across. Read through it and there are also nearest point implementations for lines, rays, and segments.

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