Hi. I have an point on edge of a circle and a direction where that point facing. When i draw a ray from that point i want that line to end at other edge of circle but i don’t know how can i calculate that point because that line does not go from center(if it would then length of line would be same as diameter of circle). if i can find the other point then i can calculate the length of it by using chord of circle formula which is what i actually need.
Let’s take the following image representing your situation.
O is the center of the circle
A is the point you know
B is the point you are looking for
v is the direction vector you know
α is the angle between AO and AB vectors
ω is the angle between OA and OB vectors
Because AOB is an isosceles triangle, the OAB and OBA angles are equal. And the sum of the angles of a triangle = 180°.
Pseudo code
α = Angle( O - A, v )
ω = 180 - 2 * a // because ω + α + α = 180
BO = Rotate(A - O, ω)
B = O + BO
Translated in C#:
private Vector3 ComputeB( Vector3 circleCenter, Vector3 circleNormal, Vector3 point, Vector3 direction )
{
float a = Vector3.SignedAngle( circleCenter - point, direction, circleNormal );
float w = 0;
if ( a >= 0 ) w = 180 - 2 * a; // because w + a + a = 180;
else w = -( 180 + 2 * a );
Vector3 BO = Quaternion.AngleAxis(w, -circleNormal) * (point - circleCenter);
return circleCenter + BO;
}