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mathgeometryangle

Calculate Point collision between a point of a given vector and the edge of a Circle

Lets say I have a point within a circle(not necessarily the origin) moving at a given vector how would I calculate the x and y coordinate of the point where it hits the edge of the circle.

Solution

  • Shift all coordinates by -cx, -cy. Now circle is centered at origin and has equation

    x^2+y^2=R^2

    Point coordinate (px, py), unit direction vector is (dx,dy). Equation of ray:

    x = px + t * dx
y = py + t * dy

    Substitute these variables into the circle equation, solve equation, find parameter t>0, then find intersection point (x,y), shift it back by (cx, cy).