Right so, I have a line which I want reflecting across another line
#Lines and circles
junior ravine
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Right so, I have a line which I want reflecting across another line
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junior ravine
the initial line is angled from the origin at phi, and intersects the origin
the line of symmetry is the line connecting the centre point of a circle with centre (x0, y0), and the first point at which the initial line intersects the circle
wondering if there's a simpler way to do this
in summary, I have a line with equation y = tan(phi)*x and it will intersect a circle and "bounce"/ reflect off it
and i want to find the equation of the reflected line
fair river
wondering if there's a simpler way to do this
Hm... I think you can start by translating and rotating the original picture so that the center of the circle is at the origin, and the tangent at the point where the ray falls is horizontal. That will probably be easier to solve, and you can easily rotate and translate back to the initial configuration.
junior ravine
Hm... I think you can start by translating and rotating the original picture so ...
I was trying to do that in a previous question but couldnt get my head round it
this was about two circles instead and working out the coords of intersection
instead I brute forced it
started off from this where the circles lie along the same x coord
granite bay
Right so, I have a line which I want reflecting across another line
reflecting like a beam of light on a mirror?
junior ravine
reflecting like a beam of light on a mirror?
it's meant to be a pinball bouncing off a bumper but it's not too relevant bc it's just about the equations of lines and not anything mechanical
junior ravine
Hm... I think you can start by translating and rotating the original picture so ...
how would I find the angle in which to rotate the picture? It would mean knowing the gradient of the tangent originally which idk how to find atm
it's annoying because the initial line could intersect the circle twice so I can't solve for an x coord intersection point to use nicely
otherwise then i could find the equation of the normal as i know the centre point and the intersection point (radius part)
junior ravine
