Collision detection between a moving circle and stationary point

AI Thread Summary
To detect a collision between a moving circle and a stationary line segment, the user initially attempted to use the equation of a circle centered at the point of interest, substituting the circle's motion equations. They derived a quadratic equation in standard form but realized they made an error by not subtracting the radius squared before collecting terms. The user also noted a complication arises when the circle has zero x velocity, prompting a need for a different approach in that scenario. Overall, the discussion centers on the mathematical formulation of collision detection and the challenges encountered in the process. Finding a solution for the stationary case remains a key concern.
ZippyDee
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I'm trying to figure out the best way to find a collision between a moving circle and a stationary line segment. I have the x and y of the point, and the x, y, radius, x velocity, and y velocity of the circle.

//Edit:
I tried using the equation of a circle with the origin at the point (P) and a radius equal to that of the original circle, and then solving that for x, substituting the equation for the line of motion of of the ball in place of y:

m=(ball.yVelocity)/(ball.xVelocity)
b=ball.y-ball.x*m
r2=((mx+b)-Py)2+(x-Px)2

I multiplied it all out and simplified it to standard form. Then I collected like terms and came up with these variables

A=m2+1;
B=2*m*b-2*m*Py-2*Px;
C=b2-2*b*Py+Py2+Px2;

Then I used the quadratic formula to find the intercepts

That should work, but it doesn't...
 
Last edited:
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Wow...never mind, I am an idiot...I forgot to subtract r2 before collecting terms!
 
Oh...but this doesn't work if the circle has an x velocity of 0...How do I deal with that?
 

Thread 'Trigonometry problem of interest'

Seemingly by some mathematical coincidence, a hexagon of sides 2,2,7,7, 11, and 11 can be inscribed in a circle of radius 7. The other day I saw a math problem on line, which they said came from a Polish Olympiad, where you compute the length x of the 3rd side which is the same as the radius, so that the sides of length 2,x, and 11 are inscribed on the arc of a semi-circle. The law of cosines applied twice gives the answer for x of exactly 7, but the arithmetic is so complex that the...
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