Collision detection between a moving circle and stationary point

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SUMMARY

The discussion focuses on implementing collision detection between a moving circle and a stationary line segment using mathematical equations. The user initially attempted to derive a quadratic equation based on the circle's motion parameters, including its radius and velocity. However, they encountered issues when the circle's x velocity was zero, which complicates the calculations. The user recognized an error in their approach regarding the subtraction of the radius squared before collecting terms, indicating a need for careful algebraic manipulation in collision detection algorithms.

PREREQUISITES
  • Understanding of basic geometry, specifically circles and line segments.
  • Familiarity with quadratic equations and the quadratic formula.
  • Knowledge of motion equations in two dimensions.
  • Experience with programming concepts for implementing mathematical algorithms.
NEXT STEPS
  • Research "Circle-Line Segment Collision Detection Algorithms".
  • Learn about "Handling Edge Cases in Collision Detection".
  • Explore "Mathematical Optimization Techniques for Collision Detection".
  • Study "Physics Engines and Their Implementation in Game Development".
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Game developers, computer graphics programmers, and anyone involved in physics simulations who needs to implement accurate collision detection algorithms.

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?
 

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