# Blackperl

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1. ## Predicting Collision time of Circle-Line segment

You're right. There is no analytical solution that can solve my problem in one shot. @raigan mentioned, I will create virtual infinite line equation that have distance (Radius) apart from real line segment.   1. Using analytical equation to find "t" of intersection between center of ball and virtual infinite line.     1.1 Prove t value by putting t into the path equation to find the future position (x, y) of ball and then check intersection between ball and real line segment. 2. Using analytical equation to find "t" of intersection between ball and start/end point of line segment.
2. ## Predicting Collision time of Circle-Line segment

Hi cadjunkie,   Thank you for your reply.   I think, your equation is analytical solution for finding collision time between point (center of circle) and infinite line?   How to make the equation (analytical) that can find collision time between circle (including radius) and line segment?
3. ## Predicting Collision time of Circle-Line segment

Hi HypnotiC and cadjunkie,   Thank you for your help.   I don't have a good knowledge for math and physics, but I'm trying. My static line segment will not parallel to X-Axis or Y-Axis. the trajectory of my circle (billiard ball) is,  r(t) = r0 + v0t + a0(t^2) r(x,y)    = current position of the ball at any time t r0(x,y)  = initial position of the ball v0(x,y) = Initial velocity of ball u0(x,y) = Initial relative velocity of the ball    I have questions about you help, 1. What you give me is the time of center of circle intersect line segment (not the radius intersect line)? 2. Could you explain me more about your equation P1(t) = C(t) + (x1-x(t0), y1-y(t0)) = (x1(t), y1(t)), what is x1 and y1? Thank you.
4. ## Predicting Collision time of Circle-Line segment

Hi 3pic_F4il_FTW,   The balls are moving in non-linear. the path of the ball is, r(t) = r0 + v0t + a0(t^2) r(x,y)    = current position of the ball at any time t r0(x,y)  = initial position of the ball v0(x,y) = Initial velocity of ball u0(x,y) = Initial relative velocity of the ball
5. ## Predicting Collision time of Circle-Line segment

Hi everyone,   I'm developing realistic billiard game. For now I've finished for predicting collision time of Circle-Circle (Thank you for Leckie,W. and Greenspan, M. POOL PHYSICS SIMULATION BY EVENT PREDICTION II:). The position as a function of time r(t) ball radius = R, so When circle-circle collide,   |d(t)| = 2R  --->   d(t)^2 = 4(R^2) and finally the equation will be A(X^4) + B(X^3) + C(X^2) + DX + E = 0 the quartic polynomial can be solved to get exact collision time.   But now I cannot find time of Circle and Line segment collision. Could you help me create equation for predicting collision time of moving circle and static line segment? Thank you Circle-Line Segment picture