I am trying to find the intersection of a ray and a swept sphere but I'm not sure where to start.

Here is my parametric equation for a swept sphere:

| A + Bs - P | = a + bs

0 <= s <= 1

A: center position at s=0

B: center velocity relative to s

a: radius at s=0

b: radius rate of change relative to s

P: points on swept sphere

Here is my parametric equation for a ray:

P = C + Dt

C: position at t=0

D: velocity relative to t

P: points on line

Plugging them together I get:

| A + Bs - ( C + Dt ) | = a + bs

0 <= s <= 1

I am trying to solve for the smallesttthat satisfies that equation when0<=s<=1, but I'm not sure how to get started.

Any help would be greatly appreciated.

Adam