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 smallest t that satisfies that equation when 0<=s<=1, but I'm not sure how to get started.
Any help would be greatly appreciated.
Adam