Hello,
I am a begin mathematica user.
I will try to find the intersection formula between a 3d sphere against 3d line.
I know the center of the sphere a 3d point (Cx,Cy,Cz) and the ray R.
The 3d line is defined how: P+D*t where the P is the line start point, D is the line direction and t is the time where intersection happen.
if intersection exist I should try the scalar value t.
I am trying to solve the equation system in mathematica but I get empty solution. Someone can help me to fix the system?
Thanks in advance.
Solve[(((x - Subscript[c, x])^2 + (y - Subscript[c, y])^2 + (z -
Subscript[c, z])^2) - r^2 == 0) && (x == Subscript[t, x]*Subscript[d, x] + Subscript[p, x]) &&
y == Subscript[t, y]*Subscript[d, y] + Subscript[p, y] && z == Subscript[t, z] + Subscript[d, z] + Subscript[p,z], {Subscript[t, x], Subscript[t, y], Subscript[t, z]}]
