Ray-Sphere Intersection I

Ray: P = P0 + tV

Sphere: |P - O|2 - r 2 = 0

Substituting for P, we get:

|P0 + tV - O|2 - r 2 = 0

Solve quadratic equation:

at2 + bt + c = 0

where:

a = 1

b = 2 V • (P0 - O)

c = |P0 - C|2 - r 2 = 0

P0

V

O

P

r

P’

Algebraic Method

P = P0 + tV

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