Two paths r 1 (t) and r 2 (t) intersect if there is a point P lying on both curves We say that r 1 (t) and r 2 (t) collide if r 1 (t 0 ) r 2 (t 0 ) at some time t 0 Which of the following statements are true (a) If r 1 (t) and r 2 (t) intersect, then they collide (b) If r 1 (t) and r 2 (t) collide, then they intersect (c) Intersection depends only on the underlying curves traced by r 1 and r 2 , but collision depends on the actual parametrizations

Question: Two paths r 1 (t) and r 2 (t) intersect if there is a point P lying on both curves. We say that r 1

Two paths r₁(t) and r₂(t) intersect if there is a point P lying on both curves. We say that r₁(t) and r₂(t) collide if r₁(t₀) = r₂(t₀) at some time t₀.

Which of the following statements are true?
(a) If r₁(t) and r₂(t) intersect, then they collide.
(b) If r₁(t) and r₂(t) collide, then they intersect.

(c) Intersection depends only on the underlying curves traced by r₁ and r₂, but collision depends on the actual parametrizations.

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