Collision with a plane

• Plane \(\mathcal{P}\): parameterized using a point \(a\) and its normal \(n\).
• • \(\{p\in\mathbb{R}^3 \in \mathcal{P} \Rightarrow (p-a)\cdot n=0\}\)

• - Sphere above plane : \((p_i-a)\cdot n > r_i\)
• - Sphere in collision: \((p_i-a)\cdot n \leq r_i\)

• - Collision detection algorithm

for(int i=0; i<N; ++i)
{
    float detection = dot(p[i]-a, n);
    if (detection <= r[i])
    {
        // ... collision response
    }
}

• What should we do when a collision is detected