/// <summary>
/// Intersects a segment and a sphere.
/// </summary>
public static bool IntersectSegmentSphere(Vector3 p0, Vector3 p1, Sphere s, out Vector3 hitPos)
{
Vector3 dir = p1 - p0;
float length = dir.magnitude;
if (Mathf.Approximately(length, 0.0f)) {
hitPos = p0;
return IntersectPointSphere(p0, s);
}
dir = dir / length; // Normalize
// Perform ray/sphere intersection, and verify t to guarantee
// collision occurred within boundaries of segment.
float t;
if (IntersectRaySphere(p0, dir, s, out t, out hitPos)) {
if (t <= length) {
return true;
}
}
return false;
}
/// <summary>
/// Intersects ray r = p + td, |d| = 1, with sphere s and, if intersecting,
/// returns t value of intersection and intersection point q
/// </summary>
public static bool IntersectRaySphere(Vector3 p, Vector3 d, Sphere s, out float t, out Vector3 q)
{
// Ref: Real-Time Collision Detection
Vector3 m = p - s.Center;
float b = Vector3.Dot(m, d);
float c = Vector3.Dot(m, m) - s.Radius * s.Radius;
// Exit if r’s origin outside s (c > 0) and r pointing away from s (b > 0)
if (c > 0.0f && b > 0.0f) {
t = 0.0f;
q = Vector3.zero;
return false;
}
float discr = b * b - c;
// A negative discriminant corresponds to ray missing sphere
if (discr < 0.0f) {
t = 0.0f;
q = Vector3.zero;
return false;
}
// Ray now found to intersect sphere, compute smallest t value of intersection
t = -b - Mathf.Sqrt(discr);
// If t is negative, ray started inside sphere so clamp t to zero
if (t < 0.0f) {
t = 0.0f;
}
q = p + t * d;
return true;
}
/// <summary>
/// Intersects a ray and sphere: r = p + td
/// </summary>
public static bool IntersectRaySphere(Vector3 p, Vector3 d, Sphere s)
{
// Ref: Real-Time Collision Detection
Vector3 m = p - s.Center;
float c = Vector3.Dot(m, m) - s.Radius * s.Radius;
// If there is definitely at least one real root, there must be an intersection
if (c <= 0.0f) {
return true;
}
float b = Vector3.Dot(m, d);
// Early exit if ray origin outside sphere and ray pointing away from sphere
if (b > 0.0f) {
return false;
}
float disc = b * b - c;
// A negative discriminant corresponds to ray missing sphere
if (disc < 0.0f) {
return false;
}
// Now ray must hit sphere
return true;
}
/// <summary>
/// Given a point p and a sphere,
/// return whether the point intersects the sphere.
/// </summary>
public static bool IntersectPointSphere(Vector3 p, Sphere s)
{
float r2 = s.Radius * s.Radius;
float distSqr = Vector3.SqrMagnitude(p - s.Center);
return distSqr <= r2;
}