/// <summary>
/// Creates the smallest <see cref="BoundingSphere"/> that can contain a specified list of points in 3D-space.
/// </summary>
/// <param name="points">List of point to create the sphere from.</param>
/// <returns>The new <see cref="BoundingSphere"/>.</returns>
public static BoundingSphere CreateFromPoints(IEnumerable <Vector3> points)
{
if (points == null)
{
throw new ArgumentNullException("points");
}
// From "Real-Time Collision Detection" (Page 89)
Vector3 minx = new Vector3(float.MaxValue, float.MaxValue, float.MaxValue);
Vector3 maxx = -minx;
Vector3 miny = minx;
Vector3 maxy = -minx;
Vector3 minz = minx;
Vector3 maxz = -minx;
// Find the most extreme points along the principle axis.
int numPoints = 0;
foreach (Vector3 pt in points)
{
numPoints += 1;
if (pt.X < minx.X)
{
minx = pt;
}
if (pt.X > maxx.X)
{
maxx = pt;
}
if (pt.Y < miny.Y)
{
miny = pt;
}
if (pt.Y > maxy.Y)
{
maxy = pt;
}
if (pt.Z < minz.Z)
{
minz = pt;
}
if (pt.Z > maxz.Z)
{
maxz = pt;
}
}
if (numPoints == 0)
{
throw new ArgumentException(
"You should have at least one point in points."
);
}
float sqDistX = Vector3.DistanceSquared(maxx, minx);
float sqDistY = Vector3.DistanceSquared(maxy, miny);
float sqDistZ = Vector3.DistanceSquared(maxz, minz);
// Pick the pair of most distant points.
Vector3 min = minx;
Vector3 max = maxx;
if (sqDistY > sqDistX && sqDistY > sqDistZ)
{
max = maxy;
min = miny;
}
if (sqDistZ > sqDistX && sqDistZ > sqDistY)
{
max = maxz;
min = minz;
}
Vector3 center = (min + max) * 0.5f;
float radius = Vector3.Distance(max, center);
// Test every point and expand the sphere.
// The current bounding sphere is just a good approximation and may not enclose all points.
// From: Mathematics for 3D Game Programming and Computer Graphics, Eric Lengyel, Third Edition.
// Page 218
float sqRadius = radius * radius;
foreach (Vector3 pt in points)
{
Vector3 diff = (pt - center);
float sqDist = diff.LengthSquared();
if (sqDist > sqRadius)
{
float distance = (float)Math.Sqrt(sqDist); // equal to diff.Length();
Vector3 direction = diff / distance;
Vector3 G = center - radius * direction;
center = (G + pt) / 2;
radius = Vector3.Distance(pt, center);
sqRadius = radius * radius;
}
}
return(new BoundingSphere(center, radius));
}