/// <summary>
/// Calculates the minimum distance between a point and a line.
/// </summary>
/// <param name="p">A point.</param>
/// <param name="origin">Line origin point.</param>
/// <param name="dir">Line direction.</param>
/// <returns>The minimum distance between the point and the line.</returns>
public static double PointLineDistance(Vector3 p, Vector3 origin, Vector3 dir)
{
double t = Vector3.DotProduct(dir, p - origin);
Vector3 pPrime = origin + t * dir;
Vector3 vec = p - pPrime;
double distanceSquared = Vector3.DotProduct(vec, vec);
return(Math.Sqrt(distanceSquared));
}
/// <summary>
/// Build the reflection matrix of a mirror plane that passes through a point.
/// </summary>
/// <param name="normal">Mirror plane normal vector.</param>
/// <param name="point">A point on the mirror plane.</param>
/// <returns>A mirror plane reflection matrix that passes through a point.</returns>
public static Matrix4 Reflection(Vector3 normal, Vector3 point)
{
// plane equation that passes through a point ax + by + cz + d = 0 where d = -point·normal
Vector3 n = Vector3.Normalize(normal);
double a = n.X;
double b = n.Y;
double c = n.Z;
double d = -Vector3.DotProduct(point, n);
return(new Matrix4(1 - 2 * a * a, -2 * a * b, -2 * a * c, -2 * a * d,
-2 * a * b, 1 - 2 * b * b, -2 * b * c, -2 * b * d,
-2 * a * c, -2 * b * c, 1 - 2 * c * c, -2 * c * d,
0, 0, 0, 1.0));
}
/// <summary>
/// Checks if a point is inside a line segment.
/// </summary>
/// <param name="p">A point.</param>
/// <param name="start">Segment start point.</param>
/// <param name="end">Segment end point.</param>
/// <returns>Zero if the point is inside the segment, 1 if the point is after the end point, and -1 if the point is before the start point.</returns>
public static int PointInSegment(Vector3 p, Vector3 start, Vector3 end)
{
Vector3 dir = end - start;
Vector3 pPrime = p - start;
double t = Vector3.DotProduct(dir, pPrime);
if (t <= 0)
{
return(-1);
}
double dot = Vector3.DotProduct(dir, dir);
if (t >= dot)
{
return(1);
}
return(0);
}
