/// <summary>
/// Creates a new bezier path along the given waypoints. The algorithm will automatically create new control points
/// between the given <paramref name="points"/> to guarantee a smooth curve along the path.
/// </summary>
/// <param name="points">The waypoints to use as bezier points for the newly created bezier path.</param>
/// <returns>A bezier path through the given bezier points.</returns>
public static BezierPath Interpolate(Vector3[] points)
{
if (points.Length < 2)
{
throw new ArgumentOutOfRangeException("There are at least two points required to interpolate a bezier path.", "points");
}
BezierPath path = new BezierPath();
for (int i = 0; i < points.Length; i++)
{
if (i == 0)
{
Vector3 p1 = points[i];
Vector3 p2 = points[i + 1];
Vector3 tangent = (p2 - p1);
Vector3 q1 = p1 + tangent;
path.points.Add(p1);
path.points.Add(q1);
}
else if (i == points.Length - 1)
{
Vector3 p0 = points[i - 1];
Vector3 p1 = points[i];
Vector3 tangent = (p1 - p0);
Vector3 q0 = p1 - tangent;
path.points.Add(q0);
path.points.Add(p1);
}
else
{
Vector3 p0 = points[i - 1];
Vector3 p1 = points[i];
Vector3 p2 = points[i + 1];
Vector3 tangent = (p2 - p0).normalized;
Vector3 q0 = p1 - tangent * (p1 - p0).magnitude;
Vector3 q1 = p1 + tangent * (p2 - p1).magnitude;
path.points.Add(q0);
path.points.Add(p1);
path.points.Add(q1);
}
}
return(path);
}
/// <summary>
/// Reduces the number of bezier points in the bezierpath and adjusts the corresponding control
/// handle points to generate a mostly accurate curve to the original one.
/// </summary>
/// <param name="minSqrDistance">Minimum square distance between two points.</param>
/// <param name="maxSqrDistance">Maximum square distance between two points.</param>
public void Optimize(float minSqrDistance, float maxSqrDistance)
{
if (this.points.Count < 4 || (this.points.Count - 1) % 3 != 0)
{
return;
}
Stack <Vector3> newPoints = new Stack <Vector3>();
Vector3[] bezierPoints = this.BezierPoints;
newPoints.Push(bezierPoints[0]);
Vector3 potentialNewPoint = bezierPoints[1];
for (int i = 2; i < bezierPoints.Length; i++)
{
if (((potentialNewPoint - bezierPoints[i]).sqrMagnitude > minSqrDistance) &&
((newPoints.Peek() - bezierPoints[i]).sqrMagnitude < maxSqrDistance))
{
newPoints.Push(potentialNewPoint);
}
potentialNewPoint = bezierPoints[i];
}
// Correct last few points of the bezier path
Vector3 p1 = newPoints.Pop();
Vector3 p0 = newPoints.Peek();
Vector3 tangent = (p0 - potentialNewPoint).normalized;
float d2 = (potentialNewPoint - p1).magnitude;
float d1 = (p1 - p0).magnitude;
p1 = p1 + tangent * ((d1 - d2) / 2);
newPoints.Push(p1);
newPoints.Push(potentialNewPoint);
this.Points = BezierPath.Interpolate(newPoints.ToArray()).Points.ToArray();
}
