| public static BinomialCoefficient ( int n, int k ) : long | ||
| n | int | The n. |
| k | int | The k. |
| return | long | |
/// <summary>
/// Calculates the point on the given bezier curve with the specified t parameter.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="t">The t parameter, a value between 0.0f and 1.0f.</param>
/// <param name="parallel">The parallel value.</param>
/// <returns>Resulting point.</returns>
/// <remarks>The <paramref name="parallel"/> parameter defines whether the curve should be calculated as a
/// parallel curve to the original bezier curve. A value of 0.0f represents
/// the original curve, 5.0f represents a curve that has always a distance
/// of 5.0f to the orignal curve.</remarks>
public static Vector2 CalculatePoint(IList <Vector2> points, float t, float parallel)
{
Vector2 r = new Vector2();
double c = 1.0d - (double)t;
float temp;
int i = 0;
foreach (Vector2 pt in points)
{
temp = (float)MathHelper.BinomialCoefficient(points.Count - 1, i) * (float)(System.Math.Pow(t, i) *
System.Math.Pow(c, (points.Count - 1) - i));
r.X += temp * pt.X;
r.Y += temp * pt.Y;
i++;
}
if (parallel == 0.0f)
{
return(r);
}
Vector2 perpendicular = new Vector2();
if (t != 0.0f)
{
perpendicular = r - BezierCurve.CalculatePointOfDerivative(points, t);
}
else
{
perpendicular = points[1] - points[0];
}
return(r + Vector2.Normalize(perpendicular).PerpendicularRight *parallel);
}
private static Vector2 CalculatePointOfDerivative(IList <Vector2> points, float t)
{
Vector2 vector2_1 = new Vector2();
double x = 1.0 - (double)t;
int k = 0;
foreach (Vector2 vector2_2 in (IEnumerable <Vector2>)points)
{
float num = (float)MathHelper.BinomialCoefficient(points.Count - 2, k) * (float)(Math.Pow((double)t, (double)k) * Math.Pow(x, (double)(points.Count - 2 - k)));
vector2_1.X += num * vector2_2.X;
vector2_1.Y += num * vector2_2.Y;
++k;
}
return(vector2_1);
}
/// <summary>
/// Calculates the point with the specified t of the derivative of the given bezier function.
/// </summary>
/// <param name="points">The points.</param>
/// <param name="t">The t parameter, value between 0.0f and 1.0f.</param>
/// <returns>Resulting point.</returns>
private static Vector2 CalculatePointOfDerivative(IList <Vector2> points, float t)
{
Vector2 r = new Vector2();
double c = 1.0d - (double)t;
float temp;
int i = 0;
foreach (Vector2 pt in points)
{
temp = (float)MathHelper.BinomialCoefficient(points.Count - 2, i) * (float)(System.Math.Pow(t, i) *
System.Math.Pow(c, (points.Count - 2) - i));
r.X += temp * pt.X;
r.Y += temp * pt.Y;
i++;
}
return(r);
}
public static Vector2 CalculatePoint(IList <Vector2> points, float t, float parallel)
{
Vector2 vector2_1 = new Vector2();
double x = 1.0 - (double)t;
int k = 0;
foreach (Vector2 vector2_2 in (IEnumerable <Vector2>)points)
{
float num = (float)MathHelper.BinomialCoefficient(points.Count - 1, k) * (float)(Math.Pow((double)t, (double)k) * Math.Pow(x, (double)(points.Count - 1 - k)));
vector2_1.X += num * vector2_2.X;
vector2_1.Y += num * vector2_2.Y;
++k;
}
if ((double)parallel == 0.0)
{
return(vector2_1);
}
Vector2 vector2_3 = new Vector2();
Vector2 vec = (double)t == 0.0 ? points[1] - points[0] : vector2_1 - BezierCurve.CalculatePointOfDerivative(points, t);
return(vector2_1 + Vector2.Normalize(vec).PerpendicularRight *parallel);
}