/// <summary>
/// Creates an arc defined by a start point, end point and a direction at the first point.
/// </summary>
/// <param name="ptStart">Start point arc.</param>
/// <param name="ptEnd">End point arc.</param>
/// <param name="dir">TangentAt direction at start.</param>
/// <returns>An arc.</returns>
public static Arc ByStartEndDirection(Point3 ptStart, Point3 ptEnd, Vector3 dir)
{
if (!ptStart.IsValid)
{
throw new Exception("The first point is not valid.");
}
if (!ptEnd.IsValid)
{
throw new Exception("The second point is not valid.");
}
if (!dir.IsValid)
{
throw new Exception("The tangent is not valid.");
}
Vector3 vec0 = dir.Unitize();
Vector3 vec1 = (ptEnd - ptStart).Unitize();
if (vec1.Length.Equals(0.0))
{
throw new Exception("Start and End point of the arc are coincident. Enable to create an arc");
}
if (vec0.IsParallelTo(vec1) != 0)
{
throw new Exception("Tangent is parallel with the endpoints. Enable to create an arc");
}
Vector3 vec2 = (vec0 + vec1).Unitize();
Vector3 vec3 = vec2 * (0.5 * ptStart.DistanceTo(ptEnd) / Vector3.DotProduct(vec2, vec0));
return(new Arc(ptStart, ptStart + vec3, ptEnd));
}
/// <summary>
/// Computes the point which is the closest point to the given point.
/// </summary>
/// <param name="pt">Point to test.</param>
/// <returns>The point closest to the given point.</returns>
public override Point3 ClosestPoint(Point3 pt)
{
// Brute force
if (ControlPointLocations.Count <= 4)
{
double distance = double.MaxValue;
Point3 closestPt = Point3.Unset;
for (int i = 0; i < ControlPointLocations.Count - 1; i++)
{
Line tempLine = new Line(ControlPointLocations[i], ControlPointLocations[i + 1]);
Point3 tempPt = tempLine.ClosestPoint(pt);
double tempDistance = tempPt.DistanceTo(pt);
if (!(tempDistance < distance))
{
continue;
}
closestPt = tempPt;
distance = tempDistance;
}
return(closestPt);
}
// Divide and conquer.
List <Point3> leftSubCollection = new List <Point3>();
List <Point3> rightSubCollection = new List <Point3>();
List <Point3> conquer = new List <Point3>(ControlPointLocations);
while (leftSubCollection.Count != 2 || rightSubCollection.Count != 2)
{
int mid = (int)((double)conquer.Count / 2);
leftSubCollection = conquer.Take(mid + 1).ToList();
rightSubCollection = conquer.Skip(mid).ToList();
PolyLine leftPoly = new PolyLine(leftSubCollection);
PolyLine rightPoly = new PolyLine(rightSubCollection);
Point3 leftPt = leftPoly.PointAt(0.5);
Point3 rightPt = rightPoly.PointAt(0.5);
double leftDistance = leftPt.DistanceTo(pt);
double rightDistance = rightPt.DistanceTo(pt);
conquer = leftDistance > rightDistance
? new List <Point3>(rightSubCollection)
: new List <Point3>(leftSubCollection);
}
Line line = new Line(conquer[0], conquer[1]);
return(line.ClosestPoint(pt));
}
/// <summary>
/// Initializes a line by start point and end point.
/// </summary>
/// <param name="startPoint">Start point.</param>
/// <param name="endPoint">End point.</param>
public Line(Point3 startPoint, Point3 endPoint)
{
if (startPoint == endPoint || !startPoint.IsValid || !endPoint.IsValid)
{
throw new Exception("Start or end point is not valid, or they are equal");
}
StartPoint = startPoint;
EndPoint = endPoint;
Length = StartPoint.DistanceTo(EndPoint);
Direction = (EndPoint - StartPoint).Unitize();
ToNurbs();
}
