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NurbCurve2d.md

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NurbCurve2d Class

Overview

The NurbCurve2d class represents a non-uniform rational B-spline (NURBS) curve in 2D space (XY plane). Like its 3D counterpart, it provides precise mathematical representation of complex curves using control points, knots, and weights.

Namespace

Autodesk.AutoCAD.Geometry

Key Properties

Property Type Description
ControlPoints Point2dCollection Gets the control points that define the curve shape
Knots KnotCollection Gets the knot vector
Weights DoubleCollection Gets the weights for rational NURBS
Degree int Gets the polynomial degree of the curve
NumControlPoints int Gets the number of control points
IsRational bool Checks if the curve has weights
IsPeriodic bool Checks if the curve is periodic (closed)

Key Methods

Method Return Type Description
EvaluatePoint(double) Point2d Evaluates point on curve at parameter
GetClosestPointTo(Point2d) Point2d Gets closest point on curve
GetDistanceTo(Point2d) double Gets distance from point to curve
GetDerivativeAt(double) Vector2d Gets tangent at parameter

Code Examples

Example 1: Creating 2D NURBS Curve

Point2dCollection controlPoints = new Point2dCollection();
controlPoints.Add(new Point2d(0, 0));
controlPoints.Add(new Point2d(10, 5));
controlPoints.Add(new Point2d(20, 5));
controlPoints.Add(new Point2d(30, 0));

DoubleCollection knots = new DoubleCollection();
knots.Add(0); knots.Add(0); knots.Add(0); knots.Add(0);
knots.Add(1); knots.Add(1); knots.Add(1); knots.Add(1);

NurbCurve2d curve = new NurbCurve2d(3, knots, controlPoints, false);

ed.WriteMessage($"\n2D NURBS created with {curve.NumControlPoints} control points");

Example 2: Evaluating 2D NURBS

NurbCurve2d curve = /* existing curve */;

for (int i = 0; i <= 10; i++)
{
    double param = i / 10.0;
    Point2d pt = curve.EvaluatePoint(param);
    Vector2d tangent = curve.GetDerivativeAt(param);
    
    ed.WriteMessage($"\nParam {param:F1}: ({pt.X:F2}, {pt.Y:F2}), Tangent: ({tangent.X:F2}, {tangent.Y:F2})");
}

Best Practices

  1. 2D Operations: Use NurbCurve2d for planar geometry
  2. Knot Vector: Same rules as 3D (length = numControlPoints + degree + 1)
  3. Performance: 2D NURBS are faster than 3D for planar work

Related Classes

  • NurbCurve3d - 3D NURBS curve
  • CubicSplineCurve2d - 2D cubic spline
  • Point2d - Control points
  • Vector2d - Tangent vectors

References