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CubicSplineCurve3d.md

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CubicSplineCurve3d.md

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CubicSplineCurve3d Class

Overview

The CubicSplineCurve3d class represents an interpolation cubic spline in 3D space. Cubic splines create smooth curves that pass through specified fit points, commonly used for smooth interpolation.

Namespace

Autodesk.AutoCAD.Geometry

Key Properties

Property Type Description
FitPoints Point3dCollection Gets the points the curve passes through
StartTangent Vector3d Gets the tangent vector at the start
EndTangent Vector3d Gets the tangent vector at the end
NumFitPoints int Gets the number of fit points

Key Methods

Method Return Type Description
EvaluatePoint(double) Point3d Evaluates point on curve at parameter
GetClosestPointTo(Point3d) Point3d Gets closest point on curve
GetDerivativeAt(double) Vector3d Gets tangent at parameter

Code Examples

Example 1: Creating Cubic Spline

// Create spline through fit points
Point3dCollection fitPoints = new Point3dCollection();
fitPoints.Add(new Point3d(0, 0, 0));
fitPoints.Add(new Point3d(5, 5, 0));
fitPoints.Add(new Point3d(10, 3, 0));
fitPoints.Add(new Point3d(15, 7, 0));
fitPoints.Add(new Point3d(20, 5, 0));

CubicSplineCurve3d spline = new CubicSplineCurve3d(fitPoints);

ed.WriteMessage($"\nCubic spline created through {spline.NumFitPoints} points");

Example 2: Spline with Tangents

Point3dCollection fitPoints = new Point3dCollection();
fitPoints.Add(new Point3d(0, 0, 0));
fitPoints.Add(new Point3d(10, 10, 0));
fitPoints.Add(new Point3d(20, 0, 0));

// Specify start and end tangents
Vector3d startTangent = Vector3d.XAxis;
Vector3d endTangent = Vector3d.XAxis;

CubicSplineCurve3d spline = new CubicSplineCurve3d(fitPoints, startTangent, endTangent);

ed.WriteMessage($"\nSpline with specified tangents");
ed.WriteMessage($"\nStart tangent: {spline.StartTangent}");
ed.WriteMessage($"\nEnd tangent: {spline.EndTangent}");

Best Practices

  1. Fit Points: Curve passes through all fit points
  2. Smoothness: Cubic splines provide C² continuity (smooth)
  3. Tangents: Specify tangents for better control at endpoints
  4. Interpolation: Use for smooth curves through known points

Related Classes

  • CubicSplineCurve2d - 2D cubic spline
  • NurbCurve3d - NURBS curve (more control)
  • Polyline3d - Piecewise linear (not smooth)

References