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NurbCurve3d.md

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NurbCurve3d Class

Overview

The NurbCurve3d class represents a non-uniform rational B-spline (NURBS) curve in 3D space. NURBS curves are fundamental to CAD systems, providing precise mathematical representations of complex freeform curves using control points, knots, and weights.

Namespace

Autodesk.AutoCAD.Geometry

Key Properties

Property Type Description
ControlPoints Point3dCollection Gets the control points that define the curve shape
Knots KnotCollection Gets the knot vector that determines parameter values
Weights DoubleCollection Gets the weights for rational NURBS (control point influence)
Degree int Gets the polynomial degree of the curve
NumControlPoints int Gets the number of control points
NumKnots int Gets the number of knots in the knot vector
NumWeights int Gets the number of weights (0 for non-rational)
IsPeriodic bool Checks if the curve is periodic (closed)
IsRational bool Checks if the curve is rational (has weights)

Key Methods

Method Return Type Description
EvaluatePoint(double) Point3d Evaluates point on curve at parameter value
GetClosestPointTo(Point3d) Point3d Gets closest point on curve to given point
GetDistanceTo(Point3d) double Gets distance from point to curve
AddControlPointAt(int, Point3d) void Adds control point at specified index
DeleteControlPointAt(int) void Removes control point at index
GetWeightAt(int) double Gets weight at specified index
SetWeightAt(int, double) void Sets weight at specified index
InsertKnot(double) void Inserts knot at parameter value
AddKnot(double) void Adds knot to knot vector
ElevateDegree(int) void Increases curve degree without changing shape
GetDerivativeAt(double) Vector3d Gets derivative (tangent) at parameter

Code Examples

Example 1: Creating a NURBS Curve

// Define control points
Point3dCollection controlPoints = new Point3dCollection();
controlPoints.Add(new Point3d(0, 0, 0));
controlPoints.Add(new Point3d(10, 5, 0));
controlPoints.Add(new Point3d(20, 5, 0));
controlPoints.Add(new Point3d(30, 0, 0));

// Define knot vector (degree 3, 4 control points = 8 knots)
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);

// Create NURBS curve (degree 3)
int degree = 3;
NurbCurve3d nurbsCurve = new NurbCurve3d(degree, knots, controlPoints, false);

ed.WriteMessage($"\nNURBS Curve created");
ed.WriteMessage($"\nDegree: {nurbsCurve.Degree}");
ed.WriteMessage($"\nControl Points: {nurbsCurve.NumControlPoints}");
ed.WriteMessage($"\nKnots: {nurbsCurve.NumKnots}");

Example 2: Evaluating Points on NURBS Curve

NurbCurve3d curve = /* existing NURBS curve */;

// Evaluate points along the curve
int numSamples = 10;
for (int i = 0; i <= numSamples; i++)
{
    double param = i / (double)numSamples;
    Point3d pt = curve.EvaluatePoint(param);
    
    ed.WriteMessage($"\nParameter {param:F2}: ({pt.X:F2}, {pt.Y:F2}, {pt.Z:F2})");
}

// Get tangent at midpoint
double midParam = 0.5;
Vector3d tangent = curve.GetDerivativeAt(midParam);
ed.WriteMessage($"\nTangent at 0.5: {tangent}");

Example 3: Creating Weighted (Rational) NURBS

Point3dCollection controlPoints = new Point3dCollection();
controlPoints.Add(new Point3d(0, 0, 0));
controlPoints.Add(new Point3d(10, 10, 0));
controlPoints.Add(new Point3d(20, 10, 0));
controlPoints.Add(new Point3d(30, 0, 0));

// Define weights (higher weight pulls curve closer to control point)
DoubleCollection weights = new DoubleCollection();
weights.Add(1.0);  // Normal weight
weights.Add(2.0);  // Double weight - pulls curve toward this point
weights.Add(2.0);  // Double weight
weights.Add(1.0);  // Normal weight

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);

// Create rational NURBS curve
NurbCurve3d rationalCurve = new NurbCurve3d(3, knots, controlPoints, weights, false);

ed.WriteMessage($"\nRational NURBS: {rationalCurve.IsRational}");
ed.WriteMessage($"\nWeights: {rationalCurve.NumWeights}");

Example 4: Modifying NURBS Curve

NurbCurve3d curve = /* existing curve */;

// Add a control point
Point3d newControlPoint = new Point3d(15, 8, 0);
curve.AddControlPointAt(2, newControlPoint);

// Modify a weight
if (curve.IsRational)
{
    curve.SetWeightAt(1, 3.0); // Increase weight at index 1
}

// Insert a knot to add detail
curve.InsertKnot(0.5);

// Elevate degree for smoother curve
curve.ElevateDegree(4);

ed.WriteMessage($"\nModified curve:");
ed.WriteMessage($"\nControl Points: {curve.NumControlPoints}");
ed.WriteMessage($"\nDegree: {curve.Degree}");

Example 5: Converting NURBS to Polyline

NurbCurve3d nurbsCurve = /* existing NURBS curve */;

// Sample the curve to create polyline approximation
int numSegments = 50;
Point3dCollection polylinePoints = new Point3dCollection();

for (int i = 0; i <= numSegments; i++)
{
    double param = i / (double)numSegments;
    Point3d pt = nurbsCurve.EvaluatePoint(param);
    polylinePoints.Add(pt);
}

// Create polyline entity
using (Transaction tr = db.TransactionManager.StartTransaction())
{
    Polyline pline = new Polyline();
    pline.SetDatabaseDefaults();
    
    for (int i = 0; i < polylinePoints.Count; i++)
    {
        Point3d pt = polylinePoints[i];
        pline.AddVertexAt(i, new Point2d(pt.X, pt.Y), 0, 0, 0);
    }
    
    BlockTableRecord btr = tr.GetObject(db.CurrentSpaceId, OpenMode.ForWrite) as BlockTableRecord;
    btr.AppendEntity(pline);
    tr.AddNewlyCreatedDBObject(pline, true);
    
    tr.Commit();
}

ed.WriteMessage($"\nNURBS converted to polyline with {polylinePoints.Count} vertices");

Example 6: Finding Closest Point on NURBS

NurbCurve3d curve = /* existing NURBS curve */;
Point3d testPoint = new Point3d(15, 7, 0);

// Find closest point on curve
Point3d closestPoint = curve.GetClosestPointTo(testPoint);
double distance = curve.GetDistanceTo(testPoint);

ed.WriteMessage($"\nTest point: {testPoint}");
ed.WriteMessage($"\nClosest point on curve: {closestPoint}");
ed.WriteMessage($"\nDistance: {distance:F4}");

// Draw line showing closest point
using (Transaction tr = db.TransactionManager.StartTransaction())
{
    Line line = new Line(testPoint, closestPoint);
    line.ColorIndex = 1; // Red
    
    BlockTableRecord btr = tr.GetObject(db.CurrentSpaceId, OpenMode.ForWrite) as BlockTableRecord;
    btr.AppendEntity(line);
    tr.AddNewlyCreatedDBObject(line, true);
    
    tr.Commit();
}

Common Patterns

Creating Uniform Knot Vector

// For degree d and n control points: knots = n + d + 1
int degree = 3;
int numControlPoints = 6;
int numKnots = numControlPoints + degree + 1; // 10 knots

DoubleCollection knots = new DoubleCollection();

// Clamped knot vector (curve passes through first and last control points)
for (int i = 0; i <= degree; i++)
    knots.Add(0.0); // d+1 zeros at start

for (int i = 1; i < numControlPoints - degree; i++)
    knots.Add(i / (double)(numControlPoints - degree));

for (int i = 0; i <= degree; i++)
    knots.Add(1.0); // d+1 ones at end

Checking NURBS Properties

NurbCurve3d curve = /* existing curve */;

if (curve.IsRational)
    ed.WriteMessage("\nCurve is rational (has weights)");
else
    ed.WriteMessage("\nCurve is non-rational");

if (curve.IsPeriodic)
    ed.WriteMessage("\nCurve is periodic (closed)");
else
    ed.WriteMessage("\nCurve is open");

ed.WriteMessage($"\nDegree: {curve.Degree}");
ed.WriteMessage($"\nControl Points: {curve.NumControlPoints}");

Best Practices

  1. Knot Vector: Ensure knot vector length = numControlPoints + degree + 1
  2. Clamped Curves: Use repeated knots at start/end for curves through endpoints
  3. Weights: Use weights > 1 to pull curve toward control point, < 1 to push away
  4. Degree: Higher degree = smoother curve, but more computation
  5. Periodic Curves: For closed curves, use periodic NURBS with matching start/end
  6. Evaluation: Sample curve with sufficient points for accurate polyline conversion
  7. Performance: Cache evaluated points if evaluating same parameters repeatedly

Related Classes

  • NurbCurve2d - 2D NURBS curve
  • CubicSplineCurve3d - Cubic interpolation spline
  • Polyline3d - Piecewise linear approximation
  • Point3d - Control points and evaluated points
  • Vector3d - Tangent vectors and derivatives

References