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NurbSurface.md

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NurbSurface Class

Overview

The NurbSurface class represents a generic NURB (Non-Uniform Rational B-Spline) parametric surface in 3D space. NURBS surfaces are the 3D extension of NURBS curves, providing precise mathematical representation of complex freeform surfaces.

Namespace

Autodesk.AutoCAD.Geometry

Key Properties

Property Type Description
ControlPoints Point3d[,] Gets the 2D grid of control points
UKnots KnotCollection Gets the knot vector in U direction
VKnots KnotCollection Gets the knot vector in V direction
UWeights DoubleCollection Gets weights in U direction
VWeights DoubleCollection Gets weights in V direction
UDegree int Gets polynomial degree in U direction
VDegree int Gets polynomial degree in V direction
NumControlPointsInU int Gets number of control points in U
NumControlPointsInV int Gets number of control points in V
IsRational bool Checks if surface has weights

Key Methods

Method Return Type Description
EvaluatePoint(double, double) Point3d Evaluates point at (u,v) parameters
GetClosestPointTo(Point3d) Point3d Gets closest point on surface
GetNormalAt(double, double) Vector3d Gets surface normal at (u,v)
GetDerivativesAt(double, double) Vector3d[] Gets partial derivatives at (u,v)

Code Examples

Example 1: Creating NURBS Surface

// Create 4x4 control point grid
int uCount = 4;
int vCount = 4;
Point3d[,] controlPoints = new Point3d[uCount, vCount];

for (int i = 0; i < uCount; i++)
{
    for (int j = 0; j < vCount; j++)
    {
        controlPoints[i, j] = new Point3d(i * 10, j * 10, Math.Sin(i) * Math.Cos(j) * 5);
    }
}

// Define knot vectors (degree 3)
DoubleCollection uKnots = new DoubleCollection();
uKnots.Add(0); uKnots.Add(0); uKnots.Add(0); uKnots.Add(0);
uKnots.Add(1); uKnots.Add(1); uKnots.Add(1); uKnots.Add(1);

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

NurbSurface surface = new NurbSurface(3, 3, uKnots, vKnots, controlPoints, false);

ed.WriteMessage($"\nNURBS Surface created");
ed.WriteMessage($"\nU degree: {surface.UDegree}, V degree: {surface.VDegree}");
ed.WriteMessage($"\nControl points: {surface.NumControlPointsInU} x {surface.NumControlPointsInV}");

Example 2: Evaluating Points on Surface

NurbSurface surface = /* existing NURBS surface */;

// Sample the surface
for (double u = 0; u <= 1.0; u += 0.25)
{
    for (double v = 0; v <= 1.0; v += 0.25)
    {
        Point3d pt = surface.EvaluatePoint(u, v);
        Vector3d normal = surface.GetNormalAt(u, v);
        
        ed.WriteMessage($"\nAt (u={u:F2}, v={v:F2}): Point={pt}, Normal={normal}");
    }
}

Example 3: Finding Closest Point on Surface

NurbSurface surface = /* existing surface */;
Point3d testPoint = new Point3d(15, 15, 10);

Point3d closestPoint = surface.GetClosestPointTo(testPoint);
double distance = testPoint.DistanceTo(closestPoint);

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

Best Practices

  1. Control Point Grid: Must be rectangular (m x n grid)
  2. Knot Vectors: U knots length = numU + degreeU + 1, V knots length = numV + degreeV + 1
  3. Parameters: U and V parameters typically range from 0 to 1
  4. Normals: Surface normal points perpendicular to surface
  5. Rational: Use weights for more control over surface shape
  6. Evaluation: Sample surface with sufficient (u,v) points for visualization

Related Classes

  • NurbCurve3d - NURBS curve (1D)
  • BoundedPlane - Planar surface
  • Point3d - Control points and evaluated points
  • Vector3d - Surface normals

References