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Torus.md

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Torus Class

Overview

The Torus class represents a toroidal segment (donut shape) in 3D space. Tori are used in modeling pipes, rings, and organic shapes.

Namespace

Autodesk.AutoCAD.Geometry

Key Properties

Property Type Description
Center Point3d Gets the center of the torus
AxisOfSymmetry Vector3d Gets the axis of rotation
MajorRadius double Gets distance from center to tube centerline
MinorRadius double Gets radius of the tube cross-section
ReferenceAxis Vector3d Gets reference axis for the torus
IsApple bool True if major radius < minor radius (apple shape)
IsDoughnut bool True if major radius > minor radius (donut shape)
IsLemon bool True if major radius = minor radius (lemon shape)
IsDegenerate bool True if either radius <= 0

Key Methods

Method Return Type Description
GetClosestPointTo(Point3d) Point3d Gets closest point on torus surface
DistanceTo(Point3d) double Gets distance from point to surface
IsOn(Point3d) bool Checks if point is on surface
GetAnglesInU(...) void Gets start/end longitudes
GetAnglesInV(...) void Gets start/end latitudes

Code Examples

Example 1: Creating a Torus (Donut)

// Standard donut torus
Point3d center = Point3d.Origin;
Vector3d axis = Vector3d.ZAxis;
double majorRadius = 10.0; // Distance from center to tube center
double minorRadius = 3.0;  // Tube radius

Torus torus = new Torus(center, axis, majorRadius, minorRadius);

ed.WriteMessage($"\nTorus created");
ed.WriteMessage($"\nCenter: {torus.Center}");
ed.WriteMessage($"\nMajor radius: {torus.MajorRadius}");
ed.WriteMessage($"\nMinor radius: {torus.MinorRadius}");
ed.WriteMessage($"\nIs doughnut: {torus.IsDoughnut}"); // true
ed.WriteMessage($"\nIs apple: {torus.IsApple}"); // false

Example 2: Torus Types

Point3d center = Point3d.Origin;
Vector3d axis = Vector3d.ZAxis;

// Doughnut (major > minor)
Torus doughnut = new Torus(center, axis, 10.0, 3.0);

// Apple (major < minor)
Torus apple = new Torus(center, axis, 3.0, 10.0);

// Lemon (major = minor)
Torus lemon = new Torus(center, axis, 5.0, 5.0);

ed.WriteMessage($"\nDoughnut: IsDoughnut={doughnut.IsDoughnut}");
ed.WriteMessage($"\nApple: IsApple={apple.IsApple}");
ed.WriteMessage($"\nLemon: IsLemon={lemon.IsLemon}");

Example 3: Torus Calculations

Torus torus = new Torus(Point3d.Origin, Vector3d.ZAxis, 10.0, 3.0);

double R = torus.MajorRadius;
double r = torus.MinorRadius;

// Surface area = 4π²Rr
double surfaceArea = 4 * Math.PI * Math.PI * R * r;

// Volume = 2π²Rr²
double volume = 2 * Math.PI * Math.PI * R * r * r;

ed.WriteMessage($"\nSurface area: {surfaceArea:F2}");
ed.WriteMessage($"\nVolume: {volume:F2}");

Example 4: Vertical Torus

// Torus with axis along X (vertical ring)
Point3d center = new Point3d(0, 5, 5);
Vector3d axis = Vector3d.XAxis;
double majorRadius = 8.0;
double minorRadius = 2.0;

Torus verticalTorus = new Torus(center, axis, majorRadius, minorRadius);

ed.WriteMessage($"\nVertical torus created");
ed.WriteMessage($"\nAxis: {verticalTorus.AxisOfSymmetry}");

Best Practices

  1. Major Radius: Distance from torus center to tube centerline
  2. Minor Radius: Radius of the tube itself
  3. Doughnut: Most common (major > minor)
  4. Apple: Self-intersecting (major < minor)
  5. Lemon: Spindle torus (major = minor)
  6. Surface Area: 4π²Rr
  7. Volume: 2π²Rr²

Related Classes

  • Sphere - Spherical surface
  • Cylinder - Cylindrical surface
  • Cone - Conical surface
  • Point3d - Center point
  • Vector3d - Axis direction

References