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Cone.md

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Cone Class

Overview

The Cone class represents a bounded right circular cone in 3D space. Cones are fundamental 3D primitives used in modeling tapered shapes and geometric calculations.

Namespace

Autodesk.AutoCAD.Geometry

Key Properties

Property Type Description
BaseCenter Point3d Gets the center of the cone base
Apex Point3d Gets the apex (tip) of the cone
AxisOfSymmetry Vector3d Gets the axis from base to apex
BaseRadius double Gets the radius of the cone base
Height double Gets the height of the cone
HalfAngle double Gets the half-angle of the cone (radians)

Key Methods

Method Return Type Description
GetClosestPointTo(Point3d) Point3d Gets closest point on cone surface
DistanceTo(Point3d) double Gets distance from point to surface
IsOn(Point3d) bool Checks if point is on surface

Code Examples

Example 1: Creating Cones

// Cone with base at origin, apex at (0, 0, 10), base radius 5
Point3d baseCenter = Point3d.Origin;
Point3d apex = new Point3d(0, 0, 10);
double baseRadius = 5.0;

Cone cone = new Cone(baseCenter, apex, baseRadius);

double height = baseCenter.DistanceTo(apex);
double halfAngle = Math.Atan(baseRadius / height);

ed.WriteMessage($"\nCone created");
ed.WriteMessage($"\nBase center: {cone.BaseCenter}");
ed.WriteMessage($"\nApex: {cone.Apex}");
ed.WriteMessage($"\nBase radius: {cone.BaseRadius}");
ed.WriteMessage($"\nHeight: {height:F2}");
ed.WriteMessage($"\nHalf angle: {halfAngle * 180 / Math.PI:F2}°");

Example 2: Cone Calculations

Cone cone = new Cone(Point3d.Origin, new Point3d(0, 0, 10), 5.0);

double height = 10.0;
double radius = 5.0;
double slantHeight = Math.Sqrt(height * height + radius * radius);

double baseArea = Math.PI * radius * radius;
double lateralArea = Math.PI * radius * slantHeight;
double totalSurfaceArea = baseArea + lateralArea;
double volume = (1.0 / 3.0) * baseArea * height;

ed.WriteMessage($"\nSlant height: {slantHeight:F2}");
ed.WriteMessage($"\nBase area: {baseArea:F2}");
ed.WriteMessage($"\nLateral surface area: {lateralArea:F2}");
ed.WriteMessage($"\nTotal surface area: {totalSurfaceArea:F2}");
ed.WriteMessage($"\nVolume: {volume:F2}");

Example 3: Frustum of Cone

// Create cone then calculate frustum (truncated cone)
Point3d baseCenter = Point3d.Origin;
Point3d apex = new Point3d(0, 0, 15);
double baseRadius = 6.0;

Cone fullCone = new Cone(baseCenter, apex, baseRadius);

// Frustum: cut at height 10 (top radius will be 2)
double cutHeight = 10.0;
double fullHeight = 15.0;
double topRadius = baseRadius * (fullHeight - cutHeight) / fullHeight;

ed.WriteMessage($"\nFrustum parameters:");
ed.WriteMessage($"\nBase radius: {baseRadius}");
ed.WriteMessage($"\nTop radius: {topRadius:F2}");
ed.WriteMessage($"\nHeight: {cutHeight}");

// Frustum volume = (1/3)πh(r1² + r1*r2 + r2²)
double frustumVolume = (1.0 / 3.0) * Math.PI * cutHeight * 
    (baseRadius * baseRadius + baseRadius * topRadius + topRadius * topRadius);

ed.WriteMessage($"\nFrustum volume: {frustumVolume:F2}");

Best Practices

  1. Apex Position: Apex must not be at base center
  2. Base Radius: Must be positive
  3. Half Angle: tan(halfAngle) = baseRadius / height
  4. Surface Area: Lateral = πrs (s = slant height), Total = πr(r + s)
  5. Volume: V = (1/3)πr²h
  6. Frustum: For truncated cone, use proportional calculations

Related Classes

  • Cylinder - Cylindrical surface (cone with 0° angle)
  • Sphere - Spherical surface
  • Point3d - Base center and apex
  • Vector3d - Axis direction

References