Class Cone

java.lang.Object

org.episteme.core.mathematics.geometry.surfaces.Cone

All Implemented Interfaces:

Function<Vector<Real>, Vector<Real>>, ContinuousFunction<Vector<Real>, Vector<Real>>, DifferentiableFunction<Vector<Real>, Vector<Real>>, Function<Vector<Real>, Vector<Real>>, Relation<Vector<Real>, Vector<Real>>, ParametricSurface

public class Cone
extends Object
implements ParametricSurface

Represents a conical surface.

A cone is a surface formed by lines connecting a point (apex) to a circular base. Parametric form: S(θ, t) = (t·r·cos(θ), t·r·sin(θ), t·h) where θ ∈ [0, 2π], t ∈ [0, 1], r is base radius, h is height

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Cone(PointND apex, Real baseRadius, Real height)	Creates a cone with the given apex, base radius, and height.
Cone(Real baseRadius, Real height)	Creates a cone with the given base radius and height.

Method Summary

Modifier and Type	Method	Description
PointND	at(Real u, Real v)	Evaluates the surface at parameters (u, v).
Real	gaussianCurvature(Real u, Real v, Real h)	Returns the Gaussian curvature at (u, v).
PointND	getApex()	Returns the apex point.
Real	getBaseRadius()	Returns the base radius.
Real	getHeight()	Returns the height.
Real	lateralSurfaceArea()	Returns the lateral surface area.
Vector<Real>	partialU(Real u, Real v, Real h)	Returns the partial derivative ∂S/∂u.
Vector<Real>	partialV(Real u, Real v, Real h)	Returns the partial derivative ∂S/∂v.
Real	slantHeight()	Returns the slant height. l = √(r² + h²)
Real	totalSurfaceArea()	Returns the total surface area (including base).
Real	volume()	Returns the volume of the cone.

Methods inherited from class Object

clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

Methods inherited from interface ContinuousFunction

isContinuous

Methods inherited from interface DifferentiableFunction

isDifferentiable

Methods inherited from interface Function

compose

Methods inherited from interface Function

andThen, apply, compose, contains, evaluate, getBackend, setBackend

Methods inherited from interface ParametricSurface

differentiate, evaluate, firstFundamentalForm, getOutputDimension, normal, surfaceArea, surfaceElement

Methods inherited from interface Relation

getCodomain, getDomain

Constructor Details

Cone

public Cone(Real baseRadius,
 Real height)

Creates a cone with the given base radius and height. Apex at origin, base at z = -height.

Parameters:

baseRadius - the radius of the base

height - the height

Cone

public Cone(PointND apex,
 Real baseRadius,
 Real height)

Creates a cone with the given apex, base radius, and height.

Parameters:

apex - the apex point

baseRadius - the radius of the base

height - the height (base is at apex - height along z)

Method Details

at

public PointND at(Real u,
 Real v)

Description copied from interface: ParametricSurface

Evaluates the surface at parameters (u, v).

Specified by:

at in interface ParametricSurface

Parameters:

u - the first parameter

v - the second parameter

Returns:

the point on the surface

partialU

public Vector<Real> partialU(Real u,
 Real v,
 Real h)

Description copied from interface: ParametricSurface

Returns the partial derivative ∂S/∂u.

This is the tangent vector in the u-direction.

Specified by:

partialU in interface ParametricSurface

Parameters:

u - the first parameter

v - the second parameter

h - the step size for numerical differentiation

Returns:

the partial derivative vector

partialV

public Vector<Real> partialV(Real u,
 Real v,
 Real h)

Description copied from interface: ParametricSurface

Returns the partial derivative ∂S/∂v.

This is the tangent vector in the v-direction.

Specified by:

partialV in interface ParametricSurface

Parameters:

u - the first parameter

v - the second parameter

h - the step size for numerical differentiation

Returns:

the partial derivative vector

gaussianCurvature

public Real gaussianCurvature(Real u,
 Real v,
 Real h)

Description copied from interface: ParametricSurface

Returns the Gaussian curvature at (u, v).

K = (LN - M²) / (EG - F²) where L, M, N are second fundamental form coefficients and E, F, G are first fundamental form coefficients.

Specified by:

gaussianCurvature in interface ParametricSurface

Parameters:

u - the first parameter

v - the second parameter

h - the step size

Returns:

the Gaussian curvature

getBaseRadius

public Real getBaseRadius()

Returns the base radius.

Returns:

the base radius

getHeight

public Real getHeight()

Returns the height.

Returns:

the height

getApex

public PointND getApex()

Returns the apex point.

Returns:

the apex

slantHeight

public Real slantHeight()

Returns the slant height. l = √(r² + h²)

Returns:

the slant height

lateralSurfaceArea

public Real lateralSurfaceArea()

Returns the lateral surface area. A = πrl where l is slant height

Returns:

the lateral surface area

totalSurfaceArea

public Real totalSurfaceArea()

Returns the total surface area (including base). A = πr(r + l)

Returns:

the total surface area

volume

public Real volume()

Returns the volume of the cone. V = (1/3)πr²h

Returns:

the volume