Class Cylinder

java.lang.Object

org.episteme.core.mathematics.geometry.surfaces.Cylinder

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 Cylinder
extends Object
implements ParametricSurface

Represents a cylindrical surface.

A cylinder is a surface of revolution with constant radius. Parametric form: S(θ, z) = (r·cos(θ), r·sin(θ), z) where θ ∈ [0, 2π] and z ∈ [z_min, z_max]

Since:

1.0

Author:

Silvere Martin-Michiellot, Gemini AI (Google DeepMind)

Constructor Summary

Constructors

Constructor	Description
Cylinder(PointND center, Real radius, Real height)	Creates a cylinder with the given center, radius, and height.
Cylinder(Real radius, Real height)	Creates a cylinder with the given 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	getCenter()	Returns the center point.
Real	getHeight()	Returns the height of the cylinder.
Real	getRadius()	Returns the radius of the cylinder.
Real	lateralSurfaceArea()	Returns the lateral surface area (excluding top and bottom).
Vector<Real>	normal(Real u, Real v, Real h)	Returns the normal vector at (u, v).
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	totalSurfaceArea()	Returns the total surface area (including top and bottom).
Real	volume()	Returns the volume of the cylinder.

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, surfaceArea, surfaceElement

Methods inherited from interface Relation

getCodomain, getDomain

Constructor Details

Cylinder

public Cylinder(Real radius,
 Real height)

Creates a cylinder with the given radius and height.

Parameters:

radius - the radius

height - the height

Cylinder

public Cylinder(PointND center,
 Real radius,
 Real height)

Creates a cylinder with the given center, radius, and height.

Parameters:

center - the center of the base

radius - the radius

height - the height

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

normal

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

Description copied from interface: ParametricSurface

Returns the normal vector at (u, v).

The normal is computed as: N = ∂S/∂u × ∂S/∂v

Specified by:

normal in interface ParametricSurface

Parameters:

u - the first parameter

v - the second parameter

h - the step size for numerical differentiation

Returns:

the unit normal 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

getRadius

public Real getRadius()

Returns the radius of the cylinder.

Returns:

the radius

getHeight

public Real getHeight()

Returns the height of the cylinder.

Returns:

the height

getCenter

public PointND getCenter()

Returns the center point.

Returns:

the center

lateralSurfaceArea

public Real lateralSurfaceArea()

Returns the lateral surface area (excluding top and bottom). A = 2Ï€rh

Returns:

the lateral surface area

totalSurfaceArea

public Real totalSurfaceArea()

Returns the total surface area (including top and bottom). A = 2Ï€r(r + h)

Returns:

the total surface area

volume

public Real volume()

Returns the volume of the cylinder. V = πr²h

Returns:

the volume