vmm3d.surface.parametric

Class WeierstrassMinimalSurface

java.lang.Object

vmm3d.core.Exhibit

vmm3d.core3D.Exhibit3D

vmm3d.surface.Surface

vmm3d.surface.parametric.SurfaceParametric

vmm3d.surface.parametric.WeierstrassMinimalSurface

All Implemented Interfaces:

java.util.EventListener, javax.swing.event.ChangeListener, Decorateable, Parameterizable

Direct Known Subclasses:

CatenoidEnneper, CatenoidFence, ChenGackstatter, CostaHoffmanMeeks, DoubleEnneper, DoublyPeriodicJD, DoublyPeriodicJE, Helicoid_Weierstrass, LidinoidHfamily, LopezRosNoGo, OtherTriangCatenoid, PlanarEnneper, Riemann, Scherk_Weierstrass, SchoenCLPsurface, SchoenGyroid, SchwarzHsurface, SchwarzPDsurface, Skew_K_noid, Symmetric_K_Noid, WavyEnneper_Weierstrass

public abstract class WeierstrassMinimalSurface
extends SurfaceParametric

Abstract Weierstrass Minimal Surface

Nested Class Summary

Nested Classes

Modifier and Type	Class and Description
class	WeierstrassMinimalSurface.WMSView The View class for WeierstrassMinimalSurfaces, overridden *only* to add the Show Conjugate Surface and number of pieces actions to the correct place in the Action menu.

Field Summary

Fields

Modifier and Type	Field and Description
RealParamAnimateable	afp
static Complex	I__C
static Complex	I_C
static Complex	I1_C
static Complex	I2_C
static Complex	I3_C
static Complex	I4_C
static Complex	IP__C
static Complex	IP_C
static Complex	ONE__C
static Complex	ONE_C
static Complex	ZERO_C

Fields inherited from class vmm3d.surface.parametric.SurfaceParametric

COLOR_GAUSS_CURVATURE, COLOR_MEAN_CURVATURE, COLOR_TWO_SIDED_DEFAULT, COLOR_TWO_SIDED_USER, COLOR_USER, COLOR_USER_FUNCTION_HSB, COLOR_USER_FUNCTION_RGB, COLOR_WHITE

Fields inherited from class vmm3d.surface.Surface

uPatchCount, vPatchCount

Constructor Summary

Constructors

Constructor and Description
WeierstrassMinimalSurface()

Method Summary

Modifier and Type	Method and Description
ComplexVector3D	ComplexVectorIntegrator(Complex zInitial, Complex zFinal, int numSteps)
ComplexVector3D	ComplexVectorOneStepIntegrator(Complex zInitial, Complex zFinal)
void	computeHalfPeriod()
void	createHelperArray() The helperArray is filled with auxiliary data from which the surface points can be computed quickly in public Vector3D surfacePoint(double u, double v).
ActionList	getAdditionalAnimationsForView(View view) This method returns a list of ActionItem that will be added to the Animation menu of the 3dxm applicaiton.
View	getDefaultView() Returns a default view of this exhibit, a View of type SurfaceView.
int	getNumberOfPieces()
ComplexVector3D	helperToMinimal(ComplexVector3D hp) The integrated values that are collected in ComplexVector3D[][] helperArray are here converted to points of the holomorphic null curve in C^3 whose real and imaginary parts are minimal surfaces in R^3.
ComplexVector3D	minimalToHelper(ComplexVector3D mn) Inverse function to the previous helperToMinimal.
void	parameterChanged(Parameter param, java.lang.Object oldValue, java.lang.Object newValue) This method will be called automatically when a parameter that has been added to this Exhibit is changed.
void	setNumberOfPieces(int numberOfPieces)
Vector3D	surfaceNormal(double u, double v) The surface normal is called often while rendering the surface.
Vector3D	surfacePoint(double u, double v) This function lets a minimal surface that is defined by Weierstrass Data behave as if it were given by an explicit parametrization.

Methods inherited from class vmm3d.surface.parametric.SurfaceParametric

addExtraXML, deriv_u, deriv_v, gaussMap, getActionsForView, getPatchCountU, getPatchCountV, readExtraXML, removeView, setEpsilon, setPatchCount, setU, setV, setViewpoint

Methods inherited from class vmm3d.surface.Surface

getBuildAnimation, getDefaultOrientation, getGrid3D, setDefaultOrientation

Methods inherited from class vmm3d.core3D.Exhibit3D

getDefaultTransform, getDefaultViewpoint, getDefaultViewUp, setDefaultViewpoint, setDefaultViewUp

Methods inherited from class vmm3d.core.Exhibit

addChangeListener, addDecoration, addView, clearDecorations, forceRedraw, getAlternativeViews, getCreateAnimation, getDecorations, getDefaultBackground, getDefaultForeground, getDefaultWindow, getFramesForMorphing, getMorphingAnimation, getName, getParameterByName, getParameters, getSettingsCommandsForView, getTitle, getUseFilmstripForMorphing, getViews, removeChangeListener, removeDecoration, render, setDefaultBackground, setDefaultForeground, setDefaultWindow, setDefaultWindow, setFramesForMorphing, setName, setUseFilmstripForMorphing, stateChanged

Methods inherited from class java.lang.Object

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

Field Detail

ZERO_C

public static final Complex ZERO_C

ONE_C

public static final Complex ONE_C

ONE__C

public static final Complex ONE__C

IP_C

public static final Complex IP_C

IP__C

public static final Complex IP__C

I_C

public static final Complex I_C

I__C

public static final Complex I__C

I1_C

public static final Complex I1_C

I2_C

public static final Complex I2_C

I3_C

public static final Complex I3_C

I4_C

public static final Complex I4_C

afp

public RealParamAnimateable afp

Constructor Detail

WeierstrassMinimalSurface

public WeierstrassMinimalSurface()

Method Detail

surfaceNormal

public Vector3D surfaceNormal(double u,
                              double v)

The surface normal is called often while rendering the surface. For Weierstrass surfaces the normal is known well before the surface points are known. The normal should never be computed numerically. Therefore the following overrides the numerical differentiation.

Overrides:

surfaceNormal in class SurfaceParametric

ComplexVectorOneStepIntegrator

public ComplexVector3D ComplexVectorOneStepIntegrator(Complex zInitial,
                                                      Complex zFinal)

ComplexVectorIntegrator

public ComplexVector3D ComplexVectorIntegrator(Complex zInitial,
                                               Complex zFinal,
                                               int numSteps)

surfacePoint

public Vector3D surfacePoint(double u,
                             double v)

This function lets a minimal surface that is defined by Weierstrass Data behave as if it were given by an explicit parametrization.

Specified by:

surfacePoint in class SurfaceParametric

helperToMinimal

public ComplexVector3D helperToMinimal(ComplexVector3D hp)

The integrated values that are collected in ComplexVector3D[][] helperArray are here converted to points of the holomorphic null curve in C^3 whose real and imaginary parts are minimal surfaces in R^3.

minimalToHelper

public ComplexVector3D minimalToHelper(ComplexVector3D mn)

Inverse function to the previous helperToMinimal.

createHelperArray

public void createHelperArray()

The helperArray is filled with auxiliary data from which the surface points can be computed quickly in public Vector3D surfacePoint(double u, double v). The routine can either start with the i-line j=0 first and use these values to start the integration along the j-curves -- or it can do the j-curve i=0 first and compute the i-curves from there. One tries to have no singular or numerically difficult points on the first curve.

computeHalfPeriod

public void computeHalfPeriod()

getAdditionalAnimationsForView

public ActionList getAdditionalAnimationsForView(View view)

Description copied from class: Exhibit

This method returns a list of ActionItem that will be added to the Animation menu of the 3dxm applicaiton. The values in the list should ordinarily be commands (i.e. AbstractActionVMM) that run animations (although there is no way to enforce this restriction). These animations commands are in addition to the standard "Morph" and "Cyclic Morph" commands. Note that these commands are added to those returned by View#getAdditionalAnimations().

In this top-level Exhibit class, the return value is a an empty list (but not null). In general, when overriding this method, subclasses should call "super.getAdditionalAnimationsForView()" to obtain a list of actions from the superclass. It can then add additional actions or remove or disable actions that are in the list from the superclass.

Overrides:

getAdditionalAnimationsForView in class Exhibit

Parameters:

view - The view in which the animations will be run.

getNumberOfPieces

public int getNumberOfPieces()

setNumberOfPieces

public void setNumberOfPieces(int numberOfPieces)

parameterChanged

public void parameterChanged(Parameter param,
                             java.lang.Object oldValue,
                             java.lang.Object newValue)

Description copied from class: Exhibit

This method will be called automatically when a parameter that has been added to this Exhibit is changed. It should not ordinarily be called directly. Note that in fact, this method simply calls forceRedraw. This method is defined in the <@link Parameterizable} interface.

Specified by:

parameterChanged in interface Parameterizable

Overrides:

parameterChanged in class Exhibit

Parameters:

param - The Parmeter whose value has been set.

oldValue - The previous value of the parameter.

newValue - The new, current value of the parameter. This is not necessarily guaranteed to be different from the old value (although it is for parameters definedin the VMM core).

See Also:

Exhibit.forceRedraw()

getDefaultView

public View getDefaultView()

Description copied from class: Surface

Returns a default view of this exhibit, a View of type SurfaceView. (Note: If a Surface is displayed in a plain View3D, it will always appear as a wireframe.)

Overrides:

getDefaultView in class Surface