vmm3d.surface.parametric

Class ChenGackstatter

java.lang.Object

vmm3d.core.Exhibit

vmm3d.core3D.Exhibit3D

vmm3d.surface.Surface

vmm3d.surface.parametric.SurfaceParametric

vmm3d.surface.parametric.WeierstrassMinimalSurface

vmm3d.surface.parametric.ChenGackstatter

All Implemented Interfaces:

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

public class ChenGackstatter
extends WeierstrassMinimalSurface

The Chen-Gackstatter surface posed surprising numerical difficulties, which increased with exponent. 1.) One cannot integrate the Weierstrass Data close enough into the three saddles to close gaping holes, starting at exponent = 5. 2.) For putting the pieces together one has to find the intersection of the symmetry planes. Only after experimentation did I find points on these symmetry lines that allowed to compute the intersection with sufficient accuracy. This then worked also in the Lopez-Ros morph. 3.) Finally, the period-closing Lopez-Ros value had to be found. One only has to solve a linear equation with coefficients depending on the minimal surface. For reasons that I could not find this worked only for symmetry parameters 2,3,4,5 and then developed visible inaccuracies. These went away after repeating the determination of the Lopez-Ros parameter three times. This indicates that the linear equation has inaccurately defined coefficients, but I do not see a reason for that. 4.) For esthetic reasons the big holes had to be closed. For the top and bottom symmetry points this worked satisfactorily. The middle symmetry point still has gaps for exponent > 5. H. Karcher

Nested Class Summary

Nested classes/interfaces inherited from class vmm3d.surface.parametric.WeierstrassMinimalSurface

WeierstrassMinimalSurface.WMSView

Field Summary

Fields inherited from class vmm3d.surface.parametric.WeierstrassMinimalSurface

afp, I__C, I_C, I1_C, I2_C, I3_C, I4_C, IP__C, IP_C, ONE__C, ONE_C, 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
ChenGackstatter()

Method Summary

Modifier and Type	Method and Description
View	getDefaultView() Returns a default view of this exhibit, a View of type SurfaceView.
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.
Vector3D	surfacePoint(double u, double v) Override surfacePoint to close the hole around the center saddle.

Methods inherited from class vmm3d.surface.parametric.WeierstrassMinimalSurface

ComplexVectorIntegrator, ComplexVectorOneStepIntegrator, computeHalfPeriod, createHelperArray, getAdditionalAnimationsForView, getNumberOfPieces, helperToMinimal, minimalToHelper, setNumberOfPieces, surfaceNormal

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

Constructor Detail

ChenGackstatter

public ChenGackstatter()

Method Detail

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 WeierstrassMinimalSurface

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 WeierstrassMinimalSurface

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()

surfacePoint

public Vector3D surfacePoint(double u,
                             double v)

Override surfacePoint to close the hole around the center saddle.

Overrides:

surfacePoint in class WeierstrassMinimalSurface