vmm.surface.parametric
Class ChenGackstatter

java.lang.Object
  vmm.core.Exhibit
      vmm.core3D.Exhibit3D
          vmm.surface.Surface
              vmm.surface.parametric.SurfaceParametric
                  vmm.surface.parametric.WeierstrassMinimalSurface
                      vmm.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 vmm.surface.parametric.WeierstrassMinimalSurface

WeierstrassMinimalSurface.WMSView

Field Summary

protected int	Ex
protected int	iP
protected double	LRP
protected double	r1
protected int	um
protected int	vm

Fields inherited from class vmm.surface.parametric.WeierstrassMinimalSurface

afp, AFP, canShowConjugateSurface, del, distFrom0, du, dv, flag0, flag05, halfPeriod, helperArray, I__C, I_C, I1_C, I2_C, I3_C, I4_C, iBeginMiddleInHelper, iFirstInHelper, inAssociateMorph, IP__C, IP_C, LRPclosed, multipleCopyOptions, needsPeriodClosed, needsValueArray, ONE__C, ONE_C, ucount, vcount, wantsToSeeDomain, wantsToSeeGaussImage, ZERO_C

Fields inherited from class vmm.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, umax, umin, vmax, vmin

Fields inherited from class vmm.surface.Surface

data, uPatchCount, vPatchCount

Fields inherited from class vmm.core3D.Exhibit3D

defaultViewpoint, defaultViewUp, previousTransform3D

Fields inherited from class vmm.core.Exhibit

decorations, exhibitNeedsRedraw, isMorphing, morphingView, parameters, previousTransform

Constructor Summary

ChenGackstatter()

Method Summary

protected double	closingLopezRos()
protected void	createData() Overrides createData from SurfaceParametric with the goal of recomputing all constants that go into the Weierstrass Data, and then do the helperArray.
protected void	doClosingJob() Dummy function.
protected Complex	domainGrid(double u, double v) Override the default Cartesian Grid.
protected Complex	gauss(Complex z) The following two functions are the Weierstrass data that define this surface.
protected ComplexVector3D	getCenter() We want to center the surface already at the helper Level.
View	getDefaultView() Returns a default view of this exhibit, a View of type SurfaceView.
protected Complex	hPrime(Complex z)
protected static double	myRad(double u, int e) Strictly monotone function with critical points of order e at (-1,0) and (0,1).
protected void	p_Index() Last index of grid point before symmetry line switches to straight line.
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.
protected void	redoConstants() redoConstants is called in createData above, before any other computations start.
Vector3D	surfacePoint(double u, double v) Override surfacePoint to close the hole around the center saddle.

Methods inherited from class vmm.surface.parametric.WeierstrassMinimalSurface

ComplexVectorFunction, ComplexVectorIntegrator, ComplexVectorOneStepIntegrator, component3, computeHalfPeriod, createHelperArray, gaussInverseTimesHPrime, gaussTimesHPrime, getAdditionalAnimationsForView, getNumberOfPieces, helperToMinimal, intersectLines, minimalToHelper, monotonPow, setNumberOfPieces, surfaceNormal

Methods inherited from class vmm.surface.parametric.SurfaceParametric

addExtraXML, deriv_u, deriv_v, gaussMap, getActionsForView, readExtraXML, removeView

Methods inherited from class vmm.surface.Surface

computeDrawData3D, doDraw3D, getBuildAnimation, getDefaultOrientation, setDefaultOrientation

Methods inherited from class vmm.core3D.Exhibit3D

computeDrawDataHook, doDrawHook, getDefaultTransform, getDefaultViewpoint, getDefaultViewUp, setDefaultViewpoint, setDefaultViewUp

Methods inherited from class vmm.core.Exhibit

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

Methods inherited from class java.lang.Object

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

Field Detail

Ex

protected int Ex

iP

protected int iP

um

protected int um

vm

protected int vm

r1

protected double r1

LRP

protected double LRP

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()

createData

protected void createData()

Description copied from class: WeierstrassMinimalSurface

Overrides createData from SurfaceParametric with the goal of recomputing all constants that go into the Weierstrass Data, and then do the helperArray. The recomputation should be done before super.createData() is called.

Overrides:

createData in class WeierstrassMinimalSurface

domainGrid

protected Complex domainGrid(double u,
                             double v)

Override the default Cartesian Grid. It is critical that the domain grid is adapted to the minimal surface.

Overrides:

domainGrid in class WeierstrassMinimalSurface

p_Index

protected void p_Index()

Last index of grid point before symmetry line switches to straight line.

myRad

protected static double myRad(double u,
                              int e)

Strictly monotone function with critical points of order e at (-1,0) and (0,1). Used to adjust the parameter lines in domainGrid.

gauss

protected Complex gauss(Complex z)

The following two functions are the Weierstrass data that define this surface. It is best shown on the above domainGrid.

Specified by:

gauss in class WeierstrassMinimalSurface

hPrime

protected Complex hPrime(Complex z)

Specified by:

hPrime in class WeierstrassMinimalSurface

closingLopezRos

protected double closingLopezRos()

doClosingJob

protected void doClosingJob()

Description copied from class: WeierstrassMinimalSurface

Dummy function. Needs to be specified if (needsPeriodClosing) is ever TRUE

Overrides:

doClosingJob in class WeierstrassMinimalSurface

redoConstants

protected void redoConstants()

Description copied from class: WeierstrassMinimalSurface

redoConstants is called in createData above, before any other computations start.

Overrides:

redoConstants in class WeierstrassMinimalSurface

getCenter

protected ComplexVector3D getCenter()

We want to center the surface already at the helper Level. We cannot use the symmetry lines of the surface and therefore need to integrate towards the image of P.

Overrides:

getCenter in class WeierstrassMinimalSurface

surfacePoint

public Vector3D surfacePoint(double u,
                             double v)

Override surfacePoint to close the hole around the center saddle.

Overrides:

surfacePoint in class WeierstrassMinimalSurface