vgp.discrete.catenoid
Class PgCatenoid

java.lang.Object
  |
  +--jv.object.PsObject
        |
        +--jv.project.PgGeometry
              |
              +--jv.geom.PgPointSet
                    |
                    +--jv.geom.PgElementSet
                          |
                          +--vgp.discrete.catenoid.PgCatenoid

All Implemented Interfaces:

java.lang.Cloneable, PgGeometryIf, PsUpdateIf, java.io.Serializable

public class PgCatenoid

extends PgElementSet

Discrete catenoid is a critical point for the discrete area functional, and its profile curve is given by an explicit formula.

Joint work of Konrad Polthier and Wayne Rossman, with help of Ekki Tjaden.

Version:

03.10.99, 2.20 revised (kp) Interpolating catenoid with root finder.
18.08.99, 2.10 revised (kp) Waist radius implemented.
20.07.99, 2.00 revised (kp) Complete explicit formulas, additional bottomHeight control.
13.05.99, 1.05 revised (kp) Explicit formulas and user interface finished.
02.05.99, 1.00 created (kp)

Author:

Konrad Polthier

See Also:

Serialized Form

Field Summary

protected boolean	m_bAlternate Flag to switch between regular, triangulated mesh, and a mesh whose vertical edges are zig-zag.
protected boolean	m_bClosed Close interior boundary of catenoid.
protected boolean	m_bFixedHeight Fix the distance between both horizontal catenoid rings on top and bottom.
protected PuDouble	m_bottomHeight Vertical offset of lower ring for unsymmetric catenoid.
protected boolean	m_bSymmetric Ensure that catenoid is symmetric with respect to horizontal plane.
protected boolean	m_bTrueInterpolant If true then the catenoid parameters are chosen such that the discrete catenoid interpolates the smooth catenoid.
protected PuDouble	m_delta Distance between two successive rings of the catenoid, constant for discrete catenoids.
protected double	m_height
protected PuInteger	m_k Dihedral symmetry of catenoid, number of meridians.
protected PuInteger	m_n Number of rings of catenoid.
protected PuDouble	m_radius Radius of Catenoid Waist.

Fields inherited from class jv.geom.PgElementSet

m_bConforming, m_bndList, m_bShowBackface, m_bShowBoundaries, m_bShowEdgeColors, m_bShowEdgeLabels, m_bShowEdges, m_bShowElementBackColor, m_bShowElementBackColors, m_bShowElementColors, m_bShowElementLabels, m_bShowElementNormalArrow, m_bShowElementNormals, m_bShowElements, m_bShowElementTexture, m_bShowOutline, m_bShowTaggedBoundaries, m_bShowTaggedEdges, m_bShowTaggedElements, m_dimOfElements, m_edge, m_edgeColor, m_element, m_elementBackColor, m_elementColor, m_elementNormal, m_elementSaved, m_elementTexture, m_globalBndColor, m_globalBndSize, m_globalBndTagColor, m_globalEdgeColor, m_globalEdgeSize, m_globalEdgeTagColor, m_globalElementBackColor, m_globalElementColor, m_globalElementNormalColor, m_globalElementNormalLength, m_globalElementNormalSize, m_globalElementTagColor, m_maxNumElements, m_neighbour, m_numEdges, m_numElements, m_savedNumVertices

Fields inherited from class jv.geom.PgPointSet

m_bDefaultLabelEnabled, m_bShowIndices, m_bShowTaggedVertices, m_bShowTransparency, m_bShowVectorArrow, m_bShowVectorColors, m_bShowVectorFields, m_bShowVertexColors, m_bShowVertexLabels, m_bShowVertexNormalArrow, m_bShowVertexNormals, m_bShowVertexTexture, m_bShowVertices, m_dimOfColors, m_dimOfTextures, m_dimOfVectors, m_globalVectorColor, m_globalVectorLength, m_globalVectorSize, m_globalVertexColor, m_globalVertexNormalColor, m_globalVertexNormalLength, m_globalVertexNormalSize, m_globalVertexSize, m_globalVertexTagColor, m_maxNumVertices, m_numVectorFields, m_numVertices, m_texture, m_transparency, m_vectorField, m_vertex, m_vertexColor, m_vertexNormal, m_vertexTexture

Fields inherited from class jv.project.PgGeometry

m_ambientProj, m_ambientSpace, m_authorInfo, m_bShowBndBox, m_bShowCenter, m_bShowing, m_bShowTitle, m_center, m_dim, m_dimOfSimplex, m_displayList, m_geometryInfo, m_labelAttribute, m_methodMenu, m_modelMatrix, m_title, m_version, m_versionType

Fields inherited from class jv.object.PsObject

HAS_CONFIG_PANEL, HAS_INFO_PANEL, HAS_MATERIAL_PANEL, INSPECTOR_INFO, INSPECTOR_INFO_EXT, IS_DELETED, IS_FIXED, IS_SELECTED, IS_USED, m_infoPanel, m_name, m_panelList, m_parent, m_tag, m_updateList, NUM_TAGS

Fields inherited from interface jv.project.PgGeometryIf

AMBIENT_H3_HYPERBOLIC, AMBIENT_PROJECTIONS, AMBIENT_R3_EUCLIDEAN, AMBIENT_R4_EUCLIDEAN, AMBIENT_S3_SPHERE, AMBIENT_SPACES, INSPECTOR_CONTROL, INSPECTOR_CONTROL_EXT, INSPECTOR_MATERIAL, INSPECTOR_MATERIAL_EXT, LABEL_BASE, LABEL_CENTER, LABEL_HEAD, LABEL_MIDDLE, LABEL_TAIL, LABEL_TOP, METHOD_EXT, PROJ_KLEIN_BALL, PROJ_PARALLEL, PROJ_POINCARE_BALL, PROJ_STEREOGRAPHIC, PROJ_UPPER_HALFSPACE

Constructor Summary

PgCatenoid()
Construct an empty discrete catenoid which is a critical value of the discrete are functional.

Method Summary

protected void	computeSurface()
void	computeSurface(int n_profile, int k_waist)
double	getDelta()
int	getProfileDiscr()
double	getRadius()
int	getWaistDiscr()
void	init() Initialize and reset instance variables after call to super.init().
void	optimalInterpolant() For a given waist discretization and given height compute the sub-optimal profile discretization such that discrete profile lies close to cosh(z) while keeping a constant height.
void	setDelta(double delta)
void	setProfileDiscr(int n)
void	setRadius(double radius)
void	setWaistDiscr(int k)
void	trueInterpolant() For a given waist discretization and given height compute the optimal profile discretization such that discrete profile interpolates cosh(z).
boolean	update(java.lang.Object event) Update the class whenever a child has changed.
protected void	updateHeight()

Methods inherited from class jv.geom.PgElementSet

addEdge, addElement, addElement, assureBoundary, assureDimOfElements, assureEdgeColors, assureElementBackColors, assureElementColors, assureElementNormals, assureElementTextures, assureNeighbours, blend, buildPolygon, buildPolygonFromCurve, buildQuadr, buildQuadrFromCurve, buildTriangle, buildTriangleFromCurve, checkNeighbour, clearTagElement, clone, close, computeCylinder, computeDisk, computePlane, computeRotation, computeSnail, computeSphere, computeTorus, copy, copyConnectivity, copyElementSet, fixBoundaries, flipEdges, flipOrientation, getArea, getAreaOfElement, getBoundaries, getDimOfElements, getEdge, getEdge, getEdgeColors, getEdgeLength, getEdgeList, getEdges, getElement, getElementBackColor, getElementBackColors, getElementColor, getElementColors, getElementNormal, getElementNormals, getElements, getElementTextures, getElementVertices, getElementWithVertex, getGlobalBndColor, getGlobalBndSize, getGlobalBndTagColor, getGlobalEdgeColor, getGlobalEdgeSize, getGlobalEdgeTagColor, getGlobalElementBackColor, getGlobalElementColor, getGlobalElementNormalColor, getGlobalElementNormalLength, getGlobalElementNormalSize, getGlobalElementTagColor, getJvx, getL2Matrix, getL2Norm, getMaxNumElements, getNeighbour, getNeighbourLocInd, getNeighbours, getNumBoundaries, getNumBoundaryComponents, getNumBoundaryEdges, getNumBoundaryVertices, getNumEdges, getNumElements, getOppVertexInd, getOppVertexLocInd, getSavedElements, getSavedNumVertices, getVertexAngle, getVolume, getVolumeOfElement, hasBoundary, hasEdgeColors, hasEdges, hasElementColors, hasElementNormals, hasElementTextures, hasTagElement, intersectionWithLine, isConforming, isShowingBackface, isShowingBoundaries, isShowingEdgeColors, isShowingEdgeLabels, isShowingEdges, isShowingElementBackColor, isShowingElementBackColors, isShowingElementColors, isShowingElementLabels, isShowingElementNormalArrow, isShowingElementNormals, isShowingElements, isShowingElementTextures, isShowingOutline, isShowingTaggedBoundaries, isShowingTaggedEdges, isShowingTaggedElements, makeAlternatingQuadrConn, makeCylinderConn, makeElementColorsFromXYZ, makeElementColorsFromZ, makeElementColorsFromZHue, makeElementNormals, makeNeighbour, makePatchConn, makeQuadrBnd, makeQuadrConn, makeQuadrElementTexture, makeQuadrVertexTexture, makeTriangleBnd, makeTriangleConn, makeVertexNormals, markBoundary, merge, paint, printEdgeList, refineGlobalIntoFour, reflect, removeBoundaries, removeElement, removeMarkedElements, removeMarkedVertices, removeUnusedVertices, setBoundary, setConforming, setDimOfColors, setDimOfElement, setDimOfElements, setDimOfVectors, setEdge, setEdgeColors, setEdges, setElement, setElement, setElement, setElement, setElementBackColor, setElementBackColors, setElementColor, setElementColors, setElementNormal, setElementNormals, setElements, setElementTexture, setElementTextures, setElementVertices, setGlobalBndColor, setGlobalBndSize, setGlobalBndTagColor, setGlobalEdgeColor, setGlobalEdgeSize, setGlobalEdgeTagColor, setGlobalElementBackColor, setGlobalElementColor, setGlobalElementNormalColor, setGlobalElementNormalLength, setGlobalElementNormalSize, setGlobalElementTagColor, setJvx, setMaxNumElements, setNeighbours, setNumEdges, setNumElements, setSavedElements, setSavedNumVertices, setTagElement, showBackface, showBoundaries, showEdgeColors, showEdgeLabels, showEdges, showElementBackColor, showElementBackColors, showElementColors, showElementLabels, showElementNormalArrow, showElementNormals, showElements, showElementTexture, showOutline, showTaggedBoundaries, showTaggedEdges, showTaggedElements, toString, triangulate

Methods inherited from class jv.geom.PgPointSet

addVectorField, addVertex, assureVertexColors, assureVertexNormals, assureVertexTextures, clearTagVertex, getBounds, getCenterOfBndBox, getCenterOfGravity, getDimOfColors, getDimOfTextures, getDimOfVectors, getGlobalVectorColor, getGlobalVectorLength, getGlobalVectorSize, getGlobalVertexColor, getGlobalVertexNormalColor, getGlobalVertexNormalLength, getGlobalVertexNormalSize, getGlobalVertexSize, getGlobalVertexTagColor, getIndexOfVectorField, getMaxNumVertices, getNumVectorFields, getNumVertices, getTexture, getTextureImage, getTextureImageName, getVectorField, getVectorField, getVectorField, getVertex, getVertexColor, getVertexColors, getVertexNormal, getVertexNormals, getVertexTextures, getVertices, hasTagVertex, hasVertex, hasVertex, hasVertexColors, hasVertexNormals, hasVertexTextures, isDefaultLabelEnabled, isShowingIndices, isShowingTaggedVertices, isShowingVectorArrow, isShowingVectorColors, isShowingVectorField, isShowingVertexColors, isShowingVertexLabels, isShowingVertexNormalArrow, isShowingVertexNormals, isShowingVertexTexture, isShowingVertices, makeColorFromVectorLength, makeVertexColorsFromXYZ, makeVertexColorsFromZ, makeVertexColorsFromZHue, makeVertexTextureFromBndBox, projectToSphere, removeAllVectorFields, removeVectorField, removeVertex, scale, scale, setCenterOfBndBox, setDefaultLabelEnabled, setDimOfTextures, setGlobalVectorColor, setGlobalVectorLength, setGlobalVectorSize, setGlobalVertexColor, setGlobalVertexNormalColor, setGlobalVertexNormalLength, setGlobalVertexNormalSize, setGlobalVertexSize, setGlobalVertexTagColor, setMaxNumVertices, setNumVertices, setTagVertex, setTexture, setTextureImage, setTextureImageName, setTransparency, setVertex, setVertex, setVertex, setVertex, setVertexColor, setVertexColors, setVertexNormal, setVertexNormals, setVertexTextures, setVertices, showIndices, showTaggedVertices, showVectorArrow, showVectorColors, showVectorField, showVertexColors, showVertexLabels, showVertexNormalArrow, showVertexNormals, showVertexTexture, showVertices, translate

Methods inherited from class jv.project.PgGeometry

addDisplay, addPolygon, clearTagPolygon, fillMethodMenu, getAmbientProjection, getAmbientSpace, getAuthorInfo, getAuthors, getCenter, getCenterOfElement, getControlPanel, getDiameter, getDimOfSimplex, getDimOfVertices, getDisplays, getGeometryInfo, getLabelAttribute, getMaterialPanel, getModelMatrix, getPolygon, getTitle, getVersion, getVersionType, hasDisplay, hasModelMatrix, hasTagPolygon, isConfigurable, isShowingBndBox, isShowingCenter, isShowingTitle, isVisible, removeDisplay, removePolygon, setAmbientProjection, setAmbientSpace, setAuthorInfo, setAuthors, setCenter, setDimOfSimplex, setGeometryInfo, setLabelAttribute, setLabelAttribute, setModelMatrix, setPolygon, setTagPolygon, setTitle, setVersion, setVersionType, setVisible, showBndBox, showCenter, showTitle

Methods inherited from class jv.object.PsObject

addInspector, addUpdateListener, clearTag, clone, clone, copy, getFather, getInfoPanel, getInspector, getName, getNumObjects, hasInspector, hasTag, hasUpdateListener, instanceOf, instanceOf, removeInspector, removeUpdateListener, setName, setParent, setTag, updatePanels

Methods inherited from class java.lang.Object

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

Methods inherited from interface jv.project.PgGeometryIf

getInfoPanel, getName, setName

Methods inherited from interface jv.object.PsUpdateIf

getFather, setParent

Field Detail

m_bAlternate

protected boolean m_bAlternate

Flag to switch between regular, triangulated mesh, and a mesh whose vertical edges are zig-zag.

m_bTrueInterpolant

protected boolean m_bTrueInterpolant

If true then the catenoid parameters are chosen such that the discrete catenoid interpolates the smooth catenoid.

m_bFixedHeight

protected boolean m_bFixedHeight

Fix the distance between both horizontal catenoid rings on top and bottom. If height is fixed and the profile discretization modified then the distance between two successive rings measured by m_delta is adjusted. If flag is false then incrementing the profile discretization leads to a taller catenoid.

m_bSymmetric

protected boolean m_bSymmetric

Ensure that catenoid is symmetric with respect to horizontal plane. If true then the variable height of the bottom ring is automatically adjusted, and its slider is disabled.

m_height

protected double m_height

m_bClosed

protected boolean m_bClosed

Close interior boundary of catenoid.

m_delta

protected PuDouble m_delta

Distance between two successive rings of the catenoid, constant for discrete catenoids.

m_bottomHeight

protected PuDouble m_bottomHeight

Vertical offset of lower ring for unsymmetric catenoid.

m_radius

protected PuDouble m_radius

Radius of Catenoid Waist. For discrete catenoids the radius is defined as the zero value of the corresponding cosh curve.

m_k

protected PuInteger m_k

Dihedral symmetry of catenoid, number of meridians.

m_n

protected PuInteger m_n

Number of rings of catenoid.

Constructor Detail

PgCatenoid

public PgCatenoid()

Construct an empty discrete catenoid which is a critical value of the discrete are functional.

Method Detail

init

public void init()

Description copied from class: PgElementSet

Initialize and reset instance variables after call to super.init().

Overrides:

init in class PgElementSet

getDelta

public double getDelta()

setDelta

public void setDelta(double delta)

getRadius

public double getRadius()

setRadius

public void setRadius(double radius)

getWaistDiscr

public int getWaistDiscr()

setWaistDiscr

public void setWaistDiscr(int k)

getProfileDiscr

public int getProfileDiscr()

setProfileDiscr

public void setProfileDiscr(int n)

updateHeight

protected void updateHeight()

optimalInterpolant

public void optimalInterpolant()

For a given waist discretization and given height compute the sub-optimal profile discretization such that discrete profile lies close to cosh(z) while keeping a constant height.

It is possible to choose height-delta such that discrete curve interpolates exact cosh(z). But since we are interested in having a constant height when experimenting with eigenfunctions and letting discretization go to zero, we modify the value preDelta, which leads to cosh(z), to delta such that constant height is ensured.

See Also:

trueInterpolant()

trueInterpolant

public void trueInterpolant()

For a given waist discretization and given height compute the optimal profile discretization such that discrete profile interpolates cosh(z).

See Also:

optimalInterpolant()

update

public boolean update(java.lang.Object event)

Update the class whenever a child has changed. Method is usually invoked from the children.

Overrides:

update in class PgElementSet

Following copied from interface: jv.object.PsUpdateIf

Parameters:

event - carries a lot of information

Returns:

true if event has been handled, otherwise false

See Also:

PsObject, PsUpdateIf.getFather(), PsUpdateIf.setParent(PsUpdateIf)

computeSurface

public void computeSurface(int n_profile,
                           int k_waist)

computeSurface

protected void computeSurface()