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

Fields inherited from class jv.object.PsObject

HAS_CONFIG_PANEL, HAS_INFO_PANEL, HAS_MATERIAL_PANEL, HAS_TEXTURE_PANEL, INSPECTOR_INFO, INSPECTOR_INFO_EXT, IS_DELETED, IS_FIXED, IS_SELECTED, IS_USED, NUM_TAGS

Fields inherited from interface jv.project.PgGeometryIf

AMBIENT_H2_HYPERBOLIC, AMBIENT_H3_HYPERBOLIC, AMBIENT_H4_HYPERBOLIC, AMBIENT_PROJECTIONS, AMBIENT_R1_EUCLIDEAN, AMBIENT_R2_EUCLIDEAN, AMBIENT_R3_EUCLIDEAN, AMBIENT_R4_EUCLIDEAN, AMBIENT_R5_EUCLIDEAN, AMBIENT_S1_SPHERE, AMBIENT_S2_SPHERE, AMBIENT_S3_SPHERE, AMBIENT_S4_SPHERE, AMBIENT_SPACES, INSPECTOR_CONTROL, INSPECTOR_CONTROL_EXT, INSPECTOR_MATERIAL, INSPECTOR_MATERIAL_EXT, INSPECTOR_TEXTURE, INSPECTOR_TEXTURE_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

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.

Methods inherited from class jv.geom.PgElementSet

addEdge, addElement, addElement, assureBoundary, assureDimOfElements, assureEdgeColors, assureElementBackColors, assureElementColors, assureElementNormals, assureElementTextures, 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, getNumElementIndices, getNumElements, getOppVertexInd, getOppVertexLocInd, getSavedElements, getSavedNumVertices, getVertexAngle, getVertexTextures, getVolume, getVolumeOfElement, hasBoundary, hasEdgeColors, hasEdges, hasElementBackColors, 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, makeElementFromVertexColors, makeElementNormals, makeNeighbour, makePatchConn, makeQuadrBnd, makeQuadrConn, makeQuadrElementTexture, makeQuadrVertexTexture, makeTriangleBnd, makeTriangleConn, makeVertexFromElementColors, makeVertexNormals, markBoundary, merge, paint, printEdgeList, refineGlobalIntoFour, reflect, removeBoundaries, removeElement, removeMarkedElements, removeMarkedVertices, removeUnusedVertices, resetBoundaryNormals, setBoundary, setConforming, setDimOfColors, 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, setNeighbours, setNumEdges, setNumElements, setSavedElements, setSavedNumVertices, setTagElement, setVertexTextures, 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, getAmbientBounds, getBounds, getCenterOfBndBox, getCenterOfGravity, getDimOfColors, getDimOfTextures, getDimOfVectors, getGlobalVectorColor, getGlobalVectorLength, getGlobalVectorSize, getGlobalVertexColor, getGlobalVertexNormalColor, getGlobalVertexNormalLength, getGlobalVertexNormalSize, getGlobalVertexSize, getGlobalVertexTagColor, getIndexOfVectorField, getMaxNumVertices, getNumVectorFields, getNumVertices, getTexture, getTextureImage, getTextureImageName, getVectorField, getVectorField, getVertex, getVertexColor, getVertexColors, getVertexNormal, getVertexNormals, getVertices, hasTagVertex, hasVertex, hasVertex, hasVertexColors, hasVertexNormals, hasVertexTextures, isDefaultLabelEnabled, isShowingIndices, isShowingTaggedVertices, isShowingVectorArrow, isShowingVectorArrows, isShowingVectorColors, isShowingVectorField, isShowingVertexColors, isShowingVertexLabels, isShowingVertexNormalArrow, isShowingVertexNormals, isShowingVertexTexture, isShowingVertices, makeColorFromVectorLength, makeVertexColorsFromXYZ, makeVertexColorsFromZ, makeVertexColorsFromZHue, makeVertexTextureFromBndBox, makeVertexTextureFromCylinder, makeVertexTextureFromSphere, projectToSphere, removeAllVectorFields, removeVectorField, removeVertex, scale, scale, setCenterOfBndBox, setDefaultLabelEnabled, setDimOfTextures, setGlobalVectorColor, setGlobalVectorLength, setGlobalVectorSize, setGlobalVertexColor, setGlobalVertexNormalColor, setGlobalVertexNormalLength, setGlobalVertexNormalSize, setGlobalVertexSize, setGlobalVertexTagColor, setNumVertices, setState, setTagVertex, setTexture, setTextureImage, setTextureImageName, setTransparency, setVertex, setVertex, setVertex, setVertex, setVertexColor, setVertexColors, setVertexNormal, setVertexNormals, setVertices, showIndices, showTaggedVertices, showVectorArrow, showVectorArrows, showVectorColors, showVectorField, showVectorFields, showVertexColors, showVertexLabels, showVertexNormalArrow, showVertexNormals, showVertexTexture, showVertices, translate

Methods inherited from class jv.project.PgGeometry

addDisplay, addPolygon, clearTagPolygon, fillMethodMenu, getAmbientInvMatrix, getAmbientMatrix, getAmbientProjection, getAmbientSpace, getAuthorInfo, getAuthors, getCenter, getCenterOfElement, getControlPanel, getDiameter, getDimOfSimplex, getDimOfVertices, getDisplays, getGeometryInfo, getLabelAttribute, getMaterialPanel, getModelMatrix, getPolygon, getTitle, getVersion, getVersionType, hasAmbientMatrix, hasDisplay, hasModelMatrix, hasTagPolygon, isConfigurable, isShowingBndBox, isShowingCenter, isShowingTitle, isVisible, removeDisplay, removePolygon, setAmbientMatrix, 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, assureInspector, 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, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface jv.project.PgGeometryIf

assureInspector, getInfoPanel, getName, setName

Methods inherited from interface jv.object.PsUpdateIf

getFather, setParent

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)

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)