vgp.surface.common

## Class PgSurface_LawsonHelicoid

- java.lang.Object
- - jv.object.PsObject
  - - jvx.surface.PgDomainDescr
    - - vgp.surface.common.PgSurfaceDescr
      - - vgp.surface.common.PgSurface_LawsonHelicoid

- All Implemented Interfaces:
    java.io.Serializable, java.lang.Cloneable, PsUpdateIf

      public class PgSurface_LawsonHelicoid
      extends PgSurfaceDescr

  Formula description of the family of minimal helicoids in the 3-sphere which was described by H.B. Lawson.

  The parameter `torsion` controls the torsion of the helicoid, that is, how fast a circle is rotated while being moved along the axis circle. The axis is the circle `axis(u)=F(u,0)`. Values of torsion = {0.5, 1., 2.} lead to {Klein Bottle, Clifford Torus, Non-orientable Snail}.

  Parametrized surface given by method, or interactively, by function expressions. If the functions of a surface are specified in `calc_f` method and, later, interactively edited, then the interactive expressions are further used. This is important for evaluation of higher order differentials since they are only approximated using finite differences in the later case.

  See Also:
    Serialized Form
  Author:
    Konrad Polthier
  Version:
    02.08.03, 1.00 created (kp)

- - ### Field Summary

    - ### Fields inherited from class vgp.surface.common.PgSurfaceDescr

      `BASE_SURFACE_NAME, BOY, BREATHER, BREATHER_PQ, CATALAN, CATENOID_HELICOID, CATENOID_HELICOID_SCENE, CLIFFORD_TORUS, CONE, CONIC_TYPE, CYLINDER, DINI, DUPIN_CYCLOID, DUPIN_SCENE, ELLIPSOID, ELLIPTIC_PARABOLOID, ENNEPER, FOOTBALL_BARREL, FRESNEL1, FRESNEL2, H3_HYPERBOLIC_HELICOID, HENNEBERG, HYPERBOLIC_PARABLOID, HYPERBOLOID_SCENE, HYPERBOLOID_TYPE, KLEINBOTTLE, KUEN, LOWER_HYPERBOLOID, MOEBIUS_STRIP, OUTER_HYPERBOLOID, PSEUDOSPHERE, S3_HOPFTORUS, S3_LAWSON_HELICOID, SIEVERT, SPHERE, STEREOGRAPHIC_SPHERE, TANNERY, TORUS, UPPER_HYPERBOLOID, ZOLL`

    - ### Fields inherited from class jv.object.PsObject

      `HAS_BOUNDARY_PANEL, HAS_CONFIG_PANEL, HAS_INFO_PANEL, HAS_LABEL_PANEL, HAS_MATERIAL_PANEL, HAS_TEXTURE_PANEL, HAS_VECTOR_PANEL, INSPECTOR_INFO, INSPECTOR_INFO_EXT, IS_DELETED, IS_FIXED, IS_FOCUSSED, IS_PICKED, IS_SELECTED, IS_USED, NUM_TAGS`

  - ### Constructor Summary

    Constructors
    Constructor and Description
    `PgSurface_LawsonHelicoid()`

  - ### Method Summary

    All Methods Instance Methods Concrete Methods
    Modifier and Type | Method and Description
    --- | ---
    `void` | `init()` Initialize and reset data structure and all instance variables.
    `boolean` | `isUPeriodic()` Determine if surface is periodic in u-direction.
    `boolean` | `isVPeriodic()` Determine if surface is periodic in v-direction.
    `boolean` | `update(java.lang.Object event)` Catch events from function strings.

    - ### Methods inherited from class vgp.surface.common.PgSurfaceDescr

      `addParameter, calc_f, christoffel, clone, copy, ddf_dUdU, ddf_dUdV, ddf_dVdV, df_dU, df_dV, df, dN_dU, dN_dV, dN, eval, firstFundamental, getAmbientProjection, getAmbientSpace, getDimOfSurface, getFunction, getListOfScenes, getListOfSurfaces, getParameter, getParameters, normal, secondFundamental, setAmbientProjection, setAmbientSpace, setDimOfSurface, setFunction, useFunctionExpression, useFunctionExpression, weingarten`

    - ### Methods inherited from class jvx.surface.PgDomainDescr

      `eval, getNameOfLines, getNumULines, getNumVLines, getUMax, getUMin, getVMax, getVMin, isShowingULine, isShowingVLine, setDiscr, setDiscrBounds, setMaxSize, setNameOfLines, setNumULines, setNumVLines, setSize, setUMax, setUMin, setVMax, setVMin, showULine, showVLine, toString`

    - ### Methods inherited from class jv.object.PsObject

      `addInspector, addUpdateListener, assureInspector, clearTag, clone, clone, getFather, getInfoPanel, getInspector, getName, getNumObjects, getSymbol, hasInspector, hasTag, hasUpdateListener, instanceOf, instanceOf, newInspector, newInspector, removeInspector, removeInspector, removeUpdateListener, setName, setParent, setSymbol, setTag, updatePanels`

    - ### Methods inherited from class java.lang.Object

      `equals, getClass, hashCode, notify, notifyAll, wait, wait, wait`

- - ### Constructor Detail

    - #### PgSurface_LawsonHelicoid

          public PgSurface_LawsonHelicoid()

  - ### Method Detail

    - #### init

          public void init()

      Description copied from class: `PgDomainDescr`
      Initialize and reset data structure and all instance variables.
      Overrides:
        `init` in class `PgSurfaceDescr`

    - #### update

          public boolean update(java.lang.Object event)

      Description copied from class: `PgSurfaceDescr`
      Catch events from function strings. Update the class whenever a child has changed. Method is usually invoked from the children.
      Specified by:
        `update` in interface `PsUpdateIf`
      Overrides:
        `update` in class `PgSurfaceDescr`
      Parameters:
        `event` - carries a lot of information
      Returns:
        true if event has been handled, otherwise false
      See Also:
        `PsObject.setParent(PsUpdateIf)`, `PsObject.getFather()`, `PsObject.addUpdateListener(PsUpdateIf)`

    - #### isUPeriodic

          public boolean isUPeriodic()

      Description copied from class: `PgSurfaceDescr`
      Determine if surface is periodic in u-direction. This method returns false, but will be overwritten by surface which are periodic.
      Overrides:
        `isUPeriodic` in class `PgSurfaceDescr`

    - #### isVPeriodic

          public boolean isVPeriodic()

      Description copied from class: `PgSurfaceDescr`
      Determine if surface is periodic in v-direction. This method returns false, but will be overwritten by surface which are periodic.
      Overrides:
        `isVPeriodic` in class `PgSurfaceDescr`

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