<?xml version="1.0" encoding="UTF-8"?>

<screensaver name="klein" _label="Klein" gl="yes">

  <command arg="--root"/>

  <video href="https://www.youtube.com/watch?v=c2gvyGVNG80"/>

  <hgroup>
    <select id="kleinbottle">
      <option id="random"        _label="Random shape"/>
      <option id="figure-8"      _label="Figure 8"      arg-set="--klein-bottle figure-8"/>
      <option id="pinched-torus" _label="Pinched torus" arg-set="--klein-bottle pinched-torus"/>
      <option id="lawson"        _label="Lawson"        arg-set="--klein-bottle lawson"/>
    </select>

    <select id="view-mode">
      <option id="walk"      _label="Random motion"/>
      <option id="walk"      _label="Walk"          arg-set="--view-mode walk"/>
      <option id="turn"      _label="Turn"          arg-set="--view-mode turn"/>
      <option id="walk-turn" _label="Walk and turn" arg-set="--view-mode walk-turn"/>
    </select>

    <boolean id="orientation-marks" _label="Show orientation marks"
              arg-set="--orientation-marks"/>
  </hgroup>

  <hgroup>
    <select id="display-mode">
      <option id="random"      _label="Random surface"/>
      <option id="wire"        _label="Wireframe mesh"      arg-set="--mode wireframe"/>
      <option id="surface"     _label="Solid surface"       arg-set="--mode surface"/>
      <option id="transparent" _label="Transparent surface" arg-set="--mode transparent"/>
    </select>

    <select id="appearance">
      <option id="random" _label="Random pattern"/>
      <option id="solid"  _label="Solid object"       arg-set="--appearance solid"/>
      <option id="bands"  _label="See-through bands"  arg-set="--appearance bands"/>
    </select>

    <select id="colors">
      <option id="random"   _label="Random coloration"/>
      <option id="twosided" _label="One-sided"       arg-set="--colors one-sided"/>
      <option id="twosided" _label="Two-sided"       arg-set="--colors two-sided"/>
      <option id="rainbow"  _label="Rainbow colors"  arg-set="--colors rainbow"/>
      <option id="depth"    _label="4d depth colors" arg-set="--colors depth"/>
    </select>

    <boolean id="change-colors" _label="Change colors"
              arg-set="--change-colors"/>

    <select id="projection3d">
      <option id="random"          _label="Random 3D"/>
      <option id="perspective-3d"  _label="Perspective 3D"  arg-set="--projection-3d perspective"/>
      <option id="orthographic-3d" _label="Orthographic 3D" arg-set="--projection-3d orthographic"/>
    </select>

    <select id="projection4d">
      <option id="random"          _label="Random 4D"/>
      <option id="perspective-4d"  _label="Perspective 4D"  arg-set="--projection-4d perspective"/>
      <option id="orthographic-4d" _label="Orthographic 4D" arg-set="--projection-4d orthographic"/>
    </select>
  </hgroup>

  <hgroup>
    <vgroup>
      <number id="speed-wx" type="slider" arg="--speed-wx %"
              _label="WX rotation speed"
              _low-label="-4.0" _high-label="4.0"
              low="-4.0" high="4.0" default="1.1"/>

      <number id="speed-wy" type="slider" arg="--speed-wy %"
              _label="WY rotation speed"
              _low-label="-4.0" _high-label="4.0"
              low="-4.0" high="4.0" default="1.3"/>

      <number id="speed-wz" type="slider" arg="--speed-wz %"
              _label="WZ rotation speed"
              _low-label="-4.0" _high-label="4.0"
              low="-4.0" high="4.0" default="1.5"/>
    </vgroup>

    <vgroup>
      <number id="speed-xy" type="slider" arg="--speed-xy %"
              _label="XY rotation speed"
              _low-label="-4.0" _high-label="4.0"
              low="-4.0" high="4.0" default="1.7"/>

      <number id="speed-xz" type="slider" arg="--speed-xz %"
              _label="XZ rotation speed"
              _low-label="-4.0" _high-label="4.0"
              low="-4.0" high="4.0" default="1.9"/>

      <number id="speed-yz" type="slider" arg="--speed-yz %"
              _label="YZ rotation speed"
              _low-label="-4.0" _high-label="4.0"
              low="-4.0" high="4.0" default="2.1"/>
    </vgroup>

    <vgroup>
     <number id="walk-direction" type="slider" arg="--walk-direction %"
             _label="Walking direction"
             _low-label="-180.0" _high-label="180.0"
             low="-180.0" high="180.0" default="7.0"/>

     <number id="walk-speed" type="slider" arg="--walk-speed %"
             _label="Walking speed"
             _low-label="1.0" _high-label="100.0"
             low="1.0" high="100.0" default="20.0"/>

     <number id="delay" type="slider" arg="--delay %"
             _label="Frame rate" _low-label="Low" _high-label="High"
             low="0" high="100000" default="25000"
             convert="invert"/>

     <boolean id="showfps" _label="Show frame rate" arg-set="--fps"/>
    </vgroup>
  </hgroup>

  <xscreensaver-updater />

  <_description>
A Klein bottle is the 4D analog of a möbius strip.

You can walk on the surface of the bottle or rotate it in 4D or walk
on it while it rotates in 4D.  Inspired by Thomas Banchoff's book
"Beyond the Third Dimension: Geometry, Computer Graphics, and Higher
Dimensions", Scientific American Library, 1990.

https://en.wikipedia.org/wiki/Klein_bottle

Written by Carsten Steger; 2008.
  </_description>
</screensaver>
