HyperSlice Applet Controls

Controls Screen Shots

Contents:

• Main Applet Window Controls
  • W Slider
  • W-Display Text Box
  • Graphics Panel
  • Start/Stop Button
  • 1-Step Button
  • Controls Button
  • Detach/Attach Button
  • View Button
  • Frame Rate Slider
  • Size Slider
  • Separation Slider
• Controls Dialog:
  • Object Tab
    • Object Drop-Down Choice
    • Orientation Drop-Down Choice
    • W-Range Drop-Down Choice
  • Motion Tab
    • W-Shift Check Box
    • 4-Rotation Check Box
    • 3-Rotation Check Box
    • Reorient on Apply Check Box
    • W-Shift Resolution Text Box
    • 4-Rotation Resolution Text Box
    • 3-Rotation Resolution Text Box
    • Apply Button
  • Graphics Tab
    • Color Scheme Drop-Down Choice
    • Re-randomize Button
    • Viewing Mode Drop-Down Choice
    • Show Hidden Wires Check Box
    • Uniform Lighting Check Box
  • About Tab
    • email Button
    • http Button

Main Applet Window Controls:

• W Slider
  (Located along the upper-left border of the window.) Drag it to move the 4-space polytope in the W direction (perpendicular to our 3-space). See my diagrams of the analogous process in 3 dimensions.

  The resulting numerical W-value is displayed in the W-Display text box.

  Dragging the W-slider will generally stop the animation (unless the animation has no W-shift).

  The slider has 1000 increments but you will not be able to mouse-drag it with that precision due to the limited pixel-resolution of your monitor. However you can click on the slider bar above or below the pointer to make it move by one increment, causing the W-value to change by 0.002. Note that during animation, the W-value will generally change by a different increment, dictated by the W-Shift resolution.

• W-Display Text Box
  Displays the current numerical W value (set by the W Slider or by the animation). The W value indicates how far the polytope is shifted relative to our 3-space. The W-value can range from -1.0 to 1.0. A W-value of 0.0 indicates that the polytope straddles our 3-space hyperplane symmetrically (its center lies in our 3-space). The actual W-shift is the W value multiplied by the W-range.

• Graphics Panel
  This is the large panel where the polyhedron is displayed. You can rotate the polyhedron by mouse-dragging there. You can rotate it in 4-space by shift-mouse-dragging. See here for further info.

• Start/Stop Button
  Starts and stops the animation. When the animation is running, the button label is Stop. When the animation is stopped, the button label is Start. Various actions (such as dragging the W-slider) may also stop the animation.

• 1-Step Button
  Stops the animation and causes it to step by a single frame. This could be useful for creating a movie or an animated GIF.

• Controls Button
  This causes the Controls Dialog Window to appear.

• Detach/Attach Button
  Detach detaches the applet from the web page and puts it into its own window. The new window can be resized by mouse-dragging on a corner. Once the applet is detached, the button label changes to Attach. Mouse-clicking Attach will re-attach the applet to the web page.

  When you resize the window, the contents of the applet are automatically resized. In a 2-image (Stereo) Viewing mode, only the vertical dimension is taken into account. This means that you have to make the window wide enough to show the two images, or adjust the Size Slider and/or Separation Slider so that the images fit. In a 1-image (Mono) Viewing mode, the size of the contents is determined by the smallest of the vertical and horizontal dimensions, so a square Graphics Panel is most efficient.

  After you detach the applet, it is nice to "minimize" the browser to get it out of the way. Don't close the browser though, or the applet will go away.

• View Button
  This is a shortcut for cycling through the Viewing mode choices.

• Frame Rate Slider
  This slider sets the minimum delay between animation frames. The frame delay is actually proportional to the inverse square of the slider setting, which reduces the sensitivity for low slider settings and increases it for high settings.

  Depending on your computer's processor speed, the processing time for an animation frame may be longer than the specified frame delay. Under these circumstances, the animation rate will vary, going faster when the calculation is easy, as it is with extreme W-values.

• Size Slider
  Adjusts the size of the image(s).

• Separation Slider
  Adjusts the separation of the images in a 2-image (Stereo) Viewing mode. This control is disabled in a 1-image (Mono) Viewing mode.

Controls Dialog, Object Tab:

• Object Drop-Down Choice
  This Choice-box allows you to select one of the following 4-Space Objects (Polytopes):

  Polytope Object	3D Cells	Faces	Edges	Vertices	Vertex Figure
  600-cell	600 tetrahedra	1200	720	120	icosahedron
  120-cell	120 dodecahedra	720	1200	600	tetrahedron
  24-cell	24 octahedra	96	96	24	cube
  Hypercube	8 cubes	24	32	16	tetrahedron
  Cross Polytope	16 tetrahedra	32	24	8	octahedron
  Simplex	5 tetrahedra	10	10	5	tetrahedron
  FC 600-cell	1200 dipyramids	?	?	?	multiple
  FC 120-cell	720 dipyramids	?	?	?	multiple
  FC 24-cell	96 dipyramids	?	?	?	multiple
  FC Hypercube	24 dipyramids	?	?	?	multiple
  FC Cross Polytope	32 dipyramids	?	?	?	multiple
  FC Simplex	10 dipyramids	?	?	?	multiple

  The FC (Face Center) polytopes are built by placing hyperplanes at all the face-centers of the corresponding regular polytopes. The hyperplanes are tangent to the hypersphere that contains all the face-centers. The FC polytope is the volume of hyperspace that is bounded by all these hyperplanes. This process is similar to the way a rhombic dodecahedron can be made by placing planes at all the edge-centers of a cube or octahedron. I imagine that these FC polytopes have their own names but I don't know what they are.

  For the regular (non-FC) polytopes:

  With extreme W-values, you will see a Cell when the Orientation is Cell-first. You will see a Vertex Figure when the Orientation is Vertex-first.

  For the FC polytopes:

  With extreme W-values, you will see a Cell when the Orientation is Face-first.

• Orientation Drop-Down Choice
  The orientation choices are:
  
  • Vertex-First
  • Edge-First
  • Face-First
  • Cell-First
  
  The orientation choice controls the alignment of the 4-Dimensional Regular Polytope relative to the W-axis. For example, with Edge-First alignment, an Edge of the Polytope will be the first thing to appear as the W-shift is increased from -1.0.

  Obviously when moving a 3-dimensional polyhedron across a 2-D plane, the orientation can be Vertex-First, Edge-First, or Face-First. In 4 dimensions, you have the additional freedom to orient the polytope Cell-First. This is because the 3-space which contains a cell is a hyperplane which can be aligned to be perpendicular to the W-axis.

  A Dodecahedral Cell :

  
  

  For the FC Polytopes, the orientation choice indicates the orientation of the corresponding regular polytope. To view a cell of the FC polytope, chose the Face-First orientation and adjust the W-Shift to a value near -1.0 or 1.0.

• W-Range Drop-Down Choice
  This control sets the range of the W-Slider based on various dimensions of the polytope. This control is automatically reset to the appropriate default value whenever you change the Object Choice or the Orientation Choice. We try to default the W-Range so that W-Slider limits are the points at which the polytope would disappear (it disappears when it is shifted so far that it no longer intersects our 3-space).

  The W-Range choices are:
  

  • R0 (vertex)
  • R1 (center of edge)
  • R2 (center of face)
  • R3 (center of cell)

  For example, R1 is the 4-space distance from the center of the regular polytope to the center of an edge (an edge is 1-dimensional, hence "R1"). When a regular polytope is oriented Edge First, it will just begin to intersect our 3-dimensional space when it is W-shifted by that distance. So with the Edge First orientation it is appropriate to make the -1.0 and 1.0 limits of the W-Slider equal to R1.

  R0 > R1 > R2 > R3

  E.g. for a hypercube with an edge-length of 2.0:

  R0	sqrt(4) = 2
  R1	sqrt(3) = 1.732
  R2	sqrt(2) = 1.414
  R3	sqrt(1) = 1.0

  The more complex the polytope, the less the spread between R0 and R3.

  If you are performing arbitrary 4-space rotations (via animation or by shift-dragging), you should probably set the W-range to the largest range: R0.

  For the FC Polytopes, the the wrange is chosen empirically so that the polytope just disappears as the W-slider is moved to -1.0 or 1.0.

Controls Dialog, Motion Tab:

• W-Shift Check Box
  Enables W-shift animation. Does not take affect until the Apply button is clicked.

• 4-Rotation Check Box
  Enables random 4-Rotation animation. The 4-rotation is a rotation from a randomly-varying direction in our 3-space into the W direction. Does not take affect until the Apply button is clicked.

• 3-Rotation Check Box
  Enables random 3-Rotation animation. The 3-rotation is a rotation around a randomly-varying axis in our 3-space. Does not take affect until the Apply button is clicked.

• Reorient on Apply Check Box
  Causes the object orientation (in both 3-space and 4-space) to be reset to its initial state when the Apply button is clicked.

• W-Shift Resolution Text Box
  Sets the number of animation frames that it takes for the W Slider to move through its full range (from -1.0 to 1.0). Does not take affect until the Apply button is clicked.

• 4-Rotation Resolution Text Box
  The per-frame angle of 4-rotation is 180 degrees divided by this number. Does not take affect until the Apply button is clicked.

• 3-Rotation Resolution Text Box
  The per-frame angle of 3-rotation is 180 degrees divided by this number. Does not take affect until the Apply button is clicked.

• Apply Button
  Applies all settings on this tab.

Controls Dialog, Graphics Tab:

• Color Scheme Drop-Down Choice
  The Color Scheme control is disabled unless the Viewing Mode Drop-Down Choice is set to a Solid mode.

  This control assigns colors to the polytope cells. These become the colors of the faces of the polyhedron that is seen in 3 dimensions.

  In the following choices, the W- prefix means that the cells are grouped by their W-position prior to assigning colors, and all cells with the same W-position are assigned the same color.

  Rainbow means that the colors are assigned from a rainbow spectrum (red through violet).

  Mirrored means that the color assignments are mirrored across the W=0 hyperplane.

  The Color Scheme choices are:
  

  • W-mirrored Rainbow
    This is the initial default.
  • W-Rainbow
    
  • W-mirrored Random
    
  • W-Random
    This is my favorite. I keep clicking the Re-randomize button.
  • Monochrome Random
    
  • Monochrome White
    
  • Pure Random
    Every cell is given a different random color.

• Re-randomize Button
  Re-randomizes a random Color Scheme. This button is disabled unless the Color Scheme is random.

• Viewing Mode Drop-Down Choice
  The choices are:
  
  • Solid, stereo
    For 3D viewing using the look-crossed method.
  • Solid, mono
    A single solid image.
  • Wireframe, white-white
    For 3D viewing using the look-crossed method.
  • Wireframe, red-blue
    For 3D viewing with red-blue glasses.
  • Wireframe, red-green
    For 3D viewing with red-green glasses.
  • Wireframe, mono
    A single white wireframe.

• Show Hidden Wires Check Box
  This checkbox causes the backside wires to be shown in a wireframe Viewing Mode. It is disabled in non-wireframe Viewing Modes.

• Uniform Lighting Check Box
  This checkbox turns off shading in a solid Viewing Mode. It is disabled in non-solid Viewing Modes.

Controls Dialog, About Tab:

• email Button
  Click to email me.

• http Button
  Click to go to my home page.