KnotPlot Parameters

Parameters may be set by typing parameter = value. Like commands, parameters may be abbreviated to any length. However it is safer to never abbreviate a parameter to less than four characters. Parameters are guaranteed to be unambiguous if this general rule is followed.

Click on one of the following subsection names to go to that subsection. To return to the top of the page, click on one of the arrows pointing upwards.

[Setting parameters] [Changing the display] [Surface geometry] [Creating new knots and links] [Relaxation of knots] [Four dimensional knots] [Postscript pictures] [Miscellaneous parameters]

Setting parameters

Parameters come in several varieties, real numbers, integers, and boolean numbers. Real numbers will be rounded off if an integer parameter is being set. Boolean parameters may be set to one of true, on, yes, or 1 to indicate true, or false, off, no, or 0 to indicate false. Some integer parameters are naturally expressed as hexadecimal values. An example is background . These parameters are also displayed in hexadecimal when using the parameters command. To set a parameter (or command argument) to a hexidecimal integer, preface the value with the characters 0x (for example back = 0xff7648 will set the background to a nice royal blue).

Random values

Parameters and all numerical arguments to commands may be set to values which are chosen randomly in several different ways. A random value is indicated by \r as in the following: An example using all of the above is in the demos directory.

Changing the display

All the parameters in this section affect only the display as seen on the screen. They have absolutely no effect on the actual surface geometry.

If auto-colour is true, the parameter hincr is automatically set when loading a knot or creating a new one, the value of hincr depending on the number of components. Set auto-colour to false to turn off this action (default is true).

The background colour of the view window. Normally set by specifying a hex value (see the note above, default is 0x444444).

Turns on or off drawing (default is on).

Controls whether or not end-caps are drawn for open components. End-caps are not properly drawn in KnotPlot currently, set this parameter to false to turn off the drawing. This problem should be fixed in upcoming versions of the software, eliminating the need for this parameter (default is true).

Grid mode, 1 is a rectangular grid, 2 is a pie grid. Use the 3doptions command to change the colours used to draw the grid.

Size of the grid (default is 10).

Minor spacing between lines on the grid (default is 1). Set to 0 to turn off minor spacing.

Major spacing between lines on the grid (default is 5). Set to 0 to turn off major spacing.

'Hue start', the hue of component 0 in smooth tubes mode. Valid range is from 0 to 360 (default is 250).

'Hue increment', the difference in hue between consecutive components in smooth tubes mode (default depends on number of components).

The colour saturation of the surface while in smooth tubes mode. Valid range is from 0 to 1 (default is 1).

The drawing scale (default is 0.35). Not to be confused with the scale command.

trx try trz
The offset in the three directions of the displayed knot. Using the right mouse button in the view window is the same as changing trx and try.

The 'value' or brightness of the surface while in smooth tubes mode. Valid range is from 0 to 1 (default is 1).

Surface geometry

All of the parameters in this section affect both the display seen on the screen and any surface description output to another program (DXF, SDL, etc.).

The radius of the cylinders or smooth tubes when drawn (0.35). This parameter may also be set using the 'cyl-rad' slider on the main control panel.

The number of sides of the drawn cylinders. Increase this for better rendering, decrease for faster rendering (default is 12). This parameter is changed by the luxo and cheapo commands. This parameter may also be set using the 'nseg' slider on the main control panel.

The number of interpolations (segments) drawn between each bead using mode s (default is 3). This parameter is changed by the luxo and cheapo commands. This parameter may also be set using the 'ncur' slider on the main control panel.

The size of the 'broken offset' when in drawing modes 'brok' or 'sbro' (default is 0.1).

Creating new knots and links

These parameters control various settings related to the creation of new knots and links.

The radius of the entire link created with the chain command (default is 10).

The radius of individual components in a link created with the chain command (default is 0.75).

The smaller radius used in constructing a knot with the torus command (default is 2.75).

If true, everything is deleted when new knots or links are created with commands such as chain or others (see the section on creating new knots and links to see which commands are affected by this parameter). Set to false if you want to keep the old knot or link while adding a new one (default is true).

Number of beads in knots constructed with the lissajous , torus or unknot commands.

The larger radius used in constructing a knot with the torus or unknot commands (default is 8.25).

Relaxation of knots

These parameters affect the dynamical system run on the knot or link during the relaxation simulation.

Parameter controlling the magnitude of bending forces (default is 1.0).

Sets bending forces on or off (default is off).

The closest distance that the cylinders are allowed to approach in the dynamical simulation (default is 0.12).

Normally when KnotPlot is relaxing a knot, the knot is displayed at each iteration step. On some machines, especially those with slow graphics but fast CPUs, it is often preferable to draw after several iterations. Setting this parameter to a value greater than one will cause KnotPlot to draw every dstep iterations during knot relaxation.

Sets the 'electrical' force on or off (default is on).

Current iteration count (the number of relaxation steps).

The maximum distance beads are allowed to move each relaxation step. In order for the relaxation to preserve knot type, this parameter should be less than close above (default is 0.1).

Sets the 'mechanical force' on or off (default is on).

Four dimensional knots

These are the relevant parameters for four dimensional knot construction and display.

Constructing the knot

These parameters are used to define the surface constructed in the spinning or suspension process.

the number of spin sections created (the number of vertices along a line of latitude) (default is 30).

the angle of the spin plane (can also be set with the splane command).

suspended knots are constructed ``hanging'' from the points (0, 0, 0, w) and (0, 0, 0, -w) where w is the value of this parameter.

Displaying the knot

These parameters control the display of the knot (or related objects).

this sets the distance of the 4D eye point. Only relevant to the perspective projection.

this controls the length of the coordinate axes and the size of the bounding hyper-cube.

(true or false) display the four coordinate axes (false).

(true or false) display a bounding hyper-cube (false).

(true or false) display the knot itself (true).

the way the knot surface is displayed. The possible values are
--- draw as a shaded surface.
--- draw as a wire frame coloured according to latitude on the sphere.
--- same as 1 except draw latitude lines only.
--- same as 1 except draw longitude lines only.
--- draw as a wire frame but colour according to the value of the dimension lost in the projection from 4D to 3D.
Portions of the knot's surface can be selectively enabled or disabled using the spactivate command (for example, to view the northern hemisphere only).

Postscript pictures

There are several parameters controlling how Postscript pictures are generated. Also, provision is made in the Postscript file for easy editing if something unusual is required. The KnotPlot Site has a page of examples (clicking on 'example' in the list below will download a GZIPPED example for that mode).

If true, backfacing polygons are removed when outputting a Postscript file. In certain situations, such as when using a 'broken' drawing function, you might want to see backfacing polygons. If so, set this parameter to false (default is true).

Will affect the type of Postscript output generated. Defaults to 1. Modes 1 and 2 generally produce smaller files and print faster than mode 0. Modes in the ``forties'' produce the smallest files of all, and print much faster too. Possible values for psmode are:
--- smoothly shaded surface (example)
--- white polygons with black outline
--- black polygons with white outline (example)
--- same as mode 1 except the polygons are slightly rounded (example)
--- flat shaded (example)
--- similar to mode 0 except a pattern can be specified.
--- output colour Postscript with colours similar to those seen with the drawing mode set to draw norm. (example)
--- same as mode 10 except use colours as in drawing mode draw spec. (example)
--- Allows a texture map in the form of a PGM ( Portable Grey Map) file to be specified.
--- Simple rendering with a black curve (example)
--- Same as mode 40 except black and white are swapped. This gives a similar rendering to the knots and links found in Appendix C of Knots and Links (example)
--- Intended to be an improvement over mode 40 but I'm not quite sure. All these modes need some minor improvements. Note that you'll have to make cyl-rad smaller with this mode to get similar results to using mode 40.
--- The mode corresponding to mode 42 with black and white swapped.
--- Maps a random Truchet pattern on the surface. (example)



Hidden surfaces are handled in the Postscript rendering by using the 'Painter's algorithm', that is by drawing the polygons back to front. In order to do this, the set of polygons is normally sorted. Set this parameter to false to override this default behaviour.

Miscellaneous parameters

That twisting stuff

A demo script is available in the demos directory that illustrates the use of the following.

Usually off, set to on if you want knots to be automatically twfix ed when they are loaded. Note that twfixing is done when using the buttons on the control panel are used to load something at random.

A flag normally set to off, but some commands such as dxf and sdl will set it to on because they require that the coordinate frame of the smooth tube match up exactly.

The twisting value used upon loading if aftwist is on.

The amount of twist in milli-radians per segment (best see me for an explanation). Default is 0. Basically, this is a way to eliminate the deficit angle seen at the tie-point in the knot. To eliminate the deficit angle, first set twist and then enter the command twfix (or just give the value as an argument to twfix). Interesting effects can be produced by setting nseg = 3 and using a twist of around 100.

Other parameters

KnotPlot will not print anything if this parameter is true (default is false).

Format used to save knots or links with the save command. See the documentation on file formats.
--- KnotPlot LOCF float format.
--- KnotPlot LOCS short format. Files saved with this format are about half the size of those saved with the LOCF format. However, a small amount of noise is introduced to to the limited precision of short integers. Users should beware of accumulated errors if files are repeatedly loaded and saved with this save format in effect.
--- KnotPlot LOCC char format. Files saved with the LOCC are only half the size the equivalent LOCS file and a quarter the size of an equivalent LOCF file. However, the same warning applies to the use of this file format as was given for the LOCS format, only more so. This format is very useful, however, for large animation databases.
--- Raw ascii (same format as used by the coords command).
--- Ascii format suitable for input into Kenny Hunt's KED program. Cannot be used for multi-component links.
--- Similar to KED format except suitable for input into Ming. Cannot be used for multi-component links.

This HTML file was produced at 5:03 p.m. on February 7, 1997 directly from the LaTeX source.

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