OPTi Rivision History

Last update: 2019.8.27

Corrected the link to OPTi 3.61. (2011.6.7)

There is nothing really new, but I have packaged OPTi 3.61 with 3.60 documents in zip format, rather than sit format. 2010.12.4.

Source files now available for further modification 2006.4.22

Now I provide the source codes of OPTi for those who are interested in the inner workings of OPTi. Modification of the program is welcomed.

Also, there has been a request for my old program called "CyclicGroup", and I am making it together with its source codes available for download.

Documents available for OPTi 2002.10.30

I have uploaded a few of my preprints related to OPTi. See below in the download section.

OPTi 3.60 (20020909)

OPTi goes 3D!! Now OPTi shows the Ford region of a given group in a realistic 3D view. Just choose "Show 3D View" from the "Group" menu. The OpenGL graphics library, which is needed in order to use the menu, is included in Mac OS X as well as in recent versions of Mac OS 9. But if you are using older versions of Mac OS, you may need to download and install appropriate versions of CarbonLib and/or OpenGLLibrary from the Apple website.

Also OPTi 3.60 now uses more feasible colors for the parameter space of the Maskit slice. The randomly looking colors shown in the Maskit's parameter space by OPTi 3.50 were due to numerical errors. Cusps are very unstable in the sense that infinitely many groups having different Ford region types reside near each cusp. Thus a very small numerical error could cause a group to look having a totally different Ford region from the original. Therefore, the pictures of Maskit slice obtained by OPTi 3.50 and by OPTi 3.60 are both correct in the mathematical sense, but of course we prefer the latter.

Server Down 2002.10.1

Our server has been down for about 3 weeks because of a malicious act of an intruder. I am sorry for any inconvenience caused by this. Now the site is up again, and I will soon post a new version of OPTi

OPTi 3.50 (20020618)

OPTi 3.50 is now a Carbon application, which means that, when run on Mac OS X, it has a look and feel of usual Mac OS X applications. It has an "Aqua" user interface, it allows you to use Navigation Services when opening and saving files, etc. OPTi 3.50 is best run on Mac OS X, but it also runs on Mac OS 9 as before.

Otherwise, OPTi 3.50 is functionally equivalent to OPTi 3.30, except that operations for closing the parameter space window is now more consistent. Choosing "Close" from "File" menu, pressing Command+W, choosing (checked) "Show Window" from "ParamSpace" menu, and clicking the go away box of the window all close the parameter space window.

OPTi 3.30 (20010918)

This is a major update.

You can now see the shape of the slice. Choose "Show Window" from "ParamSpace" menu and you get the picture of the slice in z1 coordinate. Colored region corresponds to discrete groups while surrounding black area corresponds to indiscrete groups. If the discreteness is not determined by the algorithm, the corresponding point is gray. You can click on the picture and instantly get the picture of isometric circles, Ford regions, the limit set, etc. of the corresponding group. You can also magnify the parameter window and get a fine control of the group.
Option key now lets you choose the part of the picture you want to magnify by specifying a rectangular area.
Now OPTi has so many commands that I divided them in 3 menus: Slice, Group, ParamSpace.

While staying at University of Warwick during September 4-17 I worked on this version. Though not complete yet, I decided to make it available for download. The algorithm for discreteness needs to be improved, but it may take some time. The program itself should be working fine. If you find a bug, please report it.

OPTi 3.25 (20010808)

Linear Slice command has been added. In this slice, the trace of the generator, whose isometric circle is centered at the origin, is kept invariant during the deformation. In terms of z1 and z2, the trace is the square root of 1/z1(1 - z2). Note that the Maskit slice is a special case of the linear slices where the trace of one of the generators is kept fixed at 2.

A bug where OPTi couldn't print to some non-PS printers has also been fixed.

OPTi 3.22, 3.23, 3.24

These versions of OPTi are test releases, and have never been distributed publicly. Use OPTi 3.25 instead, which contains all the functionality of these releases.

OPTi 3.21 (20000108)

For the workshop "Punctured Tori and Two-bridge Knots" held on January 10 - 12, 2000 at Nara Women's University, I updated OPTi by adding a few new functions; that are "Rotate Generators" and "Switch Generators" menus. This is the version of OPTi that I used for the demonstration during the workshop. This version of OPTi has been compiled by CodeWarrior Pro. 5.30.

OPTi 3.20 (19991227)

To the "Complex Probabilities" menu, "Isometric circles" and "Axes" submenus have been added. This trivial extension has long been waited by several people.

OPTi 3.1 (19990516)

"Demo" menu has been added to OPTi 3.0. This version of OPTi is designed specifically for the purpose of demonstration for Prof. Sakuma's talks.

OPTi 3.0 (19981017)

The name of the program is changed from "PuncturedTori" to "OPTi", but it is basically the same program.
Made icons for the program. The creator signature of "OPTi" is "PTi3".
Besides the PowerPC version, made 680x0 version and FAT binary version of the program. The program should now run on 68k macs, too; perhaps very slowly, though.
Made the necessary modification to Ford Region command for Riley Slice.
A bug which caused the picture to draw on the panel region at the bottom of the window during Save Picture command has been fixed.

PuncturedTori 2.20 (19980712)

Ford Region command implemented. It does not work well with Riley Slice yet.

PuncturedTori 2.11 (19980705)

A few bug fix + some cosmetic enhancements.

PuncturedTori 2.10 (19980630)

This is a major rewrite of the program using Metrowerks CodeWarrier Pro3. The mathematical features of the program are basically the same, but the interface design has been completely changed, and the program is now very much easier to use.

Print command now works.
Made Save As command save point locations, view area, etc.
Point locations are displayed and are editable by using digits.
Many menu items are added and conceptually organized.
Limit Set draws faster.

PuncturedTori 2.03 (1998.1.23)

Bug fix: Limit set menu is now activated for Maskit command.

PuncturedTori 2.02 (1998.1.14)

Added command

on limit set #

to allow fine drawing of the limit set. The default value of # is 1. One can specify for example #=0.1 for a much finer drawing of the limit set. Also changed the drawing procedure of the limit set slightly so that partial pictures of the limit set are drawn faster.

PuncturedTori 2.01 (1998.1.12)

Added command

Maskit
Maskit depth #
Maskit #1#2#3...

for the Maskit slice.

PuncturedTori 2.0 (1998.1.5)

First public release.

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