OPTi Support Page

Last update: 2019.8.27

What is OPTi ?

"OPTi" is a Macintosh application program which visualizes quasi-conformal deformations of the once-punctured-torus groups. It interactively draws the isometric circles, the Ford region, the limit set, etc.

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What's new ?

OPTi 4.0.4 fixes bug causing unexpected image shake while scrolling under Mac OS X 10.14. (2019.8.27)

OPTi 4.0.3 re-implemented the demonstrations of cone manifold deformation.

OPTi 4.0.2 fixes a bug where OPTi did not show windows properly under Mac OS X 10.9.

OPTi 4.0 released. Download OPTi 4.0 from the Mac App Store. OPTi 4.0 runs under Mac OS X 10.9 and later. (2016.5.18)

Revision History

License

You can download OPTi 4.0 from the Mac App Store for free. Use it freely for research, education, and any other non-commercial purposes.

Privacy Policy

OPTi collects no user data.

Download

Download OPTi 4.0 from the Mac App Store.

OPTi 3.61 --- OPTi 3.60 User's Manual, and some sample files are archived as a zip file. The program runs under Mac OS X (using Rosetta for Intel Macs) as well as Mac OS 9.

OPTi 3.61 source files --- CodeWarrior Pro 8.3 project and source files, archived in zip format. Modification of the program is welcomed, if anybody is interested.

"OPTi 3.60" program, OPTi User's Manual, and some sample files are archived as a BinHexed StuffIt file. The program runs under Mac OS X as well as Mac OS 9.

You will need "StuffIt Expander" (freeware) to expand the downloaded file.

OPTi 3.60 --- runs on Mac OS X as well as Mac OS 9. (357KB)

OPTi 3.50 --- runs on Mac OS X as well as Mac OS 9. (308KB)

If you use Mac OS 8 or older, you may need to use an older version of OPTi:

OPTi 3.30 --- runs on PPC macs only. (461KB)

OPTi 3.21 --- runs on both PPC and 68K macs. (771KB)

CyclicGroup --- Classic application, and its source files.

Here are some documents about OPTi in PDF format.

• OPTi's algorithm for discreteness determination (Japanese) --- explains the mathematical background of OPTi. The printed version of this is also available in RIMS Kokyuroku 1270 "Hyperbolic Spaces and Discrete Groups II" (2002), 67-76.
• OPTi's algorithm for discreteness determination --- This is essentially an English translation of the above.
• OPTi's algorithm for drawing the limit set (Japanese) --- This is a note for my talk in "Topology and Computer" held at Nara Women's University, November 29 - December 1, 2001. It contains a short informal description of how OPTi draws the limit set, together with an introduction to programming for mathematicians.
• OPTi's algorithm for drawing the limit set --- an English translation of the above.

Bug report

Every program of this complexity contains a bug or two. If you find any, please report it by sending email to wada@ist.osaka-u.ac.jp. It would greatly help me improve the program.