Discrete Homogenous Surfaces

Home Dedication Examples of Segments and Surfaces Games Angle Mathematics and Physics Angle Download User Manual Programmer Manual

Have you noticed that if tic-tac-toe is played on a cylinder, unless the player who started the game commits a serious mistake, it is impossible for her to lose the game? The original game on flat board doesn't behave this way! That means with the same rules but on different boards, a game requires different strategy. Here are some of our observations about various games on various boards:

• Tic-tac-toe on a cylinder, a torus, a sphere or a hemisphere degenerates. Only beginner wins.
• Chess - on a cylinder,a sphere or a hemisphere, it is impossible to checkmate the opponent king with just a king and a rook.
• Chess - it is impossible to solve 8 queens puzzle on a cylinder,a sphere, a hemisphere or helical cylinders.
• Many games are possible to play on some boards but not others. Chess - It is impossible to play on a torus (doughnut shape) but possible to play on a number of spheres.
• There are various shapes inclusive of spheres, hemispheres, helices to choose from. These shapes appear 3D but don't require any change in rules or initial positions - essentially the games remain 2D!
• Some of the shapes have properties that make game playing very interesting. For example, on a particular type of a sphere board, an unobstructed chess rook can cover all the 64 squares!

This project provides a calculator for moves on various boards. All the boards here have some common properties.

All the boards are "discrete".

You can write Chess or Reversi using these shared objects but not Carrom.

All the boards are "homogenous". That means for all rows, number of columns are the same and for all columns, number of rows are the same.

You can write games like Checkers or puzzles like Minesweeper using these shared objects but not Ludo.

All the boards have only square grid.

You can write Go or Shogi using these shared objects but not Chinese Checkers . (This is current limitation. It may go away.)

All the boards need maximum 2 parameters to describe a position and 3 parameters to calculate the next move. (See "For Programmers" for details.)

For example, on a cylinderical chess, you need only 2 numbers to describe rank and file of a piece. However, on a spherical chess, to calculate the move of a rook across north pole, you need to additionally specify whether the number of files must decrease or increase after crossing the pole - or in other words, whether the rook crossed the pole even number of times or odd number of times.

All the boards can be used for games (more than 1 player - human or computer) or puzzles (only 1 player - human or computer).

If the game needs only 1 location - for example, Monopoly - you should search for appropriate presentation in "Segments" directory.