[Picture-1] 0-dimensional point, 1-dimensional line segment,
2-dimensional square, 3-dimensional cube, and 4-dimensional tesseract.
1. Introduction
MCDE(Magic Cube Dimension Experience) provides virtual worlds help users understand how mathematics was born and dimensions concepts and it aims to give users learning, fun and collaboration activities with mathematics.
MCDE starts how mathematics was born before we get to dimension.
From MCDE, user can learn about numbering system, 1 dimension, 2 dimension, 3 dimension, and 4 dimension.
2. Application Description
MCDE consists of explanation mathmatics concept with history and game. Game is magic cube in different dimensions, and it will help user understand dimension with fun.
2.1 Explanation Mathematics Concept with History
[Picture-2] Explanation mode Screen
Screen consists three main parts. Director's Avatar will explain concepts in English.
You will see subtitle from bottom and you can change subtitle language from touch screen monitor next to the screen.
[Picture-3] Menu mode Screen
By moving wand joystict left and right, user can change dimension.
Each dimension has story. director avatar will talk about the story with animation.
You can find detail story in Apendix.
If User chooses 0 dimension,
- Counting sheeps : Mathematics was born
If User chooses 1 dimension,
- Lining sheep up : 1 dimension
- Debt : negative nubmers
- Half a dead sheep, or onl quater : rational nubmers
- Real nubmers
If User chooses 2 dimension,
- Hypothetical City of Cartesia
- 2D Coordinate space
If User chooses 3 dimension,
- 2D to 3D : Extra Dimension, extra Axis
If User chooses 4 dimension,
- 3D to 4D : Extra Dimension, extra Axis
2.2 Magic Cube Game
People are fimiliar with magic cube game. Typically, the faces of the cube are covered by 9 stickers in 6 solid colors, and there is one color for each side of the cube. When the puzzle is solved, each face of the cube is a solid color.
[Picture-4] Magic Cube
After explanation, automatically move to magic cube game in the dimension -0 dimension, and 1 dimension doesn't have game-. At game mode, screen is not separated. It's interactive virtual environment.
[Picture-5] 2 Dimension
[Picture-6] 3 Dimension
[Picture-7] 4 Dimension
This game will help user understand dimension concept and make them keep interested of this environment.
3. Representation of the Virtual World
MCDE's target is teenager and adult. People like cute things, so MCDE choose cartoon style representation for keeping them interested.
3.1 Visual Representation
Models will look like cartoon characters.
- dead sheep animations
- hypoterical city of cartesia animation
- 2D/3D/4D coordinate system (axis, position info) animation
- museum director avatar model + simple motions(in 10 differents)
- 2D/3D/4D cubic model
3.2 Aural Representation
- title sound
- selection sound
- selection moving sound
- director's voice record
- game title sound
- cubic rotation sound
- game completed souind
4. Interaction with the Virtual World
[Picture-8] Interaction
MCDE has wand and two extra sensors. The following items are supported by MCDE.
- select dimension (using wand button)
- move selections (using wand joystict)
- select subtitle language (using touch screen monitor)
- rotation of cubic (using real cubic attached sensor)
- select part(by lay & button click), rotation, action (using wand)
- select part(by lay & collision and hold for a while), rotation, pre-view (using another sensor)
- View control in game mode (using want joystict)
5. Application Imprementation
5.1 Design
Hardware Setup
- Wall-type passive display: 3m x 2.5m
- Electromagnetic tracking
- Single pair of tracked passive glasses
- Wand and extra two sensors
- Sound System
- Touch screen for selecting subtitle language
[Picture-9] Hardware setup configuration
Software
- Explanation animation control part
- Magic cube game engine
- Menu
- Interaction handling
5.2 Work Plan
It will finish in 6 monthes and with a crew of 4 people.
1st crew: modeling & sound system
- director avatar modeling (modeling in the 1st month)
- voice record & sounds (in the 2nd month)
- the other modeling - simple and basic (in the 2nd month)
- 10 simple motions (design & get data in the 3rd month, apply the motion into avartar in the 4th month)
To get motion tracking data, we will go to special company giving motion data. - new hardware set up (in the 6th month)
2nd crew: magic cube develop
- understand & design (in the 1st month)
- implementation (til 5th month)
- merge with framework (in 6th month)
3rd crew : explanation scene, first menu scene & device interaction handling
- design framework (in the 1st month)
- implement framework (in the 2nd month)
- add contents to framework(in the 3rd month)
- device interaction handling (in the 4th month)
- touch screen interface(in the 5th month)
- improve scene and merge (in the 6th month)
4th crew : Narration, Contents & Modeling
- deisgn narration (in the 1st month)
- make subtitle in different languages (in the 2nd month)
- modeling - improve quality of models made by the 1st crew (in the 3rd month)
- design exhibition hall setup. (in the 4th month)
- new hardware purchase (in the 5th month)
- setup (in the 6th month)
6. Concolusion
Dimension is little difficult for imagining. Specially it becomes 4 dimension.
MCDE help user understand dimension concept with story telling and game.
Fully virtual environment is good, but for education system and museum exhibit, I strongly think that we need guide.
Therefore, I choose two different scene, one is explanation and the other one is game in virtual environment.
References.
- Understanding Virtual Reality: interface, application, and design, William R. Sherman, Alan B. Craig, Morgan Kaufmann
- 3D Math Primer for Graphics and Game Development, Fletcher Dunn and Ian Parberry, Wordware pub.
- Magic Cube 4D, http://www.superliminal.com/cube/cube.htm
- Wikipedia: Dimension, http://en.wikipedia.org/wiki/Dimension
- Wikipedia: Magic Cube, http://en.wikipedia.org/wiki/Rubik
Appendix. : from 3D Math Primer for Graphics and Game Development
A. Conting sheeps : Mathematics was born.
Millennia ago, Natural numbers were invented, probably to track of dead sheep. The concept of "One sheep" came easily. then two sheep and three sheep, but people very quickly became convinced that this was too much work. They gave up counting at some point and invariably began using "many sheep". Eventually, civilization expanded to the point where we could afford to have people sitting around thinking about numbers instead of doing more survival-oriented tasks, such as killing sheep and eating them. These savvy thinkers immoralized the concept of zero(no sheep), and while they didn't get around to naming all of the natural numbers, they figured out various systems whereby we could name them if we really wanted to, using digits such as "1", "2", etc. Mathematics was born.
B. Lining sheep up : 1 dimension.
The habit of lining sheep up in a row so that they can easily be counted leads to the concept of a number line. that is, a line with the numbers marked off at regular intervals. This line can go on for as long as we wish, but to avoid boredom we have stopped at five sheep and put on an arraohead to let you know that the line can continue. Clear thinkers can visualize it going off to infinity, but historical perveryors of dead sheep probaly gave this concept little thought, outside of their dreams and fevered imaginings.
C. Debt : negative nubmers
At some point in history it was probably realized that you can sometimes, if you are a particularly fast talker, sell a sheep that you don't actually own, thus, simultaneously inventing the important concepts of debt and negative numbers. Having sold this putative sheep, you would in fact own "negative one" sheep. Thiswould lead to the discovery of integeter, which consiste of the natural numbers and their negative counterparts.
D. Half a dead sheep, or onl quater : rational nubmers
The concept of poverty probably predated that of debt, leading to a growing number of people who could afford to purchase only half a dead sheep, or perhaps only a quarter. This lead to a burgeoning use of fractional numbers, consisting of one integer divided by another such as 2/3 or 111/27. Mathematicians called these rational numbers, and they fit in the number line in the obvious places between the integers. At some point, people became lazy and invented decimal notation, like writing "3.1415" instead of the longer and more tedious 31415/1000.
E. Real nubmers
After a while, it was noticed that some numbers that appear to turn up in everyday life are not expressiblel as rational numbers. The classic example is the ratio of the circumference of a circle to its diameter, usually denoted as "pi". These are the so-called real numbers, which include rational numbers and numbers such as "pi" that would, if expressed in decimal form, require an infinite number of decimal places. The mathmatics of real numbers is regarded by many to be the most important area of mathematics, and since it is the basis for most forms of engineering, it can be credited with creating much of modern civilization. The coll thing about real numbers is that while rational numbers are countable, real numbers are uncountable. The study of natural numbers and integers is called discrete mathematics and the study of real number is called continuous mathemathics.
F. The Hypothetical city of Cartesia
It's fictional city named Cartesia. When the Cartesia city planners were laying out the streets, they were very particular. Center street runs east-west through the middle of town. All other east-west streets are named based on whether they are north or sourth of Center Streent and how far away they are from Center street. The other streets in Cartesia run north-south. Division street run north-south throught the middle of town. All other north-south streets are named based on whether they are east or west of division street, and how far away they are from Division street. The naming convention used by the city planners of Cartesia may not be creative, but it certainly is practical.
G. 2D Cooordinate Space
Before Cartesia was built, there was nothing but a large flat area of land. The city planners arbitrarily decided where the center of town would be, which direction to make the roads run, how far apart to space the roads, etc. Much like the Cartesia city planners laid down the city streets, we can establish a 2D cartesian corrdinate system anywhere we want.
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