MATLAB Examples

# Torus Demo

## Introduction

A Torus is a geometric surface that can be represented by a doughnut: from any point on the surface, moving up/down or left/right will eventually lead you back to where you started, to continue on indefinitely. This has the capability of representing an infinite space with a finite amount of material.

The Torus datatype provides this functionality by wrapping the raw TrueData, and using (one-based) modular arithmetic to extend its space indefinitely. The subscript implementation is meant to be intuitive and match MATLAB's behavior of the builtin datatypes as closely as possible.

An easy example is the need to have the pattern [1 2 3] repeated end-over-end in a vector of length 20. A somewhat general solution might look like the following:

```x = 1:3; % original data n = 20; y = repmat(x,1,ceil(n/length(x))); % make a new vector that is too big y(1:n) % pick off the first n elements ```
```ans = Columns 1 through 13 1 2 3 1 2 3 1 2 3 1 2 3 1 Columns 14 through 20 2 3 1 2 3 1 2 ```

Doing this with a Torus would be much more intuitive and efficient:

```T = Torus(1:3); T(1:20) ```
```ans = Columns 1 through 13 1 2 3 1 2 3 1 2 3 1 2 3 1 Columns 14 through 20 2 3 1 2 3 1 2 ```

## Creating a Torus

Create a Torus by wrapping the data with the Torus constructor:

```T = Torus(1:10) ```
```T = Torus with properties: TrueData: [1 2 3 4 5 6 7 8 9 10] ```

Torus requires an input, even if it's empty - [] or {}.

## Subscripted Reference

Access it as if you had simply done just T = 1:10.

```T(5:8) ```
```ans = 5 6 7 8 ```
```T(end) ```
```ans = 10 ```

Reference out-of-bounds indices:

```T(15) ```
```ans = 5 ```
```T(-6:2) ```
```ans = 4 5 6 7 8 9 10 1 2 ```

## Subscripted Assignment

Torus allows the assignment of values like classic datatypes do. This does not allow non-positive index assignment, but will extend the structure if the index is greater than its current length:

```T = Torus(1:10); T(5) = 30; T.TrueData ```
```ans = 1 2 3 4 30 6 7 8 9 10 ```
```T(15) = 1; T.TrueData ```
```ans = Columns 1 through 13 1 2 3 4 30 6 7 8 9 10 0 0 0 Columns 14 through 15 0 1 ```

## Cell Arrays

Torus can also wrap cell arrays:

```T = Torus({'foo','bar','baz'}); ```
```T{2} ```
```ans = bar ```
```T{122} ```
```ans = bar ```
```T(5:8,2:7) ```
```ans = 'bar' 'baz' 'foo' 'bar' 'baz' 'foo' 'bar' 'baz' 'foo' 'bar' 'baz' 'foo' 'bar' 'baz' 'foo' 'bar' 'baz' 'foo' 'bar' 'baz' 'foo' 'bar' 'baz' 'foo' ```

## Higher dimensions

Nothing intuitive should change when using higher dimensions:

```T = Torus(magic(5)) ```
```T = Torus with properties: TrueData: [5x5 double] ```
```T.TrueData ```
```ans = 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 ```
```T(23:25,45:46) ```
```ans = 22 4 3 10 9 11 ```
```T(end:end+5,:) ```
```ans = 11 18 25 2 9 17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9 ```

## Animating Graphics

Using Torus to loop graphics makes for intuitive and straight-forward code with a smaller memory footprint.

```Z = peaks;
T = Torus(Z);
S = surf(T(1:50,1:100));
axis tight manual;
for k=1:1e3
set(S,'ZData',T(1:50,k:k+100))
pause(0.01)
end
```