# Crate geomath[−][src]

## Expand description

geomath is a general purpose maths framework that aims to provide efficient real-time tools for the following domains:

- Linear algebra
- Computational Geometry
- Computer Graphics and Vision
- Physics and Kinematics simulation
- Numerical simulation

It relies on a vast API that consists on various traits each specifying a math property. It provides most of the common abstraction used in the above domains :

- 2D, 3D, 4D matrices, trajectories and points
- 2D, 3D, 4D, 6D vectors

The implementation benefits from many optimizations allowed when working with small dimensions :

- Straight forward code
- Hand-optimized operations
- Fully stack allocated

However, it still uncomplete and other features and improvements are planned, take a look at the GitHub developement branch for more details.

## Get started

If you already familiar with linear algebra libraries, you can easily get started since the API is really straight forward, basic vector space operations are implemented as operators and do not need any traits. Other operations can be imported with the prelude.

### Basic principles

Some simple conventions have been choosed either to gain clarity or performance :

- Vectors are columns matrices when operating with a matrix
- Vectors cartesian coordinates are accessible using
`vector.i`

syntax with`i`

the name of the coordinate - Matrices components can be accessed using
`matrix.ij`

where`i`

is the row index and`j`

the column index - Rows and columns are indexed with
`x`

,`y`

,`z`

, … starting with`x`

- Vectors of size N can be left multiplied by matrices of size N+1

**Note :** When left-multiplying a vector of size N with a matrix of size N+1 the vector is seen as an homogeneous
vector (ie. vector of size N) with added component at 1.
It’s a way to perfrom efficient multiplications with transformation matrices.

#### Example

```
use geomath::matrix;
let m = matrix::consts::EYE_2;
assert_eq!(m.xx, 1.);
assert_eq!(m.xy, 0.);
assert_eq!(m.yx, 0.);
assert_eq!(m.yy, 1.);
```

#### Multiply assign

The multiply assign operator between matrices and vectors reverses the order of the operands
which means `u *= m`

computes in fact `u = m * u`

. This allows faster assign multiply implementation.

### The prelude

As said above, the prelude contains the traits specifications, it is split in a root and 2 modules :

```
use geomath::prelude::*; // most of the traits
use geomath::prelude::coordinates::*; // coordinates systems and transformations
use geomath::prelude::transforms::*; // matrix transforms (translations, rotations, ...)
```

### Constants

Instead of providing static generators for unit vectors and identity matrices, these are hard coded as constants :

```
use geomath::vector;
let u = vector::consts::EX_3; // unit vector in the positive x (1, 0, 0)
let v = vector::consts::N_EZ_3; // unit vector in the negative z direction (0, 0, -1)
let w = vector::consts::ZEROS_3; // zero vector of 3D space (0, 0, 0)
```

**Note :** All the modules have a `consts`

submodule.

However if you are more familiar with the generators, you can still do :

```
use geomath::prelude::Initializer;
use geomath::vector::Vector3;
let u = Vector3::zeros(); // zero vector of 3D space (0, 0, 0)
let v = Vector3::ones(); // one vector of 3D space (1, 1, 1)
```

### Short constructors

To construct a vector a matrix, you can use short constructors :

```
use geomath::vector::vec3;
use geomath::matrix::mat2;
let u = vec3(2., 3., 5.);
let m = mat2(1., 2., 3., 4.); // ordered by rows, from left to right
```

### Metric space features

The metric space fetuares for vectors and matrices can be either computed using methods or operators :

```
use geomath::vector;
use geomath::prelude::*;
let u = vector::consts::EX_3;
let v = vector::consts::N_EZ_3;
assert_eq!(u % v, u.distance(&v));
assert_eq!(u | v, u.dot(&v));
assert_eq!(!u, u.magnitude());
```

## Modules

Macros mentioned bellow

Matrix structures and documentation

Point structures and documentation

Prelude traits and documentation

Trajectory structures and documentation

Vector structures and documentation

## Macros

Similar to `assert_eq`

but with a tolerance interval

Matrix debug trait

Vector debug trait

Implementation of basic vector space features