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:triangular_ruler: C# cross precision 3D maths library.

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# Abacus

[![Build Status](https://img.shields.io/travis/sungiant/abacus)][status]
[![License](https://img.shields.io/github/license/sungiant/abacus)][mit]
[![Nuget Version](https://img.shields.io/nuget/v/Abacus)][nuget]
[![Nuget Downloads](https://img.shields.io/nuget/dt/Abacus)][nuget]

## Overview

Abacus is a zero-dependency cross-precision 3D maths library for .NET, Mono and .NET Core.  Abacus provides implementations for 32 bit and 64 bit [fixed point Q numbers][qnumbers] and provides common 3D maths types consistently across both fixed and floating point precisions.

The rationale around building Abacus is rooted in the development of deterministic game simulations.

Documentation for Abacus can be found [here][docs].

## Supported types

Abacus provides implementations of the following common 3D maths data types:

* `Vector2`
* `Vector3`
* `Vector4`
* `Matrix44`
* `Quaternion`

consistently across the following precisions:

* `Single` (`float`)
* `Double` (`double`)
* `Fixed32` (`Q16.16`)
* `Fixed64` (`Q40.24`)

## Getting started

Abacus is available as a stand-alone library via [nuget][nuget].

Alternatively, all code associated with each supported level of precision is generated into a single C# source file - this makes it easy to simply copy the appropriate [Abacus.###.cs][sources] file.

## Example usage

Abacus makes it easy to switch/test the precision used by a block of code as the API is consitent across all supported precisions - simply use the appropriate namespace:

```cs
//using Abacus.SinglePrecision;
//using Abacus.DoublePrecision;
using Abacus.Fixed32Precision; // selected precision
//using Abacus.Fixed64Precision;

class Program {
    public static void Main (string[] args) {
        var a = new Vector2 (-100, +50);
        var b = new Vector2 (+90, -70);
        var c = new Vector2 (-20, +5);
        var d = new Vector2 (+30, -5);
        Vector2 result = Vector2.CatmullRom (a, b, c, d, 0.4);
    }
}

```

## Details

```
    +Y
     |
     |
     |______ +X     * X: right
    /               * Y: up
   /                * Z: backwards
 +Z
```
* Abacus uses a right handed coordinate system.
* Angles of rotation are measured anti-clockwise when viewed from the rotation axis (positive side) toward the origin.  Right handed rule for rotations - thumb pointing along the axis of rotation, away from the origin.
* Cameras are aligned with the main coordinate system and look in the direction of their negative Z axis (just like OpenGL).
* Near and far planes are defined by their Z positions in view-space, not as their distance from the camera in view space.  This means they will be negative in the general case.
* Normalised device coordinates are inline with the main coordinate system and range from -1 to 1 on all axes.
* Abacus has been built using [T4 text templatization][t4] as there is limited support for expressing generic type constraints in C#.
* Fixed point Q numbers in Abacus can be easily customised by adjusting the code generation logic.

## Contributing

If you find a bug or have an issue please reach out via the GitHub Issue tracking system.  Feel feel to submit PR with improvements.

## License

Abacus is licensed under the **[MIT License][mit]**; you may not use this software except in compliance with the License.

[mit]: https://raw.githubusercontent.com/sungiant/abacus/master/LICENSE
[nuget]: https://www.nuget.org/packages/Abacus/
[sources]: https://github.com/sungiant/abacus/tree/master/source/abacus/src/main
[status]: https://travis-ci.org/sungiant/abacus
[docs]: http://sungiant.github.io/abacus/annotated.html
[qnumbers]: https://en.wikipedia.org/wiki/Q_(number_format)
[t4]: https://en.wikipedia.org/wiki/Text_Template_Transformation_Toolkit

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