 Gamedev Framework (gf)  0.7.0 A C++14 framework for 2D games
Vectors, matrices and transforms

### Table of Contents

gf provides a generic gf::Vector type and a generic gf::Matrix type that are used throughout the library.

# Vectors

## Vector types

A gf::Vector represents a mathematical vector in a $$N$$-dimensional space. It has a broad range of applications. The most obvious is to represent the position of an object in the world space but it's not the only one.

#include <gf/Vector.h>

The gf::Vector type is totally generic regarding its type but also its dimension $$N$$.

## Operations on vectors

#include <gf/VectorOps.h>

gf defines common mathematical operators for two vectors but also for a vector and a scalar. In each case, type conversion is made if necessary, following the usual rules of the language. The following table gives the semantics of the main operations between two vectors $$\mathbf{a}$$ and $$\mathbf{b}$$, or between a vector $$\mathbf{a}$$ and a scalar $$\lambda$$. These operations are all defined component-wise.

$$\bullet$$ $$\mathbf{a} \bullet \mathbf{b}$$ $$\mathbf{a} \bullet \lambda$$ $$\lambda \bullet \mathbf{a}$$
$$+$$ $$a_i + b_i$$ $$a_i + \lambda$$ $$\lambda + a_i$$
$$-$$ $$a_i - b_i$$ $$a_i - \lambda$$ $$\lambda - a_i$$
$$*$$ $$a_i * b_i$$ $$a_i * \lambda$$ $$\lambda * a_i$$
$$/$$ $$a_i / b_i$$ $$a_i / \lambda$$ $$\lambda / a_i$$

gf also defines equality and inequality operators for vectors.

## Functions on vectors

#include <gf/VectorOps.h>

# Transforms

## Simple transformation

A simple transformation in gf is a rotation followed by a translation. A simple rotation is represented by the gf::Rotation type, a simple translation is represented by the gf::Translation type, and the simple transformation is represented by the gf::Transform type.

These simple transformations are useful in the physics engine.

## Affine transformation

You can define a generic affine transformation in 2D with a transformation matrix thanks to the gf::Matrix3f type.