The VulkanSceneGraph provides GLSL style vector, quaternion and matrix types which are used to represent data, they can be used both to store data on the CPU and directly mapped to GPU memory for use by shaders. A range of standard vector Math Functions are provided that we’ll discuss later in this chapter, this page will discuss the data types.

The math data types are found in the include/vsg/maths directory. All the types are declared as template<> structs with definitions provided for the specific types, supporting bool, 8, 16 and 32 bit int and unsigned ints, float and double versions of each type.

Simple structs are used, only containing the data fields required for the type. They are not subclassed from vsg::Object like other scene graph objects as they focus on representing low level data and supporting maths operations. All math types can be used as part of data objects which we will cover in the next page - Data Types.

## Available types and the associated headers

Vector & quaternion:

Matrix types:

Geometric primitive types:

## Prefix naming convention

The prefix of the type describes the numerical type, the mappings are:

 Prefix Description Type Example no prefix 32 bit floating point float vsg::vec3 d 64 bit floating point double vsg::dmat4 b signed byte std::int8_t vsg::bvec4 ub unsigned byte std::uint8_t vsg::ubvec4 s signed short std::int16_t vsg::svec2 us unsigned short std::uint16_t vsg::usvec2 i signed int std::int32_t vsg::vec3 ui unsigned int std::uint32_t vsg::uivec3

## Vectors

The vsg::vec2, vec3, vec4 types provide GLSL style access, with {x,y,z,w}, {r,g,b,a}, {s,t,p,q} and [] accessors which all map to the same underlying numerical values. All the vector types also support set(..) methods and assignment. The vector types have a range of uses and the accessors used support these:

``````// double precision position, good for GIS on CPU
vsg::dvec3 position{1.0, 2.0, 3.0);
position.x = 1.0; // equivalent to position = 1.0
position.y = 2.0; // equivalent to position = 2.0

// float vertex, good for GPU work
vsg::vec3 vertex{1.0f, 2.0f, 3.0f);
vertex.x = 1.0f; // equivalent to position = 1.0f
vertex = 2.0f; // equivalent to position.y = 2.0f

// float normals
vsg::vec3 normal(0.0f, 0.0f, 1.0f); // floating point vec3
normal.set(0.0f, 1.0f, 0.0f);

// colours
vsg::vec4 color(1.0f, 0.0f, 0.0f, 1.0f); // float vec4 representing opaque red
color.r *= 0.5f; // half the red intensity
color = 1.0f; // set the a channel to 1.0

vsg::ubvec4 packed_color(0, 255, 0, 127); // unsigned byte semi-transparent green
packed_color = vsg::ubvec4(255, 255, 255, 255); // assign an all white color

// you can use .x, .r &  etc. access interchangeably
std::cout<<"color : red = "<<color<<", green = "<<color.g<<", blue = "<<color.z<<", alpha = "<<color.a<<std::endl;
std::cout<<"number of components : color.size() = "<<color.size()<<std::endl; // will be 4 for vec4 types
``````

## Quaternion

The vsg::quat type is a rotation, defined in quaternion form, that provides {x,y,z,w} and [] accessors which all map to the same underlying numerical values:

``````// double precision quaternion useful for defining rotations, useful for GIS etc. applications
// use the angle, axis constructor to create a 90 degree rotation about the z axis.

std::cout<<"rotation = "<<rotation.x<<", "<<rotation.y<<", "<<rotation.z<<", "<<rotation.w<<std::endl;

// default constructed single precision quaternion represents non rotation
vsg::quat rot;

// set as a rotation between two vectors
rot.set(vsg::vec3(1.0f, 0.0f, 0.0f),  vsg::vec3(0.0f, 1.0f, 0.0f));

// the quat::size() method returns 4
std::cout<<"rot = ";
for(size_t i=0; i<rot.size(); ++i) std::cout<<" "<<rot[i]<<std::endl;

``````

## Matrices

The vsg::mat3, mat4 types provide GLSL style access, with [element] & [column][row] accessors which all map to the same underlying numerical values. The matrix types have a range of uses and the accessors used support these:

``````// single precision 3x3 matrix useful for rotation
vsg::mat3 rotation_matrix(1.0f, 0.0f, 0.0f,
0.0f, 1.0f, 0.0f,
0.0f, 0.0f, 1.0f);

// double precision 4x4 matrix useful for homogeneous transformations
// default constructor provides an identity matrix.
vsg::dmat4 matrix;

// set the translation of 100, 200, 300 units.
matrix = 100.0;
matrix = 200.0;
matrix = 300.0;
``````

## Geometric primitives

The vsg::plane, sphere and box types do not have a direct GLSL equivalent but are very useful for geometric primitives that are used in graphics applications. The conventions used follow the same patterns as used in the vector, quaternion and matrix types.

``````
// define a single precision horizontal plane at height of 1 unit
vsg::plane pl(0.0f, 0.0, 1.0f, -1.0f);

// create unit cube polytope from planes
std::vector<vsg::dplane> polytope = {
{1.0, 0.0, 0.0, 1.0}, // left plane at x=-1, pointing right
{-1.0, 0.0, 0.0, 1.0}, // right plane at x=1, pointing left
{0.0, 1.0, 0.0, 1.0}, // front plane at y=-1, pointing forward
{0.0, -1.0, 0.0, 1.0}, // back plane at y=1, pointing backward
{0.0, 0.0, 1.0, 1.0}, // bottom plane at z=-1, pointing upwards
{0.0, 0.0, -1.0, 1.0} // top plane at z=1, pointing downwards
};

// double precision sphere at {10, 20, 30} with radius of 40 units
vsg::dsphere bounding_sphere(10.0, 20.0, 30.0, 40.0);

// default constructed single precision box representing an undefined box
// bounding_box.min is set to maximum float values.
// bounding_box.max is set to minimum float values.
// when min.x value > max.x then box is treated as undefined/invalid/empty.
vsg::box bounding_box;

// use the vsg::box::add(..) method to compute the bounding box that encloses points