Module Gg

module Gg: sig .. end
Basic types for computer graphics.

Gg defines types and functions for floats, vectors, points, matrices, quaternions, sizes, axis aligned boxes, colors, color profiles, linear bigarrays and raster data.

Consult the basics. Open the module to use it, this defines only modules and types in your scope.

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module Float: sig .. end
Floating point number utilities.

The following type are defined so that they can be used in vector modules. The matrix modules are here.
type m2 
The type for 2x2 matrices.
type m3 
The type for 3x3 matrices.
type m4 
The type for 4x4 matrices.


An n-dimensional vector v is a sequence of n, zero indexed, floating point components. We write vi the ith component of a vector.

type v2 
The type for 2D vectors.
type v3 
The type for 3D vectors.
type v4 
The type for 4D vectors.
module type V = sig .. end
Implemented by all vector types.
module V2: sig .. end
module V3: sig .. end
module V4: sig .. end


An n-dimensional point p is a vector of the corresponding dimension. The components of the vector are the point's coordinates.

type p2 = v2 
The type for 2D points.
type p3 = v3 
The type for 3D points.
module type P = sig .. end
Implemented by all point types.
module P2: sig .. end
module P3: sig .. end


Unit quaternions represent rotations in 3D space. They allow to smoothly interpolate between orientations. A quaternion is a 4D vector, whose components x, y, z, w represents the quaternion xi+ yj + zk + w.

type quat = v4 
The type for quaternions.
module Quat: sig .. end


An mxn matrix a is an array of m rows and n columns of floating point elements. We write aij the element of a located at the ith row and jth column.

Matrix constructors specify matrix elements in row-major order so that matrix definitions look mathematically natural with proper code indentation. However elements are stored and iterated over in column-major order.

module type M = sig .. end
Implemented by all (square) matrix types.
module M2: sig .. end
module M3: sig .. end
module M4: sig .. end


An n-dimensional size s represents extents in n-dimensional space.

type size1 = float 
The type for sizes in 1D space.
type size2 = v2 
The type for sizes in 2D space.
type size3 = v3 
The type for sizes in 3D space.
module type Size = sig .. end
Implemented by all size types.
module Size1: sig .. end
module Size2: sig .. end
module Size3: sig .. end

Axis-aligned boxes

An n-dimensional axis-aligned box b is defined by an n-dimensional point o, its origin, and an n-dimensional size s. Operations on boxes with negative sizes are undefined.

The space S(b) spanned by b is [o0; o0 + s0] x ... x [on-1; on-1 + sn-1]. The extremum points of this space are the box's corners. There is a distinguished n-dimensional empty box such that S(empty) is empty.

type box1 
The type for 1D axis-aligned boxes (closed intervals).
type box2 
The type for 2D axis-aligned boxes (rectangles).
type box3 
The type for 3D axis-aligned boxes (cuboids).
module type Box = sig .. end
Implemented by all axis-aligned box types.
module Box1: sig .. end
module Box2: sig .. end
module Box3: sig .. end


type color = v4 
The type for colors, see details.
module Color: sig .. end
Colors and color profiles.

Linear bigarrays and bigarray buffers

type ('a, 'b) bigarray = ('a, 'b, Bigarray.c_layout) Bigarray.Array1.t 
The type for linear bigarrays.
type buffer = [ `Float16 of (int, Bigarray.int16_unsigned_elt) bigarray
| `Float32 of (float, Bigarray.float32_elt) bigarray
| `Float64 of (float, Bigarray.float64_elt) bigarray
| `Int16 of (int, Bigarray.int16_signed_elt) bigarray
| `Int32 of (int32, Bigarray.int32_elt) bigarray
| `Int64 of (int64, Bigarray.int64_elt) bigarray
| `Int8 of (int, Bigarray.int8_signed_elt) bigarray
| `UInt16 of (int, Bigarray.int16_unsigned_elt) bigarray
| `UInt32 of (int32, Bigarray.int32_elt) bigarray
| `UInt64 of (int64, Bigarray.int64_elt) bigarray
| `UInt8 of (int, Bigarray.int8_unsigned_elt) bigarray ]
The type for linear bigarray buffers.
module Ba: sig .. end
Linear bigarrays and bigarray buffers.

Raster data

type raster 
The type for raster data.
module Raster: sig .. end
Raster data.


Gg is designed to be opened in your module. This defines only types and modules in your scope, no values. Thus to use Gg start with :

open Gg

In the toplevel enter:

#require "";;
to automatically open Gg and install printers for the types.


Most types and their functions are defined with the following conventions. The type is first defined in Gg, like Gg.v2 for 2D vectors, a module for it follows. The name of the module is the type name capitalized, e.g. Gg.V2 for 2D vectors and it has the following definitions:

Some types are defined as simple abreviations. For example the type Gg.p2 for 2D points is equal to Gg.v2. These types also have a module whose name is the type name capitalized, Gg.P2 in our example. However this module only provides alternate constructors, constants and accessors and the extended functionality specific to the type. You should fallback on the module of the abreviated type (Gg.V2 in our example) for other operations. The aim of these types is to make your code and signatures semantically clearer without the burden of explicit conversions.

Finally there are some types and modules like Gg.Color whose structure is different because they provide specific functionality.

Here are a few other conventions :

To conclude note that it is sometimes hard to find the right place for a function. If you cannot find a function look into each of the modules of the types you want to act upon.

Mathematical conventions

Note on colors

Values of type Gg.color are in a linear sRGB space as this is the space to work in if you want to process colors correctly (e.g. for blending). The constructor Gg.Color.v_srgb takes its parameters from a non-linear sRGB space and converts them to linear sRGB.

# let c = Color.v_srgb 0.5 0.5 0.5 1.0;;
- : Gg.color = (0.214041 0.214041 0.214041 1)
This is the constructor you are likely to use when you specify color constants (e.g. to specify a color value matching a CSS color). If you need an sRGB color back from a Gg.color value use Gg.Color.to_srgb:
# Color.to_srgba c;;
- : Gg.Color.srgba = (0.5 0.5 0.5 1)

Remarks and Tips