Module Gg.M3

module M3: sig .. end

type t = Gg.m3

The type for 3D square matrices.

val dim : int

dim is the dimension of rows and columns.

type v = Gg.v3

The type for rows and columns as vectors.

Constructors, accessors and constants

val v : float ->
       float -> float -> float -> float -> float -> float -> float -> float -> Gg.m3

v e00 e01 e02 e10 e11 e12 e20 e21 e22 is a matrix whose components are specified in row-major order

val of_rows : Gg.v3 -> Gg.v3 -> Gg.v3 -> Gg.m3

of_rows r0 r1 r2 is the matrix whose rows are r0, r1 and r2.

val of_cols : Gg.v3 -> Gg.v3 -> Gg.v3 -> Gg.m3

of_cols c0 c1 c2 is the matrix whose columns are c0, c1 and c2.

val el : int -> int -> Gg.m3 -> float

el i j a is the element a_ij. See also the direct element accessors.
Raises Invalid_argument if i or j is not in [0;Gg.M3.dim[.

val row : int -> Gg.m3 -> Gg.v3

row i a is the ith row of a.
Raises Invalid_argument if i is not in [0;Gg.M3.dim[.

val col : int -> Gg.m3 -> Gg.v3

col j a is the jth column of a.
Raises Invalid_argument if j is not in [0;Gg.M3.dim[.

val zero : Gg.m3

zero is the neutral element for Gg.M3.add.

val id : Gg.m3

id is the identity matrix, the neutral element for Gg.M3.mul.

val of_m2_v2 : Gg.m2 -> Gg.v2 -> Gg.m3

of_m2_v2 m v is the matrix whose first two rows are those of m,v side by side and the third is 0 0 1.

val of_m4 : Gg.m4 -> Gg.m3

of_m4 m extracts the 3D linear part (top-left 3x3 matrix) of m.

val of_quat : Gg.quat -> Gg.m3

of_quat q is the rotation of the unit quaternion q as 3D matrix.

Functions

val neg : Gg.m3 -> Gg.m3

neg a is the negated matrix -a.

val add : Gg.m3 -> Gg.m3 -> Gg.m3

add a b is the matrix addition a + b.

val sub : Gg.m3 -> Gg.m3 -> Gg.m3

sub a b is the matrix subtraction a - b.

val mul : Gg.m3 -> Gg.m3 -> Gg.m3

mul a b is the matrix multiplication a * b.

val emul : Gg.m3 -> Gg.m3 -> Gg.m3

emul a b is the element wise multiplication of a and b.

val ediv : Gg.m3 -> Gg.m3 -> Gg.m3

ediv a b is the element wise division of a and b.

val smul : float -> Gg.m3 -> Gg.m3

smul s a is a's elements multiplied by the scalar s.

val transpose : Gg.m3 -> Gg.m3

transpose a is the transpose a^T.

val trace : Gg.m3 -> float

trace a is the matrix trace trace(a).

val det : Gg.m3 -> float

det a is the determinant |a|.

val inv : Gg.m3 -> Gg.m3

inv a is the inverse matrix a^-1.

2D space transformations

val move : Gg.v2 -> Gg.m3

move d translates 2D space in the x and y dimensions according to d.

val rot : float -> Gg.m3

See Gg.M2.rot.

val scale2 : Gg.v2 -> Gg.m3

See Gg.M2.scale.

val rigid : move:Gg.v2 -> rot:float -> Gg.m3

rigid move theta is the rigid body transformation of 2D space that rotates by theta and then translates by move.

val srigid : move:Gg.v2 -> rot:float -> scale:Gg.v2 -> Gg.m3

srigid move theta scale is like Gg.M3.rigid but starts by scaling according to scale.

3D space transformations

val rot_map : Gg.v3 -> Gg.v3 -> Gg.m3

rot_map u v rotates 3D space to map the unit vector u on the unit vector v.

val rot_axis : Gg.v3 -> float -> Gg.m3

rot_axis v theta rotates 3D space by theta around the unit vector v.

val rot_zyx : Gg.v3 -> Gg.m3

rot_zyx r rotates 3D space first by V3.x r around the x-axis, then by V3.y r around the y-axis and finally by

V3.z
      r

around the z-axis.

val scale : Gg.v3 -> Gg.m3

scale s scales 3D space in the x, y and z dimensions according to s.

Traversal

val map : (float -> float) -> Gg.m3 -> Gg.m3

map f a is the element wise application of f to a.

val mapi : (int -> int -> float -> float) -> Gg.m3 -> Gg.m3

mapi f a is like Gg.M3.map but the element indices are also given.

val fold : ('a -> float -> 'a) -> 'a -> Gg.m3 -> 'a

fold f acc a is f (...(f (f acc a₀₀) a₁₀)...).

val foldi : ('a -> int -> int -> float -> 'a) -> 'a -> Gg.m3 -> 'a

foldi f acc a is f (...(f (f acc 0 0 a₀₀) 1 0 a₁₀)...).

val iter : (float -> unit) -> Gg.m3 -> unit

iter f a is f a₀₀; f a₁₀; ...

val iteri : (int -> int -> float -> unit) -> Gg.m3 -> unit

iteri f a is f 0 0 a₀₀; f 1 0 a₁₀; ...

Predicates and comparisons

val for_all : (float -> bool) -> Gg.m3 -> bool

for_all p a is p a₀₀ && p a₁₀ && ...

val exists : (float -> bool) -> Gg.m3 -> bool

exists p a is p a₀₀ || p a₁₀ || ...

val equal : Gg.m3 -> Gg.m3 -> bool

equal a b is a = b.

val equal_f : (float -> float -> bool) -> Gg.m3 -> Gg.m3 -> bool

equal_f eq a b tests a and b like Gg.M3.equal but uses eq to test floating point values.

val compare : Gg.m3 -> Gg.m3 -> int

compare a b is Pervasives.compare a b. That is lexicographic comparison in column-major order.

val compare_f : (float -> float -> int) -> Gg.m3 -> Gg.m3 -> int

compare_f cmp a b compares a and b like Gg.M3.compare but uses cmp to compare floating point values.

Printers

val to_string : Gg.m3 -> string

to_string a is a textual representation of a.

val pp : Format.formatter -> Gg.m3 -> unit

pp ppf a prints a textual representation of a on ppf.

val pp_f : (Format.formatter -> float -> unit) -> Format.formatter -> Gg.m3 -> unit

pp_f pp_e ppf a prints a like Gg.M3.pp but uses pp_e to print floating point values.

Element accessors

val e00 : Gg.m3 -> float

val e01 : Gg.m3 -> float

val e02 : Gg.m3 -> float

val e10 : Gg.m3 -> float

val e11 : Gg.m3 -> float

val e12 : Gg.m3 -> float

val e20 : Gg.m3 -> float

val e21 : Gg.m3 -> float

val e22 : Gg.m3 -> float