Module Gg.M3

3D square matrices.

type t = m3

The type for 3D square matrices.

val dim : int

dim is the dimension of rows and columns.

type v = v3

The type for rows and columns as vectors.

Constructors, accessors and constants

val v : float -> float -> float -> float -> float -> float -> float -> float -> float -> 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 : v3 -> v3 -> v3 -> m3

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

val of_cols : v3 -> v3 -> v3 -> m3

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

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

el i j a is the element aij. See also the direct element accessors.

Raises Invalid_argument if i or j is not in [0;dim[.

val row : int -> m3 -> v3

row i a is the ith row of a.

Raises Invalid_argument if i is not in [0;dim[.

val col : int -> m3 -> v3

col j a is the jth column of a.

Raises Invalid_argument if j is not in [0;dim[.

val zero : m3

zero is the neutral element for add.

val id : m3

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

val of_m2_v2 : m2 -> v2 -> 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 : m4 -> m3

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

val of_quat : quat -> m3

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

Functions

val neg : m3 -> m3

neg a is the negated matrix -a.

val add : m3 -> m3 -> m3

add a b is the matrix addition a + b.

val sub : m3 -> m3 -> m3

sub a b is the matrix subtraction a - b.

val mul : m3 -> m3 -> m3

mul a b is the matrix multiplication a * b.

val emul : m3 -> m3 -> m3

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

val ediv : m3 -> m3 -> m3

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

val smul : float -> m3 -> m3

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

val transpose : m3 -> m3

transpose a is the transpose aT.

val trace : m3 -> float

trace a is the matrix trace trace(a).

val det : m3 -> float

det a is the determinant |a|.

val inv : m3 -> m3

inv a is the inverse matrix a-1.

2D space transformations

val move2 : v2 -> m3

move2 d translates 2D space in the x and y dimensions according to d.

val rot2 : ?pt:p2 -> float -> m3

rot2 pt theta rotates 2D space around the point pt by theta radians. pt defaults to P2.o.

val scale2 : v2 -> m3
val rigid2 : move:v2 -> rot:float -> m3

rigid2 move theta is the rigid body transformation of 2D space that rotates by theta radians and then translates by move.

val srigid2 : move:v2 -> rot:float -> scale:v2 -> m3

srigid2 move theta scale is like rigid2 but starts by scaling according to scale.

3D space transformations

val rot3_map : v3 -> v3 -> m3

rot3_map u v rotates 3D space to map the unit vector u on the unit vector v.

val rot3_axis : v3 -> float -> m3

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

val rot3_zyx : v3 -> m3

rot3_zyx r rotates 3D space first by V3.x r radians around the x-axis, then by V3.y r radians around the y-axis and finally by V3.z r radians around the z-axis.

val scale3 : v3 -> m3

scale3 s scales 3D space in the x, y and z dimensions according to s.

Traversal

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

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

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

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

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

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

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

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

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

iter f a is f a00; f a10; ...

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

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

Predicates and comparisons

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

for_all p a is p a00 && p a10 && ...

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

exists p a is p a00 || p a10 || ...

val equal : m3 -> m3 -> bool

equal a b is a = b.

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

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

val compare : m3 -> m3 -> int

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

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

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

Formatters

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

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

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

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

Element accessors

val e00 : m3 -> float
val e01 : m3 -> float
val e02 : m3 -> float
val e10 : m3 -> float
val e11 : m3 -> float
val e12 : m3 -> float
val e20 : m3 -> float
val e21 : m3 -> float
val e22 : m3 -> float