Module `Gg.V4`

type t = v4: The type for 4D vectors.

val dim : int: dim is the dimension of vectors of type v4.

type m = m4: The type for matrices representing linear transformations of 4D space.

Constructors, accessors and constants

val v : float -> float -> float -> float -> v4: v x y z w is the vector (x y z w).

val comp : int -> v4 -> float

comp i v is v_i, the ith component of v.

raises Invalid_argument: if i is not in [0;dim[.

val x : v4 -> float: x v is the x component of v.

val y : v4 -> float: y v is the y component of v.

val z : v4 -> float: z v is the z component of v.

val w : v4 -> float: z v is the z component of v.

val ox : v4: ox is the unit vector (1. 0. 0. 0.).

val oy : v4: oy is the unit vector (0. 1. 0. 0.).

val oz : v4: oz is the unit vector (0. 0. 1. 0.).

val ow : v4: ow is the unit vector (0. 0. 0. 1.).

val zero : v4: zero is the neutral element for add.

val infinity : v4: infinity is the vector whose components are infinity.

val neg_infinity : v4: neg_infinity is the vector whose components are neg_infinity.

val basis : int -> v4

basis i is the ith vector of an orthonormal basis of the vector space t with inner product dot.

raises Invalid_argument: if i is not in [0;dim[.

val of_tuple : (float * float * float * float) -> v4: of_tuple (x, y, z, w) is v x y z w.

val to_tuple : v4 -> float * float * float * float: to_tuple v is (x v, y v, z v, w v).

val of_v2 : v2 -> z:float -> w:float -> v4: of_v2 u z w is v (V2.x u) (V2.y u) z w.

val of_v3 : v3 -> w:float -> v4: of_v3 u w is v (V3.x u) (V3.y u) (V3.z u) w.

Functions

val neg : v4 -> v4: neg v is the inverse vector -v.

val add : v4 -> v4 -> v4: add u v is the vector addition u + v.

val sub : v4 -> v4 -> v4: sub u v is the vector subtraction u - v.

val mul : v4 -> v4 -> v4: mul u v is the component wise multiplication u * v.

val div : v4 -> v4 -> v4: div u v is the component wise division u / v.

val smul : float -> v4 -> v4: smul s v is the scalar multiplication sv.

val half : v4 -> v4: half v is the half vector smul 0.5 v.

val dot : v4 -> v4 -> float: dot u v is the dot product u.v.

val norm : v4 -> float: norm v is the norm |v| = sqrt v.v.

val norm2 : v4 -> float: norm2 v is the squared norm |v|² .

val unit : v4 -> v4: unit v is the unit vector v/|v|.

val homogene : v4 -> v4: homogene v is the vector v/v_w if v_w <> 0 and v otherwise.

val mix : v4 -> v4 -> float -> v4: mix u v t is the linear interpolation u + t(v - u).

val ltr : m4 -> v4 -> v4: ltr m v is the linear transform mv.

Overridden `Pervasives` operators

val (+) : v4 -> v4 -> v4: u + v is add u v.

val (-) : v4 -> v4 -> v4: u - v is sub u v.

val (*) : float -> v4 -> v4: t * v is smul t v.

val (/) : v4 -> float -> v4: v / t is smul (1. /. t) v.

Traversal

val map : (float -> float) -> v4 -> v4: map f v is the component wise application of f to v.

val mapi : (int -> float -> float) -> v4 -> v4: mapi f v is like map but the component index is also given.

val fold : ('a -> float -> 'a) -> 'a -> v4 -> 'a: fold f acc v is f (...(f (f acc v₀) v₁)...).

val foldi : ('a -> int -> float -> 'a) -> 'a -> v4 -> 'a: foldi f acc v is f (...(f (f acc 0 v₀) 1 v₁)...).

val iter : (float -> unit) -> v4 -> unit: iter f v is f v₀; f v₁; ...

val iteri : (int -> float -> unit) -> v4 -> unit: iteri f v is f 0 v₀; f 1 v₁; ...

Predicates and comparisons

val for_all : (float -> bool) -> v4 -> bool: for_all p v is p v₀ && p v₁ && ...

val exists : (float -> bool) -> v4 -> bool: exists p v is p v₀ || p v₁ || ...

val equal : v4 -> v4 -> bool: equal u v is u = v.

val equal_f : (float -> float -> bool) -> v4 -> v4 -> bool: equal_f eq u v tests u and v like equal but uses eq to test floating point values.

val compare : v4 -> v4 -> int: compare u v is Pervasives.compare u v.

val compare_f : (float -> float -> int) -> v4 -> v4 -> int: compare_f cmp u v compares u and v like compare but uses cmp to compare floating point values.

Printers

val pp : Stdlib.Format.formatter -> v4 -> unit: pp ppf v prints a textual representation of v on ppf.

val pp_f : (Stdlib.Format.formatter -> float -> unit) -> Stdlib.Format.formatter -> v4 -> unit: pp_f pp_comp ppf v prints v like pp but uses pp_comp to print floating point values.