Module type `Gg.V`

Implemented by all vector types.

type t: The type for vectors.

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

type m: The type for matrices representing linear transformations of dim space.

Constructors, accessors and constants

val comp : int -> t -> float

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

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

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

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

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

val basis : int -> t

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[.

Functions

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

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

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

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

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

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

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

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

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

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

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

val homogene : t -> t: homogene v is the vector v/(comp (dim - 1) v) if comp (dim - 1) v <> 0 and v otherwise.

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

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

Overridden `Pervasives` operators

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

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

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

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

Traversal

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

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

val fold : ('a -> float -> 'a) -> 'a -> t -> 'a: fold f acc v is f (...(f (f acc v₀) v₁)...).

val foldi : ('a -> int -> float -> 'a) -> 'a -> t -> 'a: foldi f acc v is f (...(f (f acc 0 v₀) 1 v₁)...).

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

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

Predicates and comparisons

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

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

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

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

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

val compare_f : (float -> float -> int) -> t -> t -> 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 -> t -> unit: pp ppf v prints a textual representation of v on ppf.

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