Module Gg.V3

3D vectors.

type t = v3

The type for 3D vectors.

val dim : int

dim is the dimension of vectors of type v3.

type m = m3

The type for matrices representing linear transformations of 3D space.

Constructors, accessors and constants

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

v x y z is the vector (x y z).

val comp : int -> v3 -> float

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

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

val x : v3 -> float

x v is the x component of v.

val y : v3 -> float

y v is the y component of v.

val z : v3 -> float

z v is the z component of v.

val ox : v3

ox is the unit vector (1. 0. 0.).

val oy : v3

oy is the unit vector (0. 1. 0.).

val oz : v3

oz is the unit vector (0. 0. 1.).

val zero : v3

zero is the neutral element for add.

val infinity : v3

infinity is the vector whose components are infinity.

val neg_infinity : v3

neg_infinity is the vector whose components are neg_infinity.

val basis : int -> v3

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) -> v3

of_tuple (x, y, z) is v x y z.

val to_tuple : v3 -> float * float * float

to_tuple v is (x v, y v, z v).

val of_spherical : v3 -> v3

of_spherical sv is the vector whose cartesian coordinates (x, y, z) correspond to the radial, azimuth angle and zenith angle spherical coordinates (r, theta, phi) given by (V3.x sv, V2.y sv, V3.z sv).

val to_spherical : v3 -> v3

to_spherical v is the vector whose coordinate (r, theta, phi) are the radial, azimuth angle and zenith angle spherical coordinates of v. theta is in [-pi;pi] and phi in [0;pi].

val of_v2 : v2 -> z:float -> v3

of_v2 u z is v (V2.x u) (V2.y u) z.

val of_v4 : v4 -> v3

of_v4 u z is v (V4.x u) (V4.y u) (V4.z u).

Functions

val neg : v3 -> v3

neg v is the inverse vector -v.

val add : v3 -> v3 -> v3

add u v is the vector addition u + v.

val sub : v3 -> v3 -> v3

sub u v is the vector subtraction u - v.

val mul : v3 -> v3 -> v3

mul u v is the component wise multiplication u * v.

val div : v3 -> v3 -> v3

div u v is the component wise division u / v.

val smul : float -> v3 -> v3

smul s v is the scalar multiplication sv.

val half : v3 -> v3

half v is the half vector smul 0.5 v.

val cross : v3 -> v3 -> v3

cross u v is the cross product u x v.

val dot : v3 -> v3 -> float

dot u v is the dot product u.v.

val norm : v3 -> float

norm v is the norm |v| = sqrt v.v.

val norm2 : v3 -> float

norm2 v is the squared norm |v|2 .

val unit : v3 -> v3

unit v is the unit vector v/|v|.

val spherical : float -> float -> float -> v3

spherical r theta phi is of_spherical (V3.v r theta phi).

val azimuth : v3 -> float

azimuth v is the azimuth angle spherical coordinates of v. The result is in [-pi;pi].

val zenith : v3 -> float

zenith v is the zenith angle spherical coordinates of v. The result is in [0;pi].

val homogene : v3 -> v3

homogene v is the vector v/vz if vz <> 0 and v otherwise.

val mix : v3 -> v3 -> float -> v3

mix u v t is the linear interpolation u + t(v - u).

val ltr : m3 -> v3 -> v3

ltr m v is the linear transform mv.

val tr : m4 -> v3 -> v3

tr m v is the affine transform in homogenous 3D space of the vector v by m.

Note. Since m is supposed to be affine the function ignores the last row of m. v is treated as a vector (infinite point, its last coordinate in homogenous space is 0) and is thus translationally invariant. Use P3.tr to transform finite points.

Overridden Stdlib operators

val (+) : v3 -> v3 -> v3

u + v is add u v.

val (-) : v3 -> v3 -> v3

u - v is sub u v.

val (*) : float -> v3 -> v3

t * v is smul t v.

val (/) : v3 -> float -> v3

v / t is smul (1. /. t) v.

Traversal

val map : ( float -> float ) -> v3 -> v3

map f v is the component wise application of f to v.

val mapi : ( int -> float -> float ) -> v3 -> v3

mapi f v is like map but the component index is also given.

val fold : ( 'a -> float -> 'a ) -> 'a -> v3 -> 'a

fold f acc v is f (...(f (f acc v0) v1)...).

val foldi : ( 'a -> int -> float -> 'a ) -> 'a -> v3 -> 'a

foldi f acc v is f (...(f (f acc 0 v0) 1 v1)...).

val iter : ( float -> unit ) -> v3 -> unit

iter f v is f v0; f v1; ...

val iteri : ( int -> float -> unit ) -> v3 -> unit

iteri f v is f 0 v0; f 1 v1; ...

Predicates and comparisons

val for_all : ( float -> bool ) -> v3 -> bool

for_all p v is p v0 && p v1 && ...

val exists : ( float -> bool ) -> v3 -> bool

exists p v is p v0 || p v1 || ...

val equal : v3 -> v3 -> bool

equal u v is u = v.

val equal_f : ( float -> float -> bool ) -> v3 -> v3 -> bool

equal_f eq u v tests u and v like equal but uses eq to test floating point values.

val compare : v3 -> v3 -> int

compare u v is Stdlib.compare u v.

val compare_f : ( float -> float -> int ) -> v3 -> v3 -> int

compare_f cmp u v compares u and v like compare but uses cmp to compare floating point values.

Formatters

val pp : Stdlib.Format.formatter -> v3 -> unit

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

val pp_f : ( Stdlib.Format.formatter -> float -> unit ) -> Stdlib.Format.formatter -> v3 -> unit

pp_f pp_comp ppf v prints v like pp but uses pp_comp to print floating point values.