Library
Module
Module type
Parameter
Class
Class type
type t = v3
The type for 3D vectors.
dim
is the dimension of vectors of type v3
.
type m = m3
The type for matrices representing linear transformations of 3D space.
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 v
i
, the i
th component of v
.
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 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 i
th vector of an orthonormal basis of the vector space t
with inner product dot
.
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)
.
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)
.
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
].
cross u v
is the cross product u x v
.
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 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
].
ltr m v
is the linear transform mv
.
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.
Pervasives
operatorsmapi 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 v
0) v
1)
...)
.
val foldi : ('a -> int -> float -> 'a) -> 'a -> v3 -> 'a
foldi f acc v
is f (
...(f (f acc 0 v
0) 1 v
1)
...)
.
val iter : (float -> unit) -> v3 -> unit
iter f v
is f v
0; f v
1;
...
val iteri : (int -> float -> unit) -> v3 -> unit
iteri f v
is f 0 v
0; f 1 v
1;
...
val for_all : (float -> bool) -> v3 -> bool
for_all p v
is p v
0 && p v
1 &&
...
val exists : (float -> bool) -> v3 -> bool
exists p v
is p v
0 || p v
1 ||
...
equal_f eq u v
tests u
and v
like equal
but uses eq
to test floating point values.
compare_f cmp u v
compares u
and v
like compare
but uses cmp
to compare floating point values.
val pp : Format.formatter -> v3 -> unit
pp ppf v
prints a textual representation of v
on ppf
.
val pp_f :
(Format.formatter -> float -> unit) ->
Format.formatter ->
v3 ->
unit
pp_f pp_comp ppf v
prints v
like pp
but uses pp_comp
to print floating point values.