The type for 3D vectors.

dim is the dimension of vectors of type v3.

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

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

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

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

x v is the x component of v.

y v is the y component of v.

z v is the z component of v.

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

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

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

zero is the neutral element for add.

infinity is the vector whose components are infinity.

neg_infinity is the vector whose components are neg_infinity.

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[.

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

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].

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

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

neg v is the inverse vector -v.

add u v is the vector addition u + v.

sub u v is the vector subtraction u - v.

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

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

smul s v is the scalar multiplication sv.

half v is the half vector smul 0.5 v.

cross u v is the cross product u x v.

dot u v is the dot product u.v.

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

norm2 v is the squared norm |v|² .

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

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

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

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

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

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

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.

u + v is add u v.

u - v is sub u v.

t * v is smul t v.

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

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

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

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

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

iter f v is f v₀; f v₁; ...

iteri f v is f 0 v₀; f 1 v₁; ...

for_all p v is p v₀ && p v₁ && ...

exists p v is p v₀ || p v₁ || ...

equal u v is u = v.

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

compare u v is Stdlib.compare u v.

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

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

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