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Normalized cartesian plane operations facilitating conversion between 2d and 3d space.
Normalized cartesian equation of a plane.
The type t
contains the coefficients A, B, C, and D, which describe the cartesian equation of a plane where Ax + By + Cz = D
.
val to_tup : t -> float * float * float * float
to_tup t
Return the plane t
as a tuple of its coefficients.
val of_tup : (float * float * float * float) -> t
of_tup (a, b, c, d)
Create a plane from a tuple of coefficients (xyz normal and offset).
of_v4 v
Create a plane from a 4d vector containing coefficients (xyz normal and offset).
make p1 p2 p3
Create a t
, which represents the normalized cartesian equation of a plane, with three points. Returns (a, b, c, d)
where ax + by + cz = d
is the equation of a plane. Throws Invalid_argument
if the points are colinear.
of_normal ?point normal
Create a normalized cartesian plane t
from a normal
vector, and a point
(defaulting to (0., 0.)
) located on the plane that the normal
is projecting off of.
to_affine ~op t
Compute an affine transformation matrix that moves 3d objects into (~op:`Project
) or out of (~op:`Lift
) the coordinate system of the plane t
from/to the base coordinate system (XY plane).
project t p
Project the 3d point p
onto the plane t
. On partial application of t
, a Affine3.t
is computed to perform the projection transform.
lift t p
Lift the 2d point p
onto the plane t
. On partial application of t
, a Affine3.t
is computed to perform the lift transform.
val offset : t -> float
offset t
Obtain the coefficient d of the normalized plane t
, or the scalar offset of the plane from the origin. The absolute value of this coefficient is the distance of the plane from the origin.
normalize t
Normalize the a, b, and c coefficients of the plane t
, such that their vector norm is equal to one.
distance_to_point t p
Calculate the distance to the point p
from the plane t
. A negative distance indicates that p
resides below t
.
greatest_distance t ps
Calculate the greatest absolute distance between the plane t
, and the 3d points ps
.
are_points_on ?eps t ps
Returns true
if all points ps
are within eps
distance of the plane t
.
is_point_above ?eps t p
Returns true
is point p
is eps
(default 1e-9
) distance above the plane t
.
line_angle t line
Calculate the angle between the plane t
and a 3d line
. The resulting angle is positive if the line vector lies above the plane (on the same side as the normal vector of t
).
val line_intersection :
?eps:float ->
?bounds:(bool * bool) ->
t ->
V3.line ->
[ `OutOfBounds | `OnPlane of V3.line | `Parallel | `Point of V3.t * float ]
line_intersection t line
Find the intersection between a 3d line
and the plane t
(within eps
tolerance, default 1e-9
), if it exists. bounds
indicates whether line
is capped at either (ray) or both (segment) of its ends (default is unbounded (bounds = (false, false)
).
val to_string : t -> string
val xy : t
val xz : t
val yz : t