geoml 0.1.1 (latest) · OCaml Package

This module provides basic operation over the linear equation type

type t = private

| X of float
| Y of float * float
(*
the linear equation type
*)

val print : Format.formatter -> t -> unit

printer

val to_string : t -> string

to string

type error =

| Parallel of t * t
| Same_coordinates of Point.t
(*
the type of errors
*)

exception Error of error

the type of exceptions concerning this module

val print_error : Format.formatter -> error -> unit

error printer

val make : float -> float -> float -> t

make a b c builds a line of equation: ax + by + c = 0. Raises an error if a = b = 0. in which case the equation do not correspond to a line

val make_x : float -> t

make_x a builds a line of equation: x = a

val make_y : float -> float -> t

make_y a b builds a line of equation: y = ax + b

val x_axis : t

the horizontal line of equation: y = 0

val y_axis : t

the vertical line of equation: x = 0

val of_points : Point.t -> Point.t -> t

of_points p1 p2 builds the line that goes through the points p1 and p2. It raises Error(Same_coordinates) if p1 = p2

val is_vertical : t -> bool

is_vertical l, is true if l has an equation of the form: x=cst, where cst is a constant float

val is_horizontal : t -> bool

is_horizontal l, returns true if l has an equation of the form: y=cst, where cst is a constant float

val get_coeff : t -> float * float * float

returns a tuple (a,b,c) with respect to the equation of line, as: ax + by \+ c = 0

val x_from_y : t -> float -> float

'x_from_y line y', returns 'x', the value on the x-axis corresponding to given 'y' value, with f the affine function associated to 'line', as: f(x) = y raises Parallel if 'line' doesn't intersect the horizontal line going through 'y'

val y_from_x : t -> float -> float

'y_from_x line x', returns 'y', the value on the y-axis corresponding to given 'x' value, with f the affine function associated to 'line', as: f(x) = y raises Parallel if 'line' doesn't intersect the vertical line going through 'x'

val contains : t -> Point.t -> bool

contains l1 p returns true if l1goes through p. false otherwise.

val scale_x : t -> float -> t

val scale_y : t -> float -> t

val translate : float -> float -> t -> t

val parallel : t -> t -> bool

parallel l1 l2 returns true if l1 and l2 are parallel. false otherwise.

val intersects : t -> t -> bool

intersects l1 l2 returns true if l1 and l2 intersects. false otherwise.

val intersection : t -> t -> Point.t

intersection l1 l2 returns the point at the intersection of l1 and l2. It raises Error(Parralel) if l1 and l2 dont intersect

val perpendicular : t -> t -> bool

perpendicular l1 l2 returns true if l1 and l2 are perpendicular. false otherwise.

val perpendicular_of_line : t -> Point.t -> t

perpendicular_of_line l p returns the line perpendicular to l that goes through p.

val parallel_of_line : t -> Point.t -> t

parallel_of_line l p returns the line parallel to l that goes through p.

val orth_proj : t -> Point.t -> Point.t

orth_proj l p, returns the orthogonal projection of p on l

val point_bissection : Point.t -> Point.t -> t

point_bissection p1 p2 builds the line l that bissects the segment p1p2 in its center. It Raises Error(Same_coordinates) if p1 = p2

val arbitrary_point : t -> Point.t

arbitrary_point l chooses an aribitrary point p such that contains l p is true

package geoml