package curve-sampling

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Module Curve_samplingSource

Adaptive sampling of 2D curves.

  • version 0.2.1
Sourcetype _ t

Representation of a 2D sampling. This can be thought as a path, with possible "jumps" because of discontinuities or leaving the "domain". The parameter says whether the sampling comes from evaluating a function, so it makes sense to refine it, or is just a sequence of points.

Sourceval is_empty : _ t -> bool

is_empty s returns true iff the sampling s contains no point.

Sourceval bounding_box : _ t -> Gg.box2

bounding_box s returns the smallest rectangle enclosing all the points of the sampling s.

Parametric curves

Sourceval fn : ?n:int -> ?viewport:Gg.Box2.t -> ?init:float list -> ?init_pt:(float * float) list -> (float -> float) -> float -> float -> [ `Fn ] t

fn f a b returns a sampling of the graph of f on the interval [a, b] by evaluating f at n points. For the optional arguments, see param.

Sourceval param : ?n:int -> ?viewport:Gg.Box2.t -> ?init:float list -> ?init_pt:(float * (float * float)) list -> (float -> float * float) -> float -> float -> [ `Fn ] t

param f a b returns a sampling of the range of f on the interval [a, b] by evaluating f at n points (or less).

  • parameter n

    The maximum number of evaluations of f. Default: 100. If n ≤ 10, then n = 10 is used instead.

  • parameter init

    Initial values of t such that f t must be included into the sampling in addition to the n evaluations. Only the values between a and b are taken into account. Default: empty.

  • parameter init_pt

    Initial points (t, f t) to include into the sampling in addition to the n evaluations. This allows you to use previous evaluations of f. Only the couples with first coordinate t between a and b are considered. Default: empty.

Uniform sampling

Sourceval uniform : ?n:int -> (float -> float) -> float -> float -> [ `Fn ] t

uniform f a b returns a sampling of the graph of f on n equidistant points in the interval [a, b] (the boundaries a and b being always included — so n >= 2). The resulting sampling may have less than n points because evaluations returning points with NaN components are discarded (they split the path).

  • parameter n

    the number of points. If n <= 2 is given, it is considered as if n=2 was passed. Default: n = 100.

Relation to sequences

Sourceval of_path : (float * float) list -> [ `Pt ] t

Use the provided path as the sampling.

Sourceval to_list : _ t -> (float * float) list list

to_list t return the sampling as a list of connected components of the path, each of which is given as a list of (x,y) couples.

Sourceval of_seq : ?n:int -> (float * float) Seq.t -> [ `Pt ] t

of_seq seq convert the sequence of points seq to a sampling.

  • parameter n

    only takes at most the first n entries. If n is not set (the default), this function may run into an infinite loop.

Sourceval to_seq : _ t -> (float * float) Seq.t Seq.t

to_seq t convert t to a sequence of connected compononent.

Transforming samplings

Sourceval tr : Gg.m3 -> _ t -> [ `Pt ] t

tr m t apply the transform m on t. See Gg.P2.tr for more details.

Sourceval clip : _ t -> Gg.box2 -> [ `Pt ] t

clip t b returns the sampling t but clipped to the 2D box. A path that crosses the boundary will get additional nodes at the points of crossing and the part outside the bounding box will be dropped. (Thus a path entirely out of the bounding box will be removed.)

GG interface

Sourcemodule P2 : sig ... end

Interface using Gg.p2 to represent points.

Save the sampling data

Sourceval to_channel : _ t -> out_channel -> unit

to_channel t ch writes the sampling t to the channel ch. Each point is written as "x y" on a single line (in scientific notation). If the path is interrupted, a blank line is printed. This format is compatible with gnuplot.

Sourceval to_file : _ t -> string -> unit

to_file t fname saves the sampling t to the file fname using the format described in to_channel.

Sourceval to_latex : _ t -> ?n:int -> ?arrow:string -> ?arrow_pos:float -> ?color:Gg.color -> string -> unit

to_latex t fname saves the sampling t as PGF/TikZ commands.

  • parameter n

    the maximum number of points of PGF path (after which the sampling curve is drawn as several PGF paths). Default: 20_000.

  • parameter arrow

    The type of arrow to draw. See the TikZ manual. If arrow_pos is specified and not this, it defaults to ">".

  • parameter arrow_pos

    the position of the arrow as a percent of the curve length (in the interval [0.,1.]). If arrow is specified but not this, it defaults to 0.5.

  • parameter color

    specify the color of the curve.

Sourceval to_latex_channel : _ t -> ?n:int -> ?arrow:string -> ?arrow_pos:float -> ?color:Gg.color -> out_channel -> unit

to_latex_channel t ch writes the sampling t as PGF/TikZ commands to the channel ch. See to_latex for the meaning of optional arguments.