mesh 0.8.8 · OCaml Package

Interface for the Triangle 2D mesh generator.

Triangle is a two-dimensional quality mesh generator and delaunay triangulator which was awarded the 2003 Wilkinson Prize.

Jonathan Richard Shewchuk, the author of triangle, would like that, if you use Triangle in a scientific publication, you acknowledgment it with the following citation: Jonathan Richard Shewchuk, ``Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator,'' in Applied Computational Geometry: Towards Geometric Engineering (Ming C. Lin and Dinesh Manocha, editors), volume 1148 of Lecture Notes in Computer Science, pages 203-222, Springer-Verlag, Berlin, May 1996.

author Christophe Troestler (Christophe.Troestler\@umons.ac.be)

class 'l pslg : 'l Bigarray.layout -> object ... end

Planar Straight Line Graph datastructure (Mesh.pslg enriched with methods specific to Triangle). By default, creating an object from this class results in all methods being initialized with empty arrays.

val pslg : 
  ?hole:'l Mesh.mat ->
  ?region:'l Mesh.mat ->
  ?point_attribute:'l Mesh.mat ->
  ?point_marker:'l Mesh.int_vec ->
  'l Mesh.mat ->
  ?segment_marker:'l Mesh.int_vec ->
  'l Mesh.int_mat ->
  'l pslg

pslg point segment creates a PSLG with the proper methods. The default values for unspecified values are empty arrays.

raises Invalid_argument
if a size is incorrect.

class 'l t : 'l Mesh.t -> object ... end

Object describing various characteristics of a mesh (Mesh.t enriched with methods specific to Triangle). It can also be used to construct t values from Mesh.t with empty attributes matrices.

class type 'l voronoi = object ... end

Voronoi diagram (Mesh.voronoi enriched with methods specific to Triangle).

exception Invalid_argument of string

Exception raised by the functions of this module to indicate that an argument not respecting the specifications was given.

type triunsuitable =
  float ->
  float ->
  float ->
  float ->
  float ->
  float ->
  float ->
  bool

Type of functions used to determine whether or not a selected triangle is too big (and needs to be refined). triunsuitable x1 y1 x2 y2 x3 y3 area must return true if the triangle is too big. The arguments are as follow:

x1 and y1 are the X an Y coordinates of the triangle's origin vertex.
x2 and y2 are the X an Y coordinates of the triangle's destination vertex.
x3 and y3 are the X an Y coordinates of the triangle's apex vertex.
area is the area of the triangle.

val triangulate : 
  ?delaunay:bool ->
  ?min_angle:float ->
  ?max_area:float ->
  ?region_area:bool ->
  ?max_steiner:int ->
  ?voronoi:bool ->
  ?edge:bool ->
  ?neighbor:bool ->
  ?subparam:bool ->
  ?triunsuitable:triunsuitable ->
  ?check_finite:bool ->
  ?debug:bool ->
  ?verbose:[ `V | `VV | `VVV ] ->
  'a pslg ->
  'a t * 'a voronoi

triangulate pslg returns a triangulation and a possibly a Voronoi diagram of the domain described by pslg. If pslg#segment is empty, the convex hull of the set of points is used. Note that the numbering of nodes returned by this function may be far from optimal for the FEM. See band.

Note that #point_marker are not propagated to points created on the segment. You must set #segment_marker for that. If you do not set #segment_marker, only the external boundary points will receive a marker of 1, the points on internal boundaries will have the marker 0.

If #region is non-empty, it will be used to assign an additional floating-point attribute to each triangle. It will be written as the single attribute of #triangle_attribute matrix.

#point_attribute are interpolated to all points.

parameter delaunay
generates a truly Delaunay (not just constrained Delaunay) triangulation. It usually increases the number of vertices and triangles. Default: true.

parameter min_angle
requires that all angles of triangles have at least that value. If min_angle < 0 or min_angle > 60, the default value of Triangle is used. If the minimum angle is 28.6 degrees or smaller, Triangle is mathematically guaranteed to terminate (assuming infinite precision arithmetic--Triangle may fail to terminate if you run out of precision).

parameter edge
return the edges of the triangulation in #edge. Default: true.

parameter neighbor
Outputs an array of triangles neighboring each triangle in #neighbor. The first neighbor #neighbor.{1,t} of triangle t is opposite the first corner #triangle.{1,t} of triangle t, and so on. Default: false.

parameter max_area
Imposes a maximum triangle area.

parameter region_area
uses the maximum area specified for each region in #region. Default: false even if #region is a non-empty matrix (i.e. you have to enable it explicitly).

parameter max_steiner
Specifies the maximum number of Steiner points (vertices that are not in the input, but are added to meet the constraints on minimum angle and maximum area). The default is to allow an unlimited number.

parameter triunsuitable
a routine used to determine whether is triangle needs to be further splitted.

parameter subparam
Generates second-order subparametric elements with six nodes each. Default: false.

parameter check_finite
checks that all points coordinate are finite. As non-finite coordinates (e.g. NaN) puzzle Triangle without making it fail, the default is true. Set it to false only if you are sure your coordinates are finite.

parameter debug
if true, outputs some explanation of what Triangle is doing and some statistics. Default: true as it can contain interesting information during program development.

val refine : 
  ?delaunay:bool ->
  ?min_angle:float ->
  ?max_area:float ->
  ?max_steiner:int ->
  ?voronoi:bool ->
  ?edge:bool ->
  ?neighbor:bool ->
  ?subparam:bool ->
  ?triangle_area:'a Mesh.vec ->
  ?triunsuitable:triunsuitable ->
  ?check_finite:bool ->
  ?debug:bool ->
  ?verbose:[ `V | `VV | `VVV ] ->
  'a t ->
  'a t * 'a voronoi

refine mesh returns a refined version of the mesh. The initial indices for the points are preserved, additional nodes are added at the end. However, the refinement is not hierarchical: there is no guarantee that each output element is contained in a single input element.

parameter triangle_area
allows to specify, for each triangle i, a maximum area triangle_area.{i}. If both max_area and triangle_area are specified, triangle_area is used.
For other parameters, see triangulate.

val copy : 'l t -> 'l t

See Mesh.copy.

val sub : 'l t -> ?pos:int -> int -> 'l t

sub mesh ?pos len returns a new mesh keeping only the points with indices between pos and pos + len - 1 (included). See Mesh.sub for more information.

val permute_points : 'l t -> ?inv:bool -> 'l Mesh.int_vec -> 'l t

permute_points perm mesh, see Mesh.permute_points. This version also permutes the #point_attribute matrix.

val permute_triangles : 'l t -> ?inv:bool -> 'l Mesh.int_vec -> 'l t

permute_points perm mesh, see Mesh.permute_points. This version also permutes the #point_attribute matrix.

package mesh