\( \newcommand{\E}{\mathrm{E}} \) \( \newcommand{\A}{\mathrm{A}} \) \( \newcommand{\R}{\mathrm{R}} \) \( \newcommand{\N}{\mathrm{N}} \) \( \newcommand{\Q}{\mathrm{Q}} \) \( \newcommand{\Z}{\mathrm{Z}} \) \( \def\ccSum #1#2#3{ \sum_{#1}^{#2}{#3} } \def\ccProd #1#2#3{ \sum_{#1}^{#2}{#3} }\)

CGAL 4.8 - 2D Placement of Streamlines

All Classes Namespaces Files Functions Variables Typedefs Enumerations Enumerator Groups Pages
Modules | Classes
2D Placement of Streamlines Reference

##

Abdelkrim Mebarki
Visualizing vector fields is important for many application domains. A good way to do it is to generate streamlines that describe the flow behavior. This package implements the "Farthest Point Seeding" algorithm for placing streamlines in 2D vector fields. It generates a list of streamlines corresponding to an input flow using a specified separating distance. The algorithm uses a Delaunay triangulation to model objects and address different queries, and relies on choosing the centers of the biggest empty circles to start the integration of the streamlines.

Introduced in: CGAL 3.2
Depends on: 2D Triangulation
BibTeX: cgal:m-ps-16a
License: GPL
Windows Demo: 2D Stream Lines
Common Demo Dlls: dlls

Vector and direction fields are commonly used for modeling physical phenomena, where a direction and magnitude, namely a vector is assigned to each point inside a domain.

A streamline is a curve everywhere tangent to the field. It can be considered as the path traced by an imaginary massless particle dropped into a steady fluid flow described by the field.

A streamline is represented as a polyline iteratively elongated by bidirectional numerical integration started from a seed point, until it comes close to another streamline, hits the domain boundary, or reaches a critical point.

The `CGAL::Stream_lines_2` class consists of saturating the domain with a set of tangential streamlines in accordance with a specified density.

Streamlines are represented as containers of points, manipulated by an iterator range of points, and the whole placement is accessible via an iterator range of streamlines.

The main class in this package, the class `CGAL::Stream_lines_2`, depends on two template parameters. The first template parameter stands for a class which represents both the vector field and the visualization domain with operations on them, and should be instantiated by a model of the concept `VectorField_2`. The second template parameter stands for a function object that ensures the numerical integration used to construct the streamlines, and should be instantiated by a model of the concept `Integrator_2`.

## Classified Reference Pages

## Concepts

- `StreamLinesTraits_2`
- `Integrator_2`
- `VectorField_2`

## Classes

- `CGAL::Stream_lines_2<VectorField_2,Integrator_2>`
- `CGAL::Euler_integrator_2<VectorField_2>`
- `CGAL::Runge_kutta_integrator_2<VectorField_2>`
- `CGAL::Regular_grid_2<StreamLinesTraits_2>`
- `CGAL::Triangular_field_2<StreamLinesTraits_2>`

## Modules
| Concepts

## Classes
class | CGAL::Euler_integrator_2< VectorField_2 >
| This class implements the first order Euler integrator. More...
class | CGAL::Regular_grid_2< StreamLinesTraits_2 >
| This class provides a 2D vector field specified by a set of sample points defined on a regular grid, with a bilinear interpolation scheme over its cells (i.e. for each point `p` in a cell `c`, the vector value is interpolated from the vertices of `c`). More...
class | CGAL::Runge_kutta_integrator_2< VectorField_2 >
| This class implements the second order Runge-Kutta integrator. More...
class | CGAL::Stream_lines_2< VectorField_2, Integrator_2 >
| The class `Stream_lines_2` generates a placement of streamlines in a 2D domain according to a bidimensional vector field. More...
class | CGAL::Triangular_field_2< StreamLinesTraits_2 >
| This class provides a vector field specified by a set of sample points defined on a triangulated domain. More...