Polygon

This module contains the definition of a polygon and some related subroutines More...

Data Types
type	mod_cg2_polygon::t_polygon
	Definition of a bi-dimensional polygon. More...

Functions/Subroutines
pure subroutine	mod_cg2_polygon::cg2_initialize_polygon (polygon, n)
	Initialize the polygon structure.
elemental subroutine	mod_cg2_polygon::cg2_finalize_polygon (polygon)
	Finalize the polygon structure.
double precision elemental function	mod_cg2_polygon::cg2_polygon_volume (polygon)
	Compute the area of a polygon.
pure subroutine	mod_cg2_polygon::cg2_polygon_centroid (polygon, centroid, volume)
	Compute the centroid of a polygon.
integer pure function	mod_cg2_polygon::cg2_polygon_winding_number (polygon, point)
	Compute the winding number of a point in a polygon.
integer pure function	mod_cg2_polygon::cg2_polygon_winding_number_with_boundary (polygon, point)
	Compute the winding number of a point in a polygon including its boundary.
pure subroutine	mod_cg2_polygon::cg2_split_quad_in_triangles (quad, triangle1, triangle2)
	Split a quadrilateral in two triangles.
pure subroutine	mod_cg2_polygon::cg2_copy_polygon (original, copy)
	Make a copy of a polygon.
elemental subroutine	mod_cg2_polygon::cg2_move_alloc_polygon (polygon1, polygon2)
	Move the allocation of a given polygon to another polygon.
subroutine	mod_cg2_polygon::cg2_polygon_write_vtk_file (polygon, filename)
	Print a polygon into a VTK file for debug purpose.

Detailed Description

This module contains the definition of a polygon and some related subroutines

Attention

Modify these functions at your own risk. Many algorithms depend on the specific behaviour of these functions. They are designed to not generate false negative results. Note that false positive results may occur due to the finite representation of real numbers. Take that into consideration when writing new algorithms.

Function/Subroutine Documentation

cg2_copy_polygon()

pure subroutine mod_cg2_polygon::cg2_copy_polygon	(	type(t_polygon), intent(in)	original,
		type(t_polygon), intent(out)	copy )

Make a copy of a polygon.

Parameters

[in]	original	Original polygon
[out]	copy	Copy of the original polygon

cg2_finalize_polygon()

elemental subroutine mod_cg2_polygon::cg2_finalize_polygon

(

type(t_polygon), intent(inout)

polygon

)

Finalize the polygon structure.

Parameters

[in,out]

polygon

The polygon to finalize

cg2_initialize_polygon()

pure subroutine mod_cg2_polygon::cg2_initialize_polygon	(	type(t_polygon), intent(inout)	polygon,
		integer, intent(in)	n )

Initialize the polygon structure.

Parameters

[in,out]	polygon	The polygon to initialize
[in]	n	The number of vertices of the polygon

cg2_move_alloc_polygon()

elemental subroutine mod_cg2_polygon::cg2_move_alloc_polygon	(	type(t_polygon), intent(inout)	polygon1,
		type(t_polygon), intent(inout)	polygon2 )

Move the allocation of a given polygon to another polygon.

Move the allocation of the vertices array of polygon1 into the vertices array of polygon2. After calling this routine the vertices array of polygon1 is unallocated.

Parameters

[in,out]	polygon1	Polygon to be transfered in polygon2
[in,out]	polygon2	Polygon receiving data from polygon1

cg2_polygon_centroid()

pure subroutine mod_cg2_polygon::cg2_polygon_centroid	(	type(t_polygon), intent(in)	polygon,
		double precision, dimension(2), intent(out)	centroid,
		double precision, intent(out), optional	volume )

Compute the centroid of a polygon.

May also output the volume of a polygon

The centroid \(x_c(\omega)\) of a polygon \(\omega\) is given by

\[ x_c(\omega) = x_0 + \dfrac{1}{6|\omega|}\sum_{i=1}^{n}[(x_i - x_0)\times(x_{i+1}-x_0)]((x_i - x_0) + (x_{i+1} - x_0)) \]

Where \( x_0 \) is any point of the real plane

Parameters

[in]	polygon	Any polygon
[out]	centroid	Centroid of the polygon
[out]	volume	Volume of the polygon

cg2_polygon_volume()

double precision elemental function mod_cg2_polygon::cg2_polygon_volume

(

type(t_polygon), intent(in)

polygon

)

Compute the area of a polygon.

The volume of a polygon \(\omega = \{x_1,\cdots,x_n\}\) is given by

\[ |\omega| = \sum_{i=1}^{n} ((x_i - x_0)\times(x_{i+1}-x_0)) \]

Where \( x_0 \) is any point of the real plane

Parameters

[in]

polygon

Any polygon

cg2_polygon_winding_number()

integer pure function mod_cg2_polygon::cg2_polygon_winding_number	(	type(t_polygon), intent(in)	polygon,
		double precision, dimension(2), intent(in)	point )

Compute the winding number of a point in a polygon.

A point is outside a polygon if the winding number is equal to 0.

Parameters

[in]	polygon	Any polygon
[in]	point	Any point of the plane

cg2_polygon_winding_number_with_boundary()

integer pure function mod_cg2_polygon::cg2_polygon_winding_number_with_boundary	(	type(t_polygon), intent(in)	polygon,
		double precision, dimension(2), intent(in)	point )

Compute the winding number of a point in a polygon including its boundary.

A point is outside a polygon if the winding number is equal to 0.

Parameters

[in]	polygon	Any polygon
[in]	point	Any point of the plane

cg2_polygon_write_vtk_file()

subroutine mod_cg2_polygon::cg2_polygon_write_vtk_file	(	type(t_polygon), intent(in)	polygon,
		character(len=*), intent(in)	filename )

Print a polygon into a VTK file for debug purpose.

Parameters

[in]	polygon	Any polygon
[in]	filename	File name of the VTK file

cg2_split_quad_in_triangles()

pure subroutine mod_cg2_polygon::cg2_split_quad_in_triangles	(	type(t_polygon), intent(in)	quad,
		type(t_polygon), intent(out)	triangle1,
		type(t_polygon), intent(out)	triangle2 )

Split a quadrilateral in two triangles.

Check the concavity. Two cases:

  !!                      |
  !! Case 1:              | Case 2:
  !!                      |
  !!   1           4      |      4           3
  !!   +----------+       |      +----------+
  !!    `.       /        |       `.       /
  !!      `.    /         |         `.    /
  !!        `.  \3        |           `.  \2
  !!          `. \        |             `. \
  !!            `.\       |               `.\
  !!              `\      |                 `\
  !!                2     |                   1
  !!                      |
  !!   Generate:          |       Generate:
  !!    - {1, 3, 4}       |        - {4, 2, 3}
  !!    - {1, 2, 3}       |        - {4, 1, 2}
  !! 

Parameters

[in]	quad	Quadrilateral
[out]	triangle1,triangle2	quad split in two triangles