mo_poly Module Reference

Polygon calculations. More...

Data Types
interface	areapoly
	Area of polygon. More...
interface	center_of_mass
	Center of mass of polygon. More...
interface	inpoly
	Determination point of polygon. More...
interface	mod_pole
	Modify polygon so it covers pole correctly. More...
interface	mod_shift
	Shifts the (longitude) value 180 degrees. More...
interface	orientpoly
	Check orientation of polygon. More...

Functions/Subroutines
real(sp) function	areapoly_sp (coord)
	Area of polygon.
real(sp) function, dimension(2)	center_of_mass_sp (coord)
	Center of mass of polygon.
subroutine	inpoly_sp (p, coord, erg)
	Determination point of polygon.
integer(i4) function	orientpoly_sp (coord)
	Check orientation of polygon.
real(sp) function, dimension(:,:), allocatable	mod_pole_sp (coord, meridian_arg)
	Modify polygon so it covers pole correctly.
elemental real(sp) function	mod_shift_sp (x_coord, meridian_arg)
	Shifts the (longitude) value 180 degrees.
real(dp) function	areapoly_dp (coord)
	Area of polygon.
real(dp) function, dimension(2)	center_of_mass_dp (coord)
	Center of mass of polygon.
subroutine	inpoly_dp (p, coord, erg)
	Determination point of polygon.
integer(i4) function	orientpoly_dp (coord)
	Check orientation of polygon.
real(dp) function, dimension(:,:), allocatable	mod_pole_dp (coord, meridian_arg)
	Modify polygon so it covers pole correctly.
elemental real(dp) function	mod_shift_dp (x_coord, meridian_arg)
	Shifts the (longitude) value 180 degrees.

Detailed Description

Polygon calculations.

This module determines wether a 2D point lies inside, outside, or on the vertice/edge of a 2D polygon and is part of the UFZ CHS Fortran library.

Changelog

• Juliane Mai, July 2012
  • written
• Maren Goehler, July 2012
  • area & center of mass

Author

Juliane Mai

Date

Jul 2012

Copyright

Copyright 2005-2024, the CHS Developers, Sabine Attinger: All rights reserved. FORCES is released under the LGPLv3+ license

The UFZ (CHS) FORCES code is free software. You can redistribute it and/or modify it under the terms of the GNU General Public License as published by the free Software Foundation either version 3 of the License, or (at your option) any later version.

This program is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You received a copy of the GNU Lesser General Public License along with the UFZ CHS FORCES code. It can be found in the files COPYING and COPYING.LESSER provided with this software. The complete GNU license text can also be found at http://www.gnu.org/licenses/.

Function/Subroutine Documentation

areapoly_dp()

real(dp) function mo_poly::areapoly_dp ( real(dp), dimension(:,:), intent(in)  coord )

private

Area of polygon.

Function for computing the area of a polygon (2D, convex or not). Function for computing the area of a polygon The polygon can be convex or not.

The method is only applicable for 2D polygons and points.

Example

polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
 
area = areapoly( polygon )
 
! --> area = 1

See also example in test directory.

Literature

1. http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt

Returns

Area of polygon

Parameters

[in]

coord

coordinates of the polygon in question

Definition at line 487 of file mo_poly.f90.

Referenced by mo_poly::center_of_mass::center_of_mass_dp().

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areapoly_sp()

real(sp) function mo_poly::areapoly_sp ( real(sp), dimension(:,:), intent(in)  coord )

private

Area of polygon.

Function for computing the area of a polygon (2D, convex or not). Function for computing the area of a polygon The polygon can be convex or not.

The method is only applicable for 2D polygons and points.

Example

polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
 
area = areapoly( polygon )
 
! --> area = 1

See also example in test directory.

Literature

1. http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt

Returns

Area of polygon

Parameters

[in]

coord

coordinates of the polygon in question

Definition at line 112 of file mo_poly.f90.

Referenced by mo_poly::center_of_mass::center_of_mass_sp().

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center_of_mass_dp()

real(dp) function, dimension(2) mo_poly::center_of_mass_dp ( real(dp), dimension(:,:), intent(in)  coord )

private

Center of mass of polygon.

Function for computing the center of mass of a polygon (2D, convex or not).

\[ A = \sum_{i}(x_{i}y_{i+1}-x_{i+1}y_{i}) \]

\[ x_s = \frac{1}{6A} \sum_i(x_i+x_{i+1})(x_iy_{i+1}-x_{i+1}y_i) \]

\[ y_s = \frac{1}{6A} \sum_i(y_i+y_{i+1})(x_iy_{i+1}-x_{i+1}y_i) \]

Example

polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
 
com = center_of_mass( polygon )
 
! --> com = (/1.5_dp, 1.5_dp/)

See also example in test directory

Literature

1. http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt

Returns

Center of mass of polygon.

Parameters

[in]

coord

coordinates of polygon in question

Definition at line 543 of file mo_poly.f90.

center_of_mass_sp()

real(sp) function, dimension(2) mo_poly::center_of_mass_sp ( real(sp), dimension(:,:), intent(in)  coord )

private

Center of mass of polygon.

Function for computing the center of mass of a polygon (2D, convex or not).

\[ A = \sum_{i}(x_{i}y_{i+1}-x_{i+1}y_{i}) \]

\[ x_s = \frac{1}{6A} \sum_i(x_i+x_{i+1})(x_iy_{i+1}-x_{i+1}y_i) \]

\[ y_s = \frac{1}{6A} \sum_i(y_i+y_{i+1})(x_iy_{i+1}-x_{i+1}y_i) \]

Example

polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
 
com = center_of_mass( polygon )
 
! --> com = (/1.5_dp, 1.5_dp/)

See also example in test directory

Literature

1. http://de.wikipedia.org/wiki/Geometrischer_Schwerpunkt

Returns

Center of mass of polygon.

Parameters

[in]

coord

coordinates of polygon in question

Definition at line 168 of file mo_poly.f90.

inpoly_dp()

subroutine mo_poly::inpoly_dp ( real(dp), dimension(2), intent(in)  p, real(dp), dimension(:, :), intent(in)  coord, integer(i4), intent(out)  erg  )

private

Determination point of polygon.

Determines whether a 2D point is inside, outside or on vertex of a polygon (2D, convex or not).

The original version of the source code (pnpoly) was implemented by W. Randolph Franklin. It was insufficiently assigning vertex/edge points.

Example

polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
 
point = (/ 1.5, 1.5 /)
 
call inpoly( point, polygon, inside )
 
! --> inside = 1 ... point is inside the polygon

See also example in test directory

Literature

1. https://wrf.ecse.rpi.edu/Research/Short_Notes/pnpoly.html

Returns

Whether point is inside (=1), outside (=-1) or on a vertex/edge of the polygon (=0)

Parameters

[in]	p	point in question
[in]	coord	coordinates of the polygon
[out]	erg	result: inside: erg = 1 outside: erg = -1 on vertex/edge: erg = 0

Definition at line 607 of file mo_poly.f90.

inpoly_sp()

subroutine mo_poly::inpoly_sp ( real(sp), dimension(2), intent(in)  p, real(sp), dimension(:, :), intent(in)  coord, integer(i4), intent(out)  erg  )

private

Determination point of polygon.

Determines whether a 2D point is inside, outside or on vertex of a polygon (2D, convex or not).

The original version of the source code (pnpoly) was implemented by W. Randolph Franklin. It was insufficiently assigning vertex/edge points.

Example

polygon(:,1) = (/ 1.0_dp,2.0_dp,2.0_dp,1.0_dp /)
polygon(:,2) = (/ 1.0_dp,1.0_dp,2.0_dp,2.0_dp /)
 
point = (/ 1.5, 1.5 /)
 
call inpoly( point, polygon, inside )
 
! --> inside = 1 ... point is inside the polygon

See also example in test directory

Literature

1. https://wrf.ecse.rpi.edu/Research/Short_Notes/pnpoly.html

Returns

Whether point is inside (=1), outside (=-1) or on a vertex/edge of the polygon (=0)

Parameters

[in]	p	point in question
[in]	coord	coordinates of the polygon
[out]	erg	result: inside: erg = 1 outside: erg = -1 on vertex/edge: erg = 0

Definition at line 232 of file mo_poly.f90.

mod_pole_dp()

real(dp) function, dimension(:,:), allocatable mo_poly::mod_pole_dp ( real(dp), dimension(:,:), intent(in)  coord, real(dp), intent(in), optional  meridian_arg  )

private

Modify polygon so it covers pole correctly.

Modifies a polygon (2D, convex or not) to include pole when passed to inpoly this function is intended to modify a given polygon, so it can be represented in a Cartesian grid the use case is a polygon (e.g. 120,80, -120,80, 0,80 covering the north pole) that is not represented on Cartesian lat-lon grid as polygon. The script inserts additional coordinates, so the pole is covered (e.g. 180,80, 180,90, -180,90, -180,80) See test cases for examples.

Returns

modified coordinates

Parameters

[in]	coord	coordinates of the polygon in question
[in]	meridian_arg	meridian that represents discontinuity, defaults to 180.0

Definition at line 728 of file mo_poly.f90.

mod_pole_sp()

real(sp) function, dimension(:,:), allocatable mo_poly::mod_pole_sp ( real(sp), dimension(:,:), intent(in)  coord, real(sp), intent(in), optional  meridian_arg  )

private

Modify polygon so it covers pole correctly.

Modifies a polygon (2D, convex or not) to include pole when passed to inpoly this function is intended to modify a given polygon, so it can be represented in a Cartesian grid the use case is a polygon (e.g. 120,80, -120,80, 0,80 covering the north pole) that is not represented on Cartesian lat-lon grid as polygon. The script inserts additional coordinates, so the pole is covered (e.g. 180,80, 180,90, -180,90, -180,80) See test cases for examples.

Returns

modified coordinates

Parameters

[in]	coord	coordinates of the polygon in question
[in]	meridian_arg	meridian that represents discontinuity, defaults to 180.0

Definition at line 353 of file mo_poly.f90.

mod_shift_dp()

elemental real(dp) function mo_poly::mod_shift_dp ( real(dp), intent(in)  x_coord, real(dp), intent(in), optional  meridian_arg  )

private

Shifts the (longitude) value 180 degrees.

Modify a coordinate value

Returns

Shifted value

Parameters

[in]	x_coord	coordinates of the polygon in question
[in]	meridian_arg	meridian that represents discontinuity, defaults to 180.0

Definition at line 818 of file mo_poly.f90.

mod_shift_sp()

elemental real(sp) function mo_poly::mod_shift_sp ( real(sp), intent(in)  x_coord, real(sp), intent(in), optional  meridian_arg  )

private

Shifts the (longitude) value 180 degrees.

Modify a coordinate value

Returns

Shifted value

Parameters

[in]	x_coord	coordinates of the polygon in question
[in]	meridian_arg	meridian that represents discontinuity, defaults to 180.0

Definition at line 443 of file mo_poly.f90.

orientpoly_dp()

integer(i4) function mo_poly::orientpoly_dp ( real(dp), dimension(:,:), intent(in)  coord )

private

Check orientation of polygon.

Function for checking the orientation of a polygon (2D, convex or not).

Returns

Integer indicating orientation (counter-clockwise: -1, clockwise: 1, none: 0)

Parameters

[in]

coord

coordinates of the polygon in question

result: clockwise: orientpoly = 1 counter-clockwise: orientpoly = -1 flat line or similar irregular shape: orientpoly = 0

Definition at line 691 of file mo_poly.f90.

orientpoly_sp()

integer(i4) function mo_poly::orientpoly_sp ( real(sp), dimension(:,:), intent(in)  coord )

private

Check orientation of polygon.

Function for checking the orientation of a polygon (2D, convex or not).

Returns

Integer indicating orientation (counter-clockwise: -1, clockwise: 1, none: 0)

Parameters

[in]

coord

coordinates of the polygon in question

result: clockwise: orientpoly = 1 counter-clockwise: orientpoly = -1 flat line or similar irregular shape: orientpoly = 0

Definition at line 316 of file mo_poly.f90.