Scilab Home Page | Wiki | Bug Tracker | Forge | Mailing List Archives | Scilab Online Help | ATOMS
File : Details
Please login or create an account

polygonmetrics(), polyarea

Computes the length, area, CoM, and unit vector of a plane or 3D simple polygon
(351 downloads for this version - 351 downloads for all versions)
Details
Version
1.0
Author
Samuel Gougeon
Maintainer
Samuel Gougeon
Category
License
Supported Scilab Version
5.5
Creation Date
August 19, 2015
Description
            OUTPUT EXAMPLE
--------------
--> // Equilateral triangle in a cube
--> x = [0 0 1 0]; y = [0 1 1 0]; z = [0 1 0 0]; 
--> p = polygonmetrics([x ; y ; z])
 p  =
   nbvert: 3
   length: 4.2426407
   area: 0.8660254
   com: [0.3333333,0.6666667,0.3333333]
   dir: [-0.5773503,0.5773503,-0.5773503]

-----------------------------------------------------------

--> polygonmetrics

Computes the length, area, Center of Mass, and unit vector of a plane or 3D
simple polygon

 SYNTAX
 ------
      polygonmetrics     // Displays this help
 pm = polygonmetrics(XY)
 pm = polygonmetrics(XYZ)

 PARAMETERS
 ----------
  XY : Matrix of size (2,N) or (N,2) with N>2:
       Cartesian coordinates of linked vertices of a simple plane polygon.
  XYZ: Matrix of size (3,N) or (N,3) with N>2
       Cartesian coordinates of linked vertices of a simple polygon.
    NOTES:
       * If the last point is not equal to the first one, polygonmetrics()
         closes the polygon.
       * The polygon must be simple, without self-intersections.
         In case of a self-crossing polygon, the area value is unreliable.
       * Concave as well as convex polygons are accepted.
       * In 3D, the 'pseudo-polygon' is not necessarily plane.

  pm : Geometrical parameters of the polygon. A structure with the following
        attributes is returned:
         pm.nbvert  : Number of vertices
         pm.length  : Perimeter
         pm.area    : Positive area
         pm.com     : 3D (x,y,z) coordinates of the Center of Mass
         pm.dir     : Resulting unit vector (a,b,c) orthogonal to the polygon

 DESCRIPTION
 -----------
 The same algorithm is used in 2D and in 3D, with plane and non-plane polygons:
   - The position of the Center of Mass CoM of the polygon is computed.
     In 2D, it is set to the vertices centroid.
     In 3D, its coordinates are the average of coordinates of its vertices.
   - The vectorial area of each triangle going from the CoM to an edge is
     computed. Its norm is the triangle's area. Its direction is orthogonal
     to the triangle. Its sign follows the corkscrew right hand rule.
   - The total oriented area is the sum of vectorial areas for all triangles
     set on all edges.
   - The polygon's area is the norm of the total oriented area.
   - The polygon direction is the unit vector of the total oriented area.

 In 2D, the resulting area matches with results from the Surveyor's formula:
  area = |sum_(i=1=>N){ x(i+1)*y(i) - x(i)*y(i+1) }| / 2
 The algorithm somewhat generalizes the Surveyor's formula in 3D.

 SEE ALSO
 --------
  mesharea : http://fileexchange.scilab.org/toolboxes/370000

 REFERENCE
 ---------
  Comments, scoring and bug reports are welcome on
  http://fileexchange.scilab.org/toolboxes/445000

 EXAMPLES
 --------
 da = gda(); da.isoview = "on"; da.axes_visible = "on"; clf
 yellow = color("yellow");

// Rectangle dx=2, dY = 2
 x = [0 2 2 0 0]; y = [0 0 1 1 0];
 subplot(4,2,1); xfpoly(x, y, yellow)
 p = polygonmetrics([x ; y])

// Self-intersecting rectangle
 x = [0 2 2 0 0]; y = [0 1 0 1 0];
 subplot(4,2,3); xfpoly(x, y, yellow)
 p = polygonmetrics([x ; y])

// Plane concave polygon:
 x=[0 3 3 2 2 3 3 0 0 0.5 0.5 1 1 0 0]; y=[0 0 1 1 2 2 3 3 1.5 1.5 2 2 1 1 0];
 subplot(2,2,2); xfpoly(x, y, yellow)
 p = polygonmetrics([x ; y])

// Other plane polygon
 r = grand(1,13,"unf",1,5);
 t = linspace(0, 2*%pi, 13);
 x = r.*cos(t); y = r.*sin(t);
 subplot(2,2,3); xfpoly(x, y, yellow)
 p = polygonmetrics([x ; y ])

// Equilateral triangle in a cube
 x = [0 0 1 0]; y = [0 1 1 0]; z = [0 1 0 0];
 subplot(2,2,4); param3d(x, y, z)
 e = gce(); e.fill_mode = "on"; e.background = yellow;
 ax = gca(); ax.isoview = "on"; ax.rotation_angles = [60 -50];
 p = polygonmetrics([x ; y ; z])

 da.isoview = "off"; da.axes_visible="off";
            
Files (2)
[14.87 kB]
Screenshot
Screenshot from polygonmetrics() examples, for thumbnail
[5.91 kB]
Miscellaneous file
File defining the function polygonmetrics(), help contents and examples

* MAKE polygonmetrics() AVAILABLE in EVERY SESSION: Click here to see HOW TO

* Get help: Enter "polygonmetrics" without parameters
News (0)
Comments (0)
Leave a comment
You must register and log in before leaving a comment.
Email notifications
Send me email when this toolbox has changes, new files or a new release.
You must register and log in before setting up notifications.