polygon

Python module to calculate geometric properties of arbitrary 2D polygons:

• area, centroid (center of mass)
• second moment of area (bending stiffness of beams)
• triangles: incircle and circumscribed (outer) circle
• solid of revolution: volume, surface areas, center of mass
• check if point is inside or on edge of polygon
• move, rotate and scale polygon
• plotting with matplotlib arguments (e.g. color, linestyle, label)

examples:

https://github.com/gerritnowald/polygon/blob/main/examples/examples.ipynb

installation:

pip install polygon-math

creating a polygon object:

from polygon_math import polygon
Vertices = [[x0,y0],[x1,y1],[x2,y2],...]   # 2D-coordinates of vertices
polygon_object = polygon(Vertices)

• polygon can be open or closed (i.e. first = last vertex)
• holes can be defined by self-intersecting and opposite order of vertices inside than outside

creating a solid of revolution:

polygon_object = polygon(Vertices, axis)

• axis = 0: revolution around x-axis
• axis = 1: revolution around y-axis

attributes of polygon_object (geometrical properties):

v: Vertex index
e: Edge index (next of v)
- .IsClockwise                          Boolean, order of vertices
- .Area
- .Angles[v]                            inner angles
- .EdgesLength[e]
- .EdgesMiddle[xe,ye]                   midpoints of edges
- .CenterMass[x,y]                      centroid / center of mass
- .SecondMomentArea                     [Ixx, Iyy, Ixy], with respect to origin
- triangles:
    - .CenterOuterCircle[x,y]           circumcenter / center of circumsribed (outer) circle
    - .RadiusOuterCircle                radius of circumsribed (outer) circle
    - .CenterInnerCircle[x,y]           center of incircle (inner circle)
    - .RadiusInnerCircle                radius of incircle (inner circle)
- solid of revolution:
    - .RotationVolume
    - .RotationSurfaces[e]
    - .CenterMassCrossSection[r,z]      r radial, z axial, CenterMass[r,z] now relates to solid

methods of polygon_object:

- abs(polygon_object)          returns area or volume of solid of revolution

- plotting (matplotlib optional arguments can be used)
    - .plot()                              contour of polygon
    - .plotCenterMass()
    - .plotCenterEdges()
    - triangles:
        - .plotOutCircle()                 circumscribed (outer) circle
        - .plotIncircle()                  incircle (inner circle)
    - solid of revolution:
        - .plot3d()                        3D wireframe plot of solid
        - .plotRotationAxis()              only keyword arguments
        - .plotCenterMassCrossSection()    for 2D plot

- point testing
    - polygon_object(point), .isPointInside(point)    true, if point [x,y] is inside of polygon (not on the edge)
    - .isPointOnEdge(point)                           true, if point [x,y] is on any edge of polygon

- manipulation (translation, rotation & scaling)
    - polygon_object + [dx,dy] , polygon_object - [dx,dy] , .move([dx,dy])
            translation by distances dx,dy in x,y-direction
    
    - .centerOrigin()
            moves origin of coordinate system to center of mass
                                    
    - .rotate(angle,[cx,cy]) , .rotateClockwise(angle,[cx,cy])
            (counter)-clockwise rotation by angle / °
            with respect to point [cx,cy] (optional, default center of mass)
                                    
    - polygon_object * [fx,fy] , polygon_object / [fx,fy] , .scale([fx,fy],[cx,cy])
            scaling by factors fx, fy in x,y-direction (negative: flip)
            with respect to point [cx,cy] (optional, default center of mass)

requirements

• numpy >= 1.15.0
• matplotlib >= 2.0.0

license:

MIT license. You are free to use the code any way you want, without liability or warranty.

Please reference my work if you use it.