polygon-math 1.2.0

Calculate geometric properties of arbitrary 2D polygons

polygon

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

• plotting with matplotlib kwargs (color, linestyle, label)
• area, lengths of edges, inner angles
• order of vertices (clockwise or anti-clockwise)
• centroid (center of mass)
• triangles: centers and radii of incircle and circumscribed (outer) circle
• solid of revolution: volume, surface areas, center of mass
• second moment of area (bending stiffness of beams)
• check if point is inside or on edge of polygon
• translation, rotation and scaling

Article with examples and explanations: https://gerritnowald.wordpress.com/2022/05/17/polygon-module-object-oriented/

installation

pip install polygon-math

examples:

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

creating a polygon object:

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

instance = polygon(Vertices, axis)

• axis:
  • 0: revolution with respect to x-axis
  • 1: revolution with respect to y-axis

attributes of polygon object (geometrical properties):

v: Vertex
e: Edge (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], wrt origin
- solid of revolution, if axis is specified:
    - RotationVolume
    - RotationSurfaces[e]
    - CenterMassCrossSection[r,z]      CenterMass[r,z] now relates to solid
- for 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)

methods of polygon object:

- print(instance)        gives number of vertices
- abs(instance)          gives area or volume of solid of revolution if axis is defined

- plotting (matplotlib kwargs can be used)
    - plot(numbers=False, **kwargs)            plots polygon, optionally numbers of vertices
    - plotCenterMass(**kwargs)                 plots center of mass, default style red cross
    - plotCenterEdges(**kwargs)                plots center of edges, default style black dots
    - for solid of revolution:
        - plotRotationAxis(**kwargs)           plots axis of rotation, default linestyle black dash-dotted
        - plotCenterMassCrossSection(**kwargs) plots centroid of crossSection, default style green cross
    - for triangles:
        - plotOutCircle(**kwargs)              plots circumsribed (outer) circle
        - plotIncircle(**kwargs)               plots incircle (inner circle)

- point testing
    - instance(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)
    - instance + [dx,dy] , instance - [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)
                                    
    - instance * [fx,fy] , instance / [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)

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.