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
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 around x-axis
- axis = 1: revolution around 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], with respect to origin
- solid of revolution:
- RotationVolume
- RotationSurfaces[e]
- CenterMassCrossSection[r,z] CenterMass[r,z] now relates to solid
- 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:
- abs(instance) returns area or volume of solid of revolution
- plotting (matplotlib optional arguments can be used)
- plot contour of polygon
- plotCenterMass
- plotCenterEdges
- solid of revolution:
- plot3d 3D wireframe plot of solid
- plotRotationAxis for 2D plot, only keyword arguments
- plotCenterMassCrossSection for 2D plot
- triangles:
- plotOutCircle circumscribed (outer) circle
- plotIncircle 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)
prerequisites
- NumPy
- Matplotlib
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.
