geometry.md

Geometry library

The geometry library provides geometry related primitives and functions mainly to work with polygons. All C++ functions/classes are defined within the rir:: namespace. The library provides a C interface through geometry.h. the main goal of geometry is to provide some fast routines for polygons manipulation in pure Python scripts. Following examples only use the Python wrapper of the geometry library. Within the geometry module, a polygon is a list (or numpy array) of [x,y] points.

Polygons interpolation

The function polygon_interpolate returns an interpolated polygon given 2 input polygons and a position value between 0 and 1. The resulting polygon is guaranteed to have a maximum size of (len(poly1) + len(poly1) -2). Note that there are an infinit number of ways to compute the interpolation between 2 polygons. This version uses a custom algorithm that fits our needs, and you should test it first with your use case. Usage:

from librir.geometry import polygon_interpolate

# create a polygon with a rectangular shape
poly1 = [[0,0], [1,0], [1,1], [0,1]]

# create a polygon with a rectangular shape rotated by 45° around (0,0)
poly2 = [[-1,0], [0,1], [1,0], [0,-1]]

# position argument is 0, the result is equivalent to poly1
print( polygon_interpolate(poly1, poly2,0) )
# position argument is 1, the result is equivalent to poly2
print( polygon_interpolate(poly1, poly2,1) )
# position argument is 0.5, the result is in between poly1 and poly2
print( polygon_interpolate(poly1, poly2,0.5) )

Polygon simplification

The functions rdp_simplify_polygon and rdp_simplify_polygon2 both simplify an input polygon using Ramer-Douglas-Peucker algorithm. The first version uses an epsilon value for the simplification, while the former one uses a maximum number of points for the resulting polygon. Usage:

from librir.geometry import rdp_simplify_polygon2
import math

# This function gets just one pair of coordinates based on the angle theta
def get_circle_coord(theta, x_center, y_center, radius):
    x = radius * math.cos(theta) + x_center
    y = radius * math.sin(theta) + y_center
    return (x,y)

# This function gets all the pairs of coordinates
def get_all_circle_coords(x_center, y_center, radius, n_points):
    thetas = [i/n_points * math.tau for i in range(n_points)]
    circle_coords = [get_circle_coord(theta, x_center, y_center, radius) for theta in thetas]
    return circle_coords

# Create a polygon with a circular shape
circle_coords = get_all_circle_coords(x_center = 5, 
                                      y_center = 15,
                                      radius = 2.5,
                                      n_points = 1000)
                                      
# simplify it down to 10 points maximum
print(rdp_simplify_polygon2(circle_coords, 10))

Polygon drawing

The function draw_polygon fills a polygon surface inside an existing numpty array. Usage:

from librir.geometry import draw_polygon
import numpy as np

img = np.zeros((10,10))
# create rectangular polygon
poly = [[1,1], [6,1], [6,6], [1,6]]

print(draw_polygon(img,poly, 1))

Extract polygons from images

The function extract_polygon extract a polygon from a grayscale image. Usage:

from librir.geometry import extract_polygon, draw_polygon
import numpy as np

img = np.zeros((10,10))
# create rectangular polygon
poly = [[1,1], [6,1], [6,6], [1,6]]
# draw polygon with value 1
draw_polygon(img,poly, 1)

# extract polygon for pixels of value 1..
# note that if the input image contains multiple closed regions of value 1, only the first one is extracted (scanning line by line).
poly2 = extract_polygon(img,1)
print(poly2)

Additional functions

In addition, the geometry module provides the following functions:

• extract_convex_hull: extract convex hull polygon from a set of points
• minimum_area_bbox: extract the minimum area oriented bounding box around given polygon