Creating an equilateral triangle grid / mesh inside a larger equilateral triangle

I have a list of vertices from a polygon and I'm trying to create an equilateral triangular grid inside a larger triangle centered around the current vertex from the input polygon.

The size of the internal triangle's sides is determined by L which divides the container side to L equal parts. Finally I'd like to store the coordinates of the vertices of all these triangles (including the original larger triangle) in a list in Python.

One approach I have come up with is the following:

• Find equidistant points with respect to L on each side of the large triangle
• Connect these points to the adjacent larger side
• Create a Shapely LineString from each of corresponding points
• Run a for loop that utilizes Shapely's object.intersection() function that returns the coordinates

However I'm open to ideas and other approaches possibly more efficient ones.

Here's my code so far:

import math  import sys      # Constructs the larger, container triangle given the centroid (a vertex from the input polygon)  def construct_eq_triangle(centroid, radius):      side_length = radius * math.sqrt(3)      # Calculate three vertices of the container triangle      a = [centroid[0], centroid[1] + (math.sqrt(3) / 3) * side_length]  # Top vertex      b = [centroid[0] - (side_length / 2), centroid[1] - (math.sqrt(3) / 6) * side_length]  # Bottom left vertex      c = [centroid[0] + (side_length / 2), centroid[1] - (math.sqrt(3) / 6) * side_length]  # Bottom right vertex        return a, b, c      def draw_triangular_grid(vertex, radius, L):        grid_x = []      grid_y = []            # contruct the container equilateral triangler around this vertex      a, b, c = construct_eq_triangle(vertex, radius)      # Draw the grid here inside a,b,c and fill 'grid_x' and 'grid_y'           # but for now just print the mother triangle      print("\n Equilateral triangle for vertex " + str(vertex) + ":")      print((a, b, c))        return grid_x, grid_y      def main(args):      # demo data, 4 vertices of a simple square with a length of 8      vertices = [(2.0, 10.0), (10.0, 10.10), (10.0, 2.0), (2.0, 2.0)]      radius = 2      L = 7      i = 0      while i <= len(vertices) - 1:          grid_x, grid_y = draw_triangular_grid(vertices[i], radius, L)          # process the grid coordinates          i += 1      # Main entry point  if __name__ == "__main__":      main(sys.argv[1:])      

https://stackoverflow.com/questions/65544295/creating-an-equilateral-triangle-grid-mesh-inside-a-larger-equilateral-triangl January 03, 2021 at 05:30AM