Tessellating triangle mesh

thingiverse

Here's a script to generate tessellating triangles that connect seamlessly into a cohesive mesh: ```python import math def create_triangle(point1, point2, point3): """Create a triangle with the given points.""" return { 'point1': point1, 'point2': point2, 'point3': point3 } def tessellate_triangles(triangle_list, max_distance=10.0): """Tessellate triangles by connecting each pair of adjacent triangles.""" for i in range(len(triangle_list)): triangle = triangle_list[i] for j in range(i + 1, len(triangle_list)): adjacent_triangle = triangle_list[j] distance = math.sqrt( (triangle['point2']['x'] - adjacent_triangle['point2']['x'])**2 + (triangle['point2']['y'] - adjacent_triangle['point2']['y'])**2 ) if distance < max_distance: # Connect the two triangles by adding a new edge triangle_list.append({ 'edge1': {'from': triangle, 'to': adjacent_triangle}, 'edge2': {'from': adjacent_triangle, 'to': triangle} }) return triangle_list def create_mesh(triangle_list): """Create a mesh from the given tessellating triangles.""" # Initialize an empty mesh mesh = [] # Add each triangle to the mesh for triangle in triangle_list: mesh.append(triangle) return mesh # Example usage: triangle1 = create_triangle({'x': 0, 'y': 0}, {'x': 10, 'y': 0}, {'x': 5, 'y': 5}) triangle2 = create_triangle({'x': 15, 'y': 0}, {'x': 20, 'y': 0}, {'x': 18, 'y': 5}) tessellated_triangles = tessellate_triangles([triangle1, triangle2]) mesh = create_mesh(tessellated_triangles) print("Mesh:") for triangle in mesh: print(triangle) ``` This script creates a list of triangles and then connects each pair of adjacent triangles by adding a new edge between them. The `create_triangle` function takes three points as input and returns a dictionary representing the triangle. The `tessellate_triangles` function connects each pair of adjacent triangles by checking the distance between their second points. If the distance is less than a specified maximum distance, it adds a new edge to connect the two triangles. The `create_mesh` function initializes an empty mesh and then adds each tessellated triangle to it.