Demo Fractal Tree

In this demo, we will create a binray tree using the Tree module in vSCAD.

Creating a project

vSCAD uses a preset file structure to organize projects. After installing the package, you can create a new project by running the following command:

$ python3 ~/path/to/vSCAD/src/vSCAD/io/new_project.py

This will create a new project in the current directory. The project directory will contain: 1. vscad.py: The main script for generating the 3D model. 2. image_data/: A directory for storing the point and diameter data. 3. scad/: A directory for storing the OpenSCAD files. 4. scad-stl/: A directory for storing the generated 3D models generated from OpenSCAD

In this demo, we will not use the image_data directory.

Writing the Tree

We will now begin editing the vscad.py script to generate the 3D model. Creating a binray tree is simple with the Tree module. We create the tree object using the following code:

fractal_tree = vs.Tree.BinaryTree(start_point=(0, 0, 0),
                                  length=10,
                                  angle=np.pi/6,
                                  depth=4,
                                  diameter=1,
                                  num_points_base=10)

The BinaryTree method creates a binary tree object. The arguments are as follows: - start_point: The starting point of the tree. This is a tuple of the form (x, y, z). - length: The length of the base tree. - angle: The angle between the branches. - depth: The depth of the tree. - diameter: The diameter of the tree. - num_points_base: The number of points in the base of the tree.

By default, each child branch will be 0.7 times the length of the parent branch. We can change by using the following code:

fractal_tree.set_branch_length_reduction(alpha)

where alpha is the reduction factor.

The child branch diameter will additionally be calculated using Murray’s law with and exponent of 3.0. We can change the exponent by using the following code:

fractal_tree.set_murray_exponent(beta)

where beta is the exponent.

Writing the Vessels

vSCAD uses the Vessel object as the main object for generating 3D models. In order to create a 3D model of the tree we just generated, we need to convert the tree object into a vessel object. Tree objects contain branch subobjects that contain the points and diameters of each branch. We can convert the branch subobjects into vessel objects using a for loop:

branches = fractal_tree.draw_tree()

vessel_object = []
for branch in branches:
    vessel_name = f'branch_{branches.index(branch)}'
    vessel = vs.Vessel(name=vessel_name)
    vessel.set_scale_factor(scale_factor=1.0)
    vessel.set_path(branch.points)
    vessel.set_diameters(branch.diameters)
    vessel.interpolate_paths(n=3)
    vessel.get_direction_vectors()
    vessel.get_euler_angles()
    vessel_object.append(vessel)

Here, we’ve given the data within the branch object to a new vessel object. We give each vessel object a unique name and append it to a list. We then interpolate the paths, get the direction vectors, and get the Euler angles used in OpenSCAD.

Writing the OpenSCAD file

We can now write the OpenSCAD file. We will import the Vessel objects we created to the OpenSCAD file. We will also import lofting modules:

scad_file = vs.SCADFile('vessel.scad')

scad_file.modules.import_circle_at()
scad_file.modules.import_loft_path()

for object in vessel_object:
    scad_file.import_vessel(object)

Next, we need to loft each vessel and merge their geometries:

scad_file.modules.start_union()

for object in vessel_object:
    scad_file.loft_path(object)

scad_file.modules.end_union()

Finally, we call OpenSCAD to write the STL mesh:

scad_file.write_scad_file('binray_tree.scad')

The full script

import numpy as np
import vSCAD as vs

# ---- Draw a fractal tree with 4 levels of recursion ---- #
fractal_tree = vs.Tree.BinaryTree(start_point=(0, 0, 0), length=10, angle=np.pi/6, depth=4, diameter=1, num_points_base=10)

# ---- Get the branches of the tree ---- #
branches = fractal_tree.draw_tree()

# ---- Create a vessel object for each branch ---- #
vessel_object = []
for branch in branches:
    vessel_name = f'branch_{branches.index(branch)}'
    vessel = vs.Vessel(name=vessel_name)
    vessel.set_scale_factor(scale_factor=1.0)
    vessel.set_path(branch.points)
    vessel.set_diameters(branch.diameters)
    vessel.interpolate_paths(n=3)
    vessel.get_direction_vectors()
    vessel.get_euler_angles()
    vessel_object.append(vessel)

# ---- Prepare OpenSCAD file ---- #
scad_file = vs.SCADFile('vessel.scad')

# ---- Import OpenSCAD functions ---- #
scad_file.modules.import_circle_at()
scad_file.modules.import_loft_path()

# ---- Import vessel data ---- #
for object in vessel_object:
    scad_file.import_vessel(object)

# ---- Write OpenSCAD code ---- #
scad_file.modules.start_union()

for object in vessel_object:
    scad_file.modules.function_loft_path(object)

scad_file.modules.end_union()

scad_file.write_stl('binary_tree.stl')