Blender-Python API Meshing

🔗Introduction

Blender is a free and open-source 3D computer graphics software toolset used for creating animated films, visual effects, art, 3D-printed models, motion graphics, interactive 3D applications, virtual reality, and, formerly, video games.

It is a tutorial to teach you how to create mesh by Blender-Python.

First of all, to be able to use the Blender-Python API, you need to import the bpy library.

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import bpy

When you open your new blender python, you can find a cube in the origin. And there is only one area for operating. What we are going to do is to create two new areas.

And set the different regions like the figure shown below. It's my personal preferrence, you can set the region as your like.

🔗Python Console

Let’s firstly use the python console.

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>>> bpy.data.objects
<bpy_collection[3], BlendDataObjects>

>>> bpy.data.objects.keys()
['Camera', 'Cube', 'Light']

And we can assign the object 'Cube' to a variable name cube. And move the cube to another position.

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>>> cube = bpy.data.objects['Cube']
>>> cube.location
Vector((0.0, 0.0, 0.0))

>>> cube.location = (1, 1, 1)

Then the centroid of the cube will move to (1, 1, 1).

🔗Text Editor

The operations above can be done by using the script in the text editor.

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import bpy

cube = bpy.data.objects['Cube']
cube.location = (1, 1, 1)
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## Mesh

In order to create mesh for a desirable objects. We need to define the vertices and faces.

### Mesh a plate
Let's create a plate

```python
import bpy

# Select and delete all the objects
bpy.ops.object.select_all(action = 'SELECT')
bpy.ops.object.delete()

vertices = [(-1, -1, 0), (1, -0, 0), (1, 1, 0), (-1, 1, 0)] # The coordinates of different vertices
faces = [(0, 1, 2, 3)] # Only one face, so the shape is a plate.

name = 'New Plate'
mesh = bpy.data.meshes.new(name)

obj = bpy.data.objects.new(name, mesh)

bpy.context.scene.collection.objects.link(obj)

mesh.from_pydata(vertices,[],faces)
mesh.update(calc_edges=True)

🔗Mesh a 3D Supershape

🔗3D Supershape

A 3D supershape can be parameterized by the Superformula1.

The superformula is a generalization of the superellipse and was proposed by Johan Gielis around 2000. Gielis suggested that the formula can be used to describe many complex shapes and curves that are found in nature. Gielis has filed a patent application related to the synthesis of patterns generated by the superformula.

In polar coordinates, with rr the radius and φ\varphi the angle, the superformula is,

r(φ)=(∣cos⁡(mφ4)a∣n2+∣sin⁡(mφ4)b∣n3)n1r(\varphi) = (|\frac{\cos(\frac{m\varphi}4)}a|^{n_2} + |\frac{\sin(\frac{m\varphi}4)}b|^{n_3})^{n_1}

By changing a,b,m,n1,n2,n3a, b, m, n_1, n_2, n_3, we can get different shapes.

🔗Demonstration (adapted by THE PROVING GROUND2)

Firstly, import the libraries, delete the existing objects, and then define the parameters and empty lists to store vertices, faces and edges.

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import bpy
import numpy as np
bpy.ops.object.select_all(action = 'SELECT')
bpy.ops.object.delete()
# mesh arrays
verts = []
faces = []
edges = []
 
# Initialize 3D supershape parameters
m = 17
a = -0.06
b = 6
n1 = 0.5
n2 = -.48
n3 = 1


scale = 3
 
Unum = 50
Vnum = 50
 
dU = 2 * np.pi / Unum
dV = np.pi / Vnum

Then create the vertices,

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# create vertices
theta = -np.pi            # Set the initial value for theta
for i in range (0, Unum + 1):
    phi = -np.pi/2
    r1 = 1/(((abs(np.cos(m*theta/4)/a))**n2+(abs(np.sin(m*theta/4)/b))**n3)**n1)
    for j in range(0, Vnum + 1):
        r2 = 1/(((abs(np.cos(m*phi/4)/a))**n2+(abs(np.sin(m*phi/4)/b))**n3)**n1)
        x = scale * (r1 * np.cos(theta) * r2 * np.cos(phi))
        y = scale * (r1 * np.sin(theta) * r2 * np.cos(phi))
        z = scale * (r2 * np.sin(phi))
 
        vert = (x,y,z)
        verts.append(vert)
        # update phi
        phi += dV
    # update theta
    theta += dU

Create the faces, and make sure the face will not intersect.

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count = 0
for i in range (0, (Vnum + 1) *(Unum)):
    if count < Vnum:
        A = i
        B = i+1
        C = (i+(Vnum+1))+1
        D = (i+(Vnum+1))
 
        face = (A,B,C,D)
        faces.append(face)
 
        count = count + 1
    else:
        count = 0

Create mesh.

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#create mesh and object
mymesh = bpy.data.meshes.new("supershape")
myobject = bpy.data.objects.new("supershape",mymesh)
 
#set mesh location
myobject.location = (0, 0, 0)
bpy.context.scene.collection.objects.link(myobject)
 
#create mesh from python data
mymesh.from_pydata(verts,edges,faces)
mymesh.update(calc_edges=True)

Then we will get a shape like that

We can also make some other operations like smoothing.

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#set the object to edit mode
bpy.context.view_layer.objects.active = myobject
bpy.ops.object.mode_set(mode='EDIT')
 
# remove duplicate vertices
bpy.ops.mesh.remove_doubles() 
 
# recalculate normals
bpy.ops.mesh.normals_make_consistent(inside=False)
bpy.ops.object.mode_set(mode='OBJECT')
 
# subdivide modifier
myobject.modifiers.new("subd", type='SUBSURF')
myobject.modifiers['subd'].levels = 3
 
# show mesh as smooth
mypolys = mymesh.polygons
for p in mypolys:
    p.use_smooth = True

Final shape will be displayed like

You can also change the parameters to get a different shape as you want,

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m = 17
a = -0.06
b = 6
n1 = 0.6
n2 = -.6
n3 = 2
 
scale = 3
 
Unum = 80
Vnum = 80

1. https://en.wikipedia.org/wiki/Superformula#3D_plots↩

2. http://wiki.theprovingground.org/blender-py-supershape↩