The power of Python for parametric mesh modeling

Parametric modeling is a widely used technique in 3D modeling and design. At its core, parametric modeling involves defining a 3D model through a set of parameters, such as dimensions. By modifying these parameters, designers can quickly generate variants of the original model, making this approach highly efficient and versatile. 

In traditional workflows, parametric modeling is typically applied to exact geometry in the field of computer-aided design (CAD). Well-known CAD solutions like CATIA, Solidworks, and Siemens NX provide robust tools for creating and managing parametric models. These tools are invaluable for engineers and designers working on complex 3D designs.

The Limitations of Traditional Workflows 

In the field of computer-aided engineering (CAE), a common workflow involves exporting a parametric CAD model to meshing or simulation software, such as Abaqus or Ansys. These software tools then generate a computational mesh based on the CAD geometry, which is essential for simulations like finite element analysis (FEA) or computational fluid dynamics (CFD). 

However, this workflow has a significant limitation: while the original CAD model is parametric, the resulting mesh is not. If users need to analyze multiple variants of a parametric CAD model, the mesh generation process must be repeated for each variant. This can be a time-consuming and labor-intensive process, especially for projects requiring extensive mesh sensitivity analyses or multiple design iterations. 

Introducing Parametric Mesh Modeling 

In this article, we explore an alternative concept: parametric mesh modeling. This approach offers a more streamlined and flexible solution by enabling the direct generation of parametric meshes through scripting. With a single Python script, users can define both the geometry of a 3D model and the characteristics of its mesh, such as element size or density. 

The Advantages of Script-Based Parametric Mesh Modeling 

By leveraging Python scripting, parametric mesh modeling provides several key benefits over traditional workflows: 

1. Elimination of CAD-to-Mesh Conversion:  There’s no need to convert an exact CAD model into a high-quality mesh. The Python script directly defines the parametric mesh, simplifying the workflow and reducing potential issues during mesh generation. 

2. Efficient Variant Generation:  A single script can generate multiple variants of the 3D model by adjusting geometry parameters. Additionally, it allows for the creation of different mesh configurations, such as varying element densities, without altering the underlying geometry. 

3. Enhanced Mesh Sensitivity Analysis:  This approach makes it easy to perform mesh sensitivity studies by automating the generation of meshes with different densities. Such analyses are critical for ensuring the accuracy and stability of physics-based simulations, including CFD and FEA. 

An Example: Hexahedral Mesh Generation 

To illustrate this, consider a HelloTriangle Python script that generates a hexahedral mesh of a simple 3D geometry. The script includes parameters for both the geometry (e.g., dimensions) and the mesh (e.g., element size).

from hellotriangle import shapes

# mesh parameters
n1 = 4
n2 = 6
n3 = 30

# geometrical parameters 2D profile
width = 4.0
height = 4.0
radiusProfile = 1.5

# geometrical parameter 3D piece
radiusOuter = 6.0
angle = 270.0

# generate quad pattern
cir = shapes.arc(90.0, 2*n1).scale(radiusProfile)
line = shapes.polyline([[width, 0.0, 0.0], [width, height, 0.0], [0.0, height, 0.0]], n1)
quad = cir.connect(line, div = n2).translate([-radiusOuter, 0.0, 0.0])

# revolve to generate hex elements
hex = quad.revolve(n3, axis = 1, angle = angle)

# draw hex mesh with edges
draw(hex, color = "#2BB786", show_edges = True)

• Geometry Variants: By modifying the geometry parameters, the script can produce multiple variants of the 3D model while keeping the mesh settings constant (see figure below).

• Mesh Variants: Alternatively, the script can adjust mesh parameters, such as element size or density, while maintaining the same geometry. This flexibility is especially useful for studying the effects of mesh refinement on simulation results. 

  

Why Choose Parametric Mesh Modeling? 

Parametric mesh modeling with Python scripting is a game-changer for engineers and designers. It provides a faster, more flexible way to generate high-quality meshes. By combining geometry definition and mesh generation in a single script, this approach eliminates redundant steps, reduces manual effort, and accelerates the design-to-simulation or 3D printing pipeline. Of course, this script-based parametric mesh modeling approach also comes with limitations. Not all 3D models can be generated with this approach.

👉 If you’re looking to streamline your workflow and harness the full potential of parametric modeling, try parametric mesh modeling with HelloTriangle. Sign up for HelloTriangle today.