“All You Need is a Few Functions: Fundamentals of Computational Engineering, Part 5.”


Unlocking the Power of Implicit Functions and Voxel Fields###

In our previous blog posts, we have delved into the exciting world of Computational Engineering and explored the foundations of this revolutionary concept. We have discussed the history, the technology, the role of voxels, and the creation of implicit functions in generating complex geometries.

In this installment, we will focus on another crucial aspect of building objects within a voxel field – the use of triangle meshes. While some may see mesh as a dirty word due to its association with messy geometries in CAD packages, we assure you that our clean computational approach eliminates any concerns.

By utilizing algorithms, we can generate meshes that are free of triangle artifacts and adapt the resolution to suit the needs of the voxel field. Rendering a mesh into our signed-distance voxel field is a simple process. As long as we can determine the distance to the mesh’s surface (nearest triangle) and ascertain whether we are inside or outside, we can transform the mesh into voxels. This capability, combined with implicits and lattice structures, provides us with all the necessary tools to create sophisticated Computational Engineering Models (CEM).

One of the key advantages of working within a voxel field is the clarity and consistency it offers. The voxel field serves as a single source of truth, eliminating ambiguity or potential instability. At any point in the design process, we can examine the voxel field and confidently say, “This is how the final object will look.”

To make our geometry kernel even more powerful and versatile, we need to incorporate a few additional functions. One such function is the ability to combine multiple parts using Boolean operations. These operations include Add (combining all voxels), Subtract (removing voxels from another voxel field), and Intersect (retaining only the voxels present in both voxel fields).

Boolean operations in a voxel field are remarkably simple. By comparing the values of each voxel and its counterpart, we can easily apply the desired operation – Add, Subtract, or Intersect. This simplicity and reliability are in stark contrast to the cumbersome and error-prone nature of vector-based Boolean operations commonly used in CAD.

The decision to use voxels as the base geometry representation stems from their inherent suitability for Boolean operations. These operations, known for their complexity and potential failure in vector math, always work flawlessly in voxel fields.

This reliability and stability are essential in the construction of a robust geometry kernel that supports complex engineering models. Booleans allow us to seamlessly fuse individual base geometries, forming the foundation of computational modeling. And most importantly, they must never fail.

As we continue to unlock the full potential of our geometry kernel, there is one more crucial function to address – offsetting. Offset vector geometry plays a vital role in Computational Engineering, particularly in creating shells and outer structures. By incorporating Boolean Subtract, we can accurately produce intricate designs that meet specific requirements.

At Leap71, we are constantly pushing the boundaries of what is possible in Computational Engineering. Our commitment to leveraging the power of implicit functions, voxel fields, Boolean operations, and offsetting allows us to create complex and precise engineering models.

Join us in the next part of this blog series as we explore further advancements and innovations in this exciting field.

Why Computing with Voxels is the Future of Engineering

In the world of engineering, there are often complex edge cases that make it difficult to achieve desired outcomes. However, when it comes to offsetting a voxel field, things become much simpler. You can easily examine each voxel, consider its neighboring voxels, and execute a few operations. These operations are always local to the voxel in question, and they never fail. Contrast this with the process of creating a shell of an object in a CAD program, which can be a surprisingly challenging task for even a moderately simple object.

Let’s take a closer look at how voxels make computational engineering much more feasible. To begin, you start by creating the inside of the object using a mesh, lattice, or implicit representation. This inside can be as complex or as simple as you want it to be, as voxel geometry complexity is irrelevant. Once you have the inside, you perform the offset operation to generate a larger version of the object. Finally, you subtract the smaller object from the larger one, effectively hollowing it out to create the desired shell. The beauty of this process is that it can be easily accomplished with voxels, whereas it would be far more challenging in a CAD program.

So why are voxels so powerful? The answer lies in their inherent reliability. When you have a robust implementation of a voxel-based computational engineering kernel, you can rest assured that the base operations will never break your geometry, unless there is a bug in the code. This is because the mathematics behind voxel operations are quite trivial. As a result, voxels provide a solid foundation upon which you can build more complex engineering solutions without worrying about fundamental failures.

To illustrate the potential of computational engineering with voxels, consider the case of Josefine, who last year created arguably the most complex 3D printed object ever built. This feat was made possible because voxels never fail. The ability to work with voxels allowed Josefine to push the limits of what was thought to be achievable in 3D printing.

In conclusion, the advent of computational engineering using voxels opens up new possibilities in the field of engineering. By leveraging the simplicity and reliability of voxel operations, engineers can tackle complex problems with ease. With a robust voxel-based computational engineering kernel, the focus can shift to higher-tier tasks, knowing that the foundation is solid. As we continue to explore the potential of computational engineering, it’s clear that voxels are here to stay.

Editor’s note: This blog post is part of a six-part series introducing the new concept of Computational Engineering being developed by Leap71. To read the other parts of the series, click on the links below:

– Fundamentals of Computational Engineering: Prologue

– Fundamentals of Computational Engineering: Part 1 — A Bit of History

– Fundamentals of Computational Engineering: Part 2 — The Technology

– Fundamentals of Computational Engineering: Part 3 — Voxels to the Rescue

– Fundamentals of Computational Engineering: Part 4 — Implicits

– Fundamentals of Computational Engineering: Part 5 — All You Need is a Few Functions

Original source


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