In traditional CAD environments, geometry can be defined and represented in more ways than one. If you have ever used a 3D modeling program, you’ve most likely worked with meshes, BReps, or both, depending on the task at hand. Although meshes and BReps have their strong points, their weaknesses rear their head as product geometry becomes more complex. Managing the size and performance of complex geometry requires a computationally lighter means of defining and representing geometry. By integrating a field-driven design approach based on the implicit modeling technology, designers can focus on engineering work that matters, and spend less time with non-value-added tasks.

Implicit Geometry

Implicit modeling is a powerful way to define, change and represent 3D geometry. Geometry is defined through equations in such an approach, rather than through a network of vertices, edges, and faces like meshes and BReps. This means that implicits are significantly lighter to compute and maintain their pure form because they are not discretized like meshes and BReps, which don’t always capture continuity perfectly.

For instance, mesh geometry, regardless of its resolution, is a faceted representation of the actual form. At some point in the design-to-manufacturing pipeline, some form of discretization will be required, whether it is through meshes, BReps, or producing slice data for additive manufacturing (AM). By discretizing data from implicit models directly to a manufacturing-ready output, the discretization occurs at the very end of the process instead of at the beginning or throughout. This means that outgoing manufacturing data is more precise. In addition to being orders of magnitude faster to compute, implicit geometry also results in super-lightweight files, as only a minimal amount of information is needed. 

Shown above is a mesh representation compared to an implicit representation of a sphere. In this example, the mesh face count of the sphere is purposely low to exaggerate the discretization. Note, that if the mesh face count was significantly increased to more accurately represent the sphere then file size would also increase, which is problematic for design and analysis. (Image Credit: nTopology)

Rather than discretizing implicit geometry, sampling and previewing geometry through “shaders” is a form of rendering that enables users to quickly view geometry at very low or very high resolution, while also leveraging a computer’s graphic processing unit. This improves speed while accurately representing geometry. (Image Credit: nTopology)

Understanding Fields—an analogy taken from the weather

Field-driven design is an empowering concept that builds upon implicit modeling. It has several benefits to end users and organizations, such as increased flexibility and efficiency of design. To better understand the concept of fields, let’s first explain how it works by using weather as an analogy.

Imagine driving along the east coast of the United States from Florida to Maine, with the goal of finding optimal places to camp along the way based on simple weather data. At each mile, using a weather app, you could sample information such as temperature, wind, humidity, visibility and air quality. Each information type, such as temperature, is continuous, meaning it is everywhere. This is a field, and you can sample this temperature field and all other weather fields at every mile, half-mile, yard, foot, inch, etc. The key takeaway is that we can use one type of weather data or combine all of it to inform our decision on where to camp. In a similar way, fields representing different types of data such as distance, force, or velocity values can be used and even combined to enhance implicit geometry for optimal performance.

Although many different types of data can be converted into fields, we’ll only focus on distance fields, since they are the first type of field you’ll encounter in a computational modeling platform. When creating models through a visual programming interface, the output is more than just the representation of implicit geometry. Under the hood of each implicit operation resides an equation that outputs the distance values to the boundary of the geometry.

Like temperature in our environment, distance data is everywhere. It can be sampled at very large or very small increments from any height or depth in any axis. It is everywhere. Why are these distance values relevant to the representation of geometry? Distance values that equal zero define the boundary of geometry. Negative distance values define what is inside, while positive values define what is outside.

An example of distance fields, sampled at the cross-section of a sphere, torus, and cube. Values beyond the boundary of each primitive are positive, while values internal are negative. The radiating white lines represent the resolution at which the distance field is sampled, in this case, every 2 millimeters. (Image Credit: nTopology)

Distance Fields for Modeling Operations

Other than the zero values that define the boundary of our geometry, how can the positive and negative values of a field be utilized? Imagine wanting to offset a sphere. We now know that the boundary of the sphere is composed of zeros. If we wanted to offset the sphere by one millimeter, we would need the zero values to be one millimeter away from where they are currently.

Boolean operations are some of the first commands any designer or engineer learns when introduced to 3D modeling. But as we become more skilled, we notice that these commands become more volatile as geometric complexity increases. When Boolean-unioning one mesh with another, two networks of vertices, edges, and faces are recalculated into one new network.

When Boolean unioning two mesh spheres, a new network of vertices, edges, and faces is formed. This network is composed of network geometry from each original sphere and new geometry in order to connect the two. (Image Credit: nTopology)

Combining two simple mesh geometries is easy, but performing this operation among complex mesh parts such as lattices most certainly results in a failure at some point. However, implicit modeling treats these problems entirely differently and they never fail. Computing the Boolean union of two geometries implicitly is just a matter of extracting the minimum values of two overlapping distance fields. Inverting this condition to extract the maximum values between the two fields will result in a Boolean intersect.

Left: The Boolean union of two fields extracts the minimum values between two fields. Right: The Boolean intersect of two fields extracts the maximum values between two fields. (Image Credit: nTopology)

Innovative Design for Manufacturing

Just as weather data can determine camping conditions, distance fields determine the result of modeling operations such as Booleans, offsets and fillets, to name a few. Engineers and designers using a field-driven approach to driving implicit models are freed from frustrating manual setup, rework and data repair, and have the ability to fine-tune and control their data.

They can focus on creative, breakthrough designs with a smooth pathway to manufacturing. From modeling to simulation to manufacturing, fields are ever-present in core workflows and enable designers to drive geometry with layers of synthesized data. The outcome can be products with highly complex features and characteristics yet with more reliable, robust performance.

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