How Do I 3D Model This?

This is one of the most frequently asked questions I ever get during my classes and consulting training sessions. While the question is too general to answer in a single blog post, I will give you a general, high-level answer, looking at the forest, instead of the trees.

Divide and Conquer

Some projects, scenes or objects will be a 3d modeling challenge because of their size and complexity. Don’t worry. Take a step back and make a list of all objects and features you notice. Take another step in and break objects down to their simplest geometrical representations, such as a cube or box, sphere, wedge, etc.

Finite Element Analysis

If the previous suggestion wasn’t enough help, then it may be time to call FEA (technically it comes from Finite Element Analysis… jokingly and inspiringly here, it comes from FEAr NOT!). Simply keep in mind that perfection belongs only to God, philosophers or mathematicians. The rest of us mortals must simply be happy to approximate solutions, not necessarily get them exactly, perfectly right. In other words, Good Enough is good enough.

If you don’t have the exact measurements for an object or feature, then guess or approximate them. Part of the beauty of CAD is its forgiving nature. Things are NOT chiseled in stone. Therefore, go ahead and try something and fix it or modify it later as necessary.

Heisenberg Uncertainty Principle

Finally, if the first two suggestions fail to help, then it’s time we take a more scientific approach to the matter of 3d modeling. In the end, CAD in general and 3D modeling in particular is about tracking the location of matter in space.

Think of your 3d model as an ordered and trackable cloud of 3d points. Don’t think or worry about your project in terms that describe the object you are creating. Instead, think about the object in terms of the molecules or atoms that make up its visible surface, and track their location.

Put simply, the Heisenberg Uncertainty Principle states that we can’t express the “exact” location of subatomic particles at any given moment. We can only express a “probability” for their location. This is due to the fact that matter vibrates and subatomic particles such as electrons are constantly moving around. They don’t sit and rest that often. There is a way to artificially track the location of particles accurately, but doing so takes a lot of energy because you have to constantly re-evaluate the results. Likewise, having a detailed, accurate 3d model takes as much effort as the level of detail and “perfection” you want to achieve.

First Degree Linear Regression or Nth degree Approximation

Although the number of atoms or molecules in a give ojbect is finite, it can easily feel like it was infinite. Therefore, pick instead a practical number of points to track for each object. The number you pick will be a function or depend on the accuray and margin of error that you will want to achieve (see FEA above). The more points, and the more wisely spread out or strategically located they are, the better the quality of your approximation and the lower the error that will result.

If your budget allows it, you can use a 3d scanner to automatically capture a cloud of points that describes the object you want to model. The disadvantage of this approach is that it requires acess to the physical prototype or object you want to model. In some cases, such a prototype may only exist in your brain or your client’s imagination.

Either way, the method of linear regression allows you to create an approximation by taking points and finding a suitable line (first degree) or nth degree polynomial equation to mathematically describe the location of points. This is where NURBS (Non Uniform Rational Bezier Splines) come into play. Lines are too simplistic to describe certain objects. in those cases using curvy polynomial functions works much better. In fact, circles (roughly 2nd degree), cubic (3rd degree) are already pretty efficient methods.

Therefore, if standard solid modeling tools don’t work for you, look into the NURBS tools. In AutoCAD, look at the relatively recent LOFT command.


I hope this blog entry will be the cause for some thoughts that will help you deal effectively with your future 3D modeling challenges. If you have a 3d modeling challenge please feel free to contact me for help. If you’re in a philosophical mood and have time to spare, then think about and answer the question: “How many angels fit in a pin head?” and rejoice in the fact that your project, whatever it is, is not as difficult as the problem that philosophical question poses. Ask and you shall receive help. But make sure you ask the right question or you will certainly get the wrong answer.

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