Natural forms
By: Tim Foldy-Porto
Tags: 3d Modeling, VR, AR, Extended Reality, Haptics

A procedural landscape rendered in Terragen.

While programs like Rhino, AutoCAD, Solidworks, and Maya (among others) deal with content that we think of as 3D, every representation of and interaction with this content happens on a 2D screen. The software programs mentioned above differ in the way they allow users to convert 2D actions into 3D actions. Users of Solidworks are accustomed to extrude and cut operations, wherein a 3D form is created by sweeping a planar sketch along a path normal to the sketch plane. The most complicated operation I’ve used in Solidworks is the loft feature, which, while sweeping a sketch, varies its cross section. The resulting form is somewhat more complex than an extruded box, but it still contains a cross section parameterized by distance along the sweep path. In other words, it would be very difficult to create a fluffy pillow using Solidworks. Luckily for Dassault Systems, the makers of Solidworks, users of their programs are typically engineers, not animators or sculptors, and thus are happy to work with only fundamental forms.

For those who desire a less dimensionally-constrained workflow, there are programs like Rhino. As part of the customer research process, one question I like to ask is “how would you make a pillow in [insert their CAD program of choice]?” From what I’ve gathered, pillow-making in Rhino is done using lines swept into surfaces. While Solidworks deals primarily with volumes, Rhino works with surfaces. Instead of the planar sketch forming the basis of 3D form-creation, users of Rhino make 3D spline curves and then loft those curves along some other path through 3-space (pardon the jargon, my background is in physics). Mathematically, this works out to defining a parametric surface { x(t, s), y(t, s), z(t, s) } where t parameterizes a spline path at a given point along the loft path s.

Theoretically, this process of defining a surface allows users to create any 3D form their mind can imagine. In this case, however, the tractability of the desired form replaces the limitations of the interface as the bottleneck in the modeling process. Modeling something like a lumpy sphere is fairly straightforward: first, draw a circular arc from one pole of the sphere to the other; use control points to add a few bumps to the arc; define the loft path s to be a circle centered at the midpoint of the line between the two poles, normal to that line, parameterized by angle p; finally, have the amplitude of the bumps be some smooth function of p, with appropriate boundary conditions such that spline(p = 0) = spline (p = 2 pi). Boom, you have a lumpy ball — making a comparable shape with a Solidworks-type interface would be a nightmare.

However, say you dream a little bigger. Say you want to model a dusty old book, with the pages bent and wrinkled, half falling out. Now suppose that book had been resting on a small stone for a long time, so that gravity had induced some overall curvature in the shape of the book. Your mind can probably picture the form I’m describing, but could you model it in Rhino? Maybe, but it would be difficult. Decomposing such a form into curves that can be lofted requires a very experienced mind. For this reason, 3D modelers (myself included) tend to fall into the habit of reproducing the same forms over and over again. Why? Because these are the forms that 1) they know how to make, and 2) their software of choice allows them to make. These are what I refer to as natural forms, as they are a natural function of a given medium.

For example, the forms natural to Solidworks are perpendicular and rectilinear. In Rhino, we see hyperboloid surfaces over and over again, because they are easy to make. Natural forms exist not only in the digital world, but in the physical one as well. Forms that are created in marble differ from those created in papier-mache, simply as an artifact of the different way gravity affects these two materials. To artists who desire complete freedom, the existence of natural forms is a constant nuisance. A sculptor to whom I spoke expressed displeasure over the clumsiness of “clay modes” in current 3D modeling programs, on the basis that they made it difficult to create forms which would be simple to make with real clay. The problem, he thought, lay not with the representation of 3D data, but rather with the interface through which he communicated his artistic intentions to the software.

There exists a normalizing factor when things move to certain softwares. Forms become normalized, curves and surfaces become normalized. A canon of shapes emerges. This is a serious problem for artists who care about discovery and expression through form—for those who believe that everyone has a particular way of drawing or making, and that their personal style of engaging with material is irreplicable. When the medium of creation filters out idiosyncratic tendencies, an artist’s meaning and intention can be lost.

To others, however, the phenomena of natural forms is not inherently problematic. Something I’ve heard from several architects is that Rhino is good for architecture because it’s rational in the way that building materials are rational. What they mean by this sentiment is that the constraints imposed upon them by Rhino aren’t an issue because those are the same constraints imposed upon buildings by the laws of physics. The software forces them to think in a way appropriate for the discipline of architecture, and this results in buildings that can be physically constructed without falling over.

One architect I talked to described her encounter with the natural forms of Grasshopper, a mathematics-based extension to Rhino. Initially, she said, the architecture community was very excited about the program because it allowed them to create “really cool cell-like patterns that had a mathematical basis.” Such forms were previously constructible, but were most likely too difficult to model for anyone to seriously pursue them. Over time, however, these cell-like designs started to pop up everywhere. Architects could tell that a structure had been designed in Grasshopper simply by observing its form. At this point, she noted, some architects started to feel as if they had lost control of the tool, and that their artistic intent was being steamrolled by the natural forms of Grasshopper. Of course, Grasshopper is widely used today, so clearly this erosion of personal style was not a dealbreaker for the architecture community as a whole.

Looking to the future, I anticipate that a whole new class of 3D modelers will emerge. Up until now, 3D modeling has primarily been used as a step in creating physical objects. Architects and engineers have been able to save time and money by modeling forms on the computer before sending them to fabrication. With the rise of virtual reality, however, there is a growing demand for stand-alone 3D models—models that exist purely in the digital world. We’ve already seen a preview of these types of models from the video game and animation industries.

The key difference between what’s coming and what has been is scale. Video game artists and animators have been able to devote their time to crafting characters in meticulous detail because the worlds in which they work are limited in size. They haven’t had to create millions of characters, only hundreds. The environments they create haven’t been galaxies, only worlds. As the improvement in virtual reality technology increases our expectations of virtual landscapes, exponentially more 3D models will be required to keep up with demand. Right now, 3D artists can afford to spend a week on a single character. In the future, they’re going to have to churn out a character an hour.

You might be asking, isn’t this where automation comes in? Yes, to some extent. We’ve already seen procedural generation used to create armies of soldiers in the Lord of the Rings movies, and the landscapes in The Mandalorian. However, automated tools still require human direction. 3D artists of the future will still have to communicate their intentions to computers. No matter the software they use, natural forms will emerge. The question is, what do we want these natural forms to look like? And, more importantly, how does the answer to that question influence our design of 3D modeling software today?