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Technical Perspective: Linking Form, Function, and Fabrication

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"Computer graphics are pictures and movies created using computers." This opening sentence from Wikipedia's entry on computer graphics becomes increasingly outdated as graphics is about to close the loop between virtual and physical reality and from digital design to fabrication. Is this a new trend? Not quite, but the magnitude of the current development and the potential impact may be bigger than ever before.

Geometric modeling, a subfield of computer graphics, has been motivated by industrial needs at the advent of computer-aided manufacturing, aiming at increased productivity via a completely digital workflow from design to production. Research in geometric modeling has been highly successful in creating a huge variety of shape modeling functionalities for 3D-design systems. The possibilities for digital shape design are almost unlimited and highly effective for the creation of "pictures and movies." But did the field achieve the goals toward manufacturing? I am not convinced here, since purely geometry-driven shape modeling creates bottlenecks when moving toward engineering and fabrication.

Some of the problems are related to geometry representations. B-splines and subdivision schemes proved to be highly effective for freeform shape modeling, but the resulting digital models are not yet suitable for simulation. There are various reasons for this: The models are usually not watertight and need to be "repaired" in a time-consuming laborious process; for example, at surface/surface intersections. Moreover, the models are surface based. For simulation, one requires meshes, not just for bounding surfaces, but also for the interior. For the actual production, which often employs CNC machining of molds, there are further conversion issues since the machines are not capable of precisely following splines.

There are various efforts to change this picture: a prominent reaction from mathematics is "isogeometric analysis," which eliminates re-meshing by using the same spline-based representation for both modeling and simulation. However, the result of a simulation may reveal a design problem; for example, a mismatch of form and function, or the presence of geometry, which contradicts a certain manufacturing process or material behavior, requiring changes to the design. To avoid such costly feedback loops between design, engineering, and fabrication, research in computer graphics has recently tried to incorporate key aspects of function and fabrication into an "intelligent" shape modeling process. This is not easy at all, since one wants to achieve interactivity of the modeling tools, but at the same time satisfy numerous constraints.

A great example for this trend is depicted in the following paperit couples shape and function and results in unexpected, almost miraculous behavior of objects. In the present case, these objects are toys, namely spinning tops or yo-yos of nearly arbitrary shape. However, the research is far deeper. It merges the previously mentioned research focus with another hot topic of research: Additive manufacturing (AM). With AM, geometric complexity comes almost for free. Here, complexity is not restricted to the outer surface, but also applies to the interior of an object. This is in perfect harmony with the goals of the highlighted article: Compute and fabricate the interior of an object so that it possesses perfect spinning properties. Mathematically, one "just" has to get right a few integrals over the entire body, namely the ones that determine barycenter and moments of inertia. While this can be nicely cast into an algorithm, one cannot ask a designer to care about such properties. It is basically impossible to model a non-rotationally symmetric object with great spinning behavior with any of the available modeling systems. We have here an excellent example for "computational fabrication." Computation not only accelerates the design and fabrication process, but in fact is the only way of creating such objects.

This is a step in a new direction, namely the exploitation of the nearly unlimited design space for objects fabricated with AM. Computer graphics is about to take a leading role in AM research, including the authors of the following paper. I just mention here work on "geometric materials," which act in a surprising, predefined way, or on the design of musical instruments of unconventional shape. A related classical topic is "topology optimization," where one optimizes the interior of objects so that minimal material usage results in sufficient strength to resist predefined loads.

Finally, let me point to work on the much larger architectural scale. A recent direction of research, called "architectural geometry," aims at making geometrically complex architectural structures affordable through novel computational tools by linking design, function, and fabrication. Substantial contributions to this field, for example, on self-supporting freeform structures, have also been made by some of the authors of the following paper (in cooperation with Philippe Block;

Computer graphics is a field where technology meets design. We are in strong need for this type of research, on all scales, from the micro-level of material behavior to the macro-level of buildings or even entire cities.

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Helmut Pottmann is a professor of applied geometry at Technische Universität Wien, Vienna, Austria.

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