Simanaitis Says

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GMAX, THE SCHMID LSR—AND SET THEORY

DO YOU remember set theory? This amalgam of logic and geometry is fundamental to mathematics and was part of The New Math of the 1960s. Do you remember New Math? This educational reform was inflicted on several generations of kids, alas, often with little rational understanding on the part of its inflictors, er… educators.

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GMax screen for the Schmid LSR.

But, wouldn’t you know, set theory is also at the heart of GMax, software used to build my computer model of yesterday’s Schmid Land Speed Record car (http://wp.me/p2ETap-2bC).

Other GMax models of mine have also appeared in Vintage Aero items at this website (see, for example, http://wp.me/p2ETap-1nY).

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The 1909 Goupy II, modeled with GMax for Microsoft Flight Simulator.

There are other software packages for building and importing virtual aircraft and scenery into Microsoft Flight Simulator. I prefer GMax because it and its necessary links to the sim were included in several versions of Microsoft Flight Simulator. These days, GMax software is available free, albeit with support only for download and registration, from www.turbosquid.com/gmax.

GMax is a simplified version of 3ds Max, full-blown computer graphics software from Autodesk Inc. The company (www.autodesk.com) also makes AutoCAD and other computer-aided design tools employed by a variety of architects, designers and engineers.

Once matters of setup, file definition and background images are addressed (no trivial feat), the basic GMax techniques involve click-and-drag creations of box, sphere, cylinder, torus, plane, cone, geodesic sphere, tube and teapot.

Why a teapot?

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A GMax teapot.

A teapot’s lid, handle and spout contain an interesting variety of shapes. When computer graphics packages are compared, a common challenge is “Show me your teapot.” It’s something of an inside joke that GMax includes the object as a click-and-drag Primitive Shape.

Modeling the Schmid LSR’s cabin is a good example of GMax capabilities and a fine application of set theory.

Essentially, the cabin is a tube for the cockpit and canopy, together with a tapered nose.

GMax offers an abundance of ways to model any particular shape, but there’s usually a most efficient one. Here, the nose is part of a sphere with its elements coaxed into a point.

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At left, the nose begins as a portion of a sphere. Center, the GMax process of Soft Selection molds it into shape. Right, the cockpit and canopy begin as a tube.

A lot of GMax modeling involves moving an object’s vertices in what’s called Editable Mesh format. Soft Selection, for instance, allows controlled deformation of chosen vertices with a straightforward click-and-drag.

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GMax Attach combines the two elements into one, though it’s still cylindrical.

Next, the cabin is given its appropriate shaping in side, top and front view. A Scale process reshapes chosen vertices in one or two dimensions.

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From left to right, the modeled cabin’s side view, top view, front view and in perspective, after multiple Scale operations.

The cabin is now ready for some set-theoretic thinking and Boolean magic. George Boole, 1815 – 1864, was an English mathematician, philosopher and logician, best known for An Investigation of the Laws of Thought that define what’s now called Boolean logic.

The cockpit and canopy are formed in two separate Boolean operations, Subtraction and Intersection. In set-theoretic parlance, these are A−B and A∩B.

First, a canopy template is formed starting with a box.

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From left to right, a box is formed, and then its lower vertices are moved to model the cockpit/canopy separation.

Then the Boolean operation of “Cabin Minus Template” yields the cockpit.

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Voilà! In set-theoretic terms, Cabin – Template = Cockpit.

Next, another Boolean operation, this one “Cabin Intersect Template,” gives the canopy.

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More Boolean magic! Cabin ∩ Template = Canopy. Semi-transparency is a GMax materials option.

Last, the two objects (“Scenes” in GMax) are merged.

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Fini.

Our Schmid LSR cabin is fabricated.

All in good time-gobbling fun—with set theory tossed in for good measure. ds

© Dennis Simanaitis, SimanaitisSays.com, 2014

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This entry was posted on June 8, 2014 by in Sci-Tech and tagged , , , , .
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