dataengine

[dataengine-blog]

Cartesian Product

I had a confusing situation recently. A colleague said a sql cross join would produce a cartesian product. Just checked it with Wolfram Mathematica. He appears to be right. Going to show him tomorrow: 

Wolfram Mathematica

SQL Server 

I don’t know how about you. But I blindly trust Mathematica. Normally if it gives me something unexpected I find an issue with my input...

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And here is a very first prototype being printed assembled and running...

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Some days ago, I've decided to do something more out of the small servo which I've connected to Mathematica on my IMac. Today I finally had a first useful mount for my IPhone which ideally should allow me to use the servo for rotating the phone during taking pictures or video. The very first prototype is above.

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Here you see Mathematica steering Arduino. A random sample function chooses an integer within a range between 1 and 180 and sends it to the Arduino Uno via serial. A driver compiled on the Arduino composes the integer from a series of ASCII values and drives the servo. Servo is steered by Servo class (s. Arduino documentation). To set up your mac Mathematica please have a look at the guide written by William J Turkel. His blog page was very helpful to make Mathematica communicate via serial with Arduino.

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Finally found some time to play with Mathematica. Really nice. 

Here is something to warm up:

A dice with some thousand polygons as GraphicsComplex. Quickly designed with a CAD program. The dice is not complete. I didn't want to spend too much time for preparations.

81 affine transformations. 

A bit more then one second computing time on one core.

The result is rotating above...

Mathematica code: 

Dice = Import["/Volumes/STORE N GO/Dice.3ds", "GraphicsComplex"]; frame[t_, x_: 1, y_: 1, z_: 0] :=   Style[Graphics3D[{EdgeForm[None],      GeometricTransformation[Dice, RotationTransform[t*Pi/8, {x, y, z}]]},     Boxed -> True, ViewPoint -> {Pi, Pi/2, 2}, PlotRange -> All,     ImageSize -> {600, 600}], Antialiasing -> True]; frames = Monitor[Table[frame[t], {t, 0, 16, 1/6}],    ProgressIndicator[t, {0, 16}]]; FileName = "Dice3D.gif"; Export[FileName, frames, Antialiasing -> True, "RasterSize" -> 1200,    "ImageResolution" -> {1200, 1200}]; // AbsoluteTiming SystemOpen[DirectoryName[AbsoluteFileName[FileName]]];