Unity3D Math Sims w/Companion 
Wolfram Notebooks 
for Active Learning

Jay Alan Jackson, Rochester Institute of Technology

(RowDefault[, (Spacer1), , (Spacer1), ])  #WolframTechConf

ABSTRACT

This talk will present four Unity3D Math Games/Simulations with companion Wolfram Notebooks, the development of which is  ongoing.  The potential for melds such as these to evolve into active learning resources for science education will be explored.

Instruments of Ingenuity

This simulation/game features Ingenuity, NASA’s dual rotor helicopter designed to hover in the thin atmosphere above the Mars landscape.  The companion Wolfram Notebook provides programmable controls and instrumentation to study the craft’s motion while conducting experiments with parameters such as blade rotation rate/lift and steering, affecting its position, velocity, and orientation.

Key topics to be explored in this sim: rotation matrices, yaw, pitch, roll, Euler angles, quaternions, vector representation of physical quantities, projection, local/global coordinate systems.

RozXy, the Figure Sk8ing Robot 
 “a new kind of etch-a-sketch”

For this simulation/game, players choreograph RozXy, a robotic figure skater constructed out of geometric primitives, to accompany some favorite tune or expressive rhythmic patterns.  The resulting curve, referred to as a “groove graph” can then be played back and analyzed as a 3D space curve, where the up axis is time.  

In a manner similar to the way that multitrack recordings are produced, additional moves (or a dance partner), sounds, and audio/visual effects can be mixed in.  I dub this process “mapping notable facets of musical numbers and festooning tunes”.    

Key topics covered in this sim: parametric curves, osculating circles, curvature, arc length, tangential and normal components of acceleration, center of mass and moment of inertia.

Perseverance on a Mars Surface Surveying Mission

This game/simulation provides the player with the means to procedurally generate terrain, upon which the rover then roams about searching for distinctive topographical and geological features.  
 
Key topics covered in this sim: surface normals, tangent planes, gradient, local max/min, contour plot/level curves, projections

CALIPSO (with an I) in the sky

In this game/simulation, players investigate the details associated with the motion of this satellite and produce various visualizations of it.  For example, the paths over a 24 hour period, during which time it makes 16 polar orbits, which can be charted as shown below.


Key topics covered in this sim: spherical coordinates, rotation & revolution, mapping, projection, octahedron tessellation.

There are many other possibilities to go beyond the aforementioned exercises:

Determine how to rotate the solar panels, so as to maximize their exposure to sun

Produce a more accurate simulation of CALIPSO’s path, engineered to cover much more of earth’s surface area, as shown here:



Include the other 6 satellites in the so-called “A-train” as shown here:



Analyze/visualize some of CALIPSO’s actual atmospheric data available from NASA

Devise methods to display both earth and satellite using accurate representations of relative sizes and orbital radius.

Conclusions

UnityLink offers a largely unexplored capability for combining the Unity Game Engine with Wolfram Notebooks, with a potential to provide engaging graphical math/physics simulations for active learning.

Questions ?

Please contact me at :  jajvks@rit .edu

Thanks for coming today!