CODEWITHSUNDEEP
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Franz R. A.
Franz R. A.

Reputation: 1

Projected Area calculation of a cube

I am working on measuring the projected area of a cube facing the sun for my spacecraft coursework. The cube is of 1x1x1 dimensions, and constantly rotates due to its orbit. Using a program called "STK", data for the angle shift according to a reference was obtained. So now I have the shift of orientation of the cube every 30 minutes but now I need to calculate how much of the projected area will be exposed to the sun (I can assume the Sunlight is coming from a single direction).

I need to be able to translate the coordinate shift in orientation of the cube to how much of a projected area will be facing the sun at each interval of time. Let me give you an example:

At the initial time, the cube is facing you (you are the sun...because you are my sunshine ;) ) and no shift has occurred, hence the projected area will be 1 m^2.

After 30 mins, there has been a shift only on the x axis of 45 degrees. Now the projected area is 1.4142 m^2 (since cos 45 * 1 = 0.7071 and now you have 2 faces facing you).

After 60 mins, only a shift in the y axis occurs (45 degrees). Now you have 3 partial faces of the cube facing you and possess a projected area of 1.707 m^2.

This isn't to hard to do with little shifts, but I need to do this for multiple (more than a 100 shifts). I am thinking of writing a python program that rotates a 3D object and measures the projected area at each interval. Any recommendations on libraries that allow 3D body definition and rotation? libraries that can measure areas of projected surfaces?

Upvotes: 0

Views: 740

Answers (1)

AirSquid
AirSquid

Reputation: 11938

  • Establish a unit vector perpendicular to each face of the cube. Depending on the output of your rotation program, you may be using angular rotations from the base axes or you can take vector cross product of 2 edges of face (be careful w/ right hand rule to ensure result faces outward)
  • take the dot product of each of the resultant 6 vectors individually with a vector "pointing to the sun"
  • drop any negative results (facing away from sun)
  • sum the remainder

Unit vectors will suffice because the surface area of each face is 1 sq unit.

Upvotes: 1

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