Fighting with spherical coordinates Simon Strange Pipeworks

1. Fighting with spherical coordinatesSimon StrangePipeworks

7. The Point of all this: Some concepts we’ve already learned could be giving us new and important insights into the problems we’re solving.

8. Backing Up!

9. Backing Up! (Who is this guy?)

10. Simon Strange

11. (Shameless Plug)

14. Surface Warfare

15. Surface Warfare • ASMD

16. Surface Warfare • ASMD • Sensors & Signals

17. Surface Warfare • ASMD • Sensors & Signals • EW Softkill

24. Spherical Coordinates! (finally)

26. (R+h)^2 = R^2 + d^2 (R+h)^2 = R^2 + 2Rh +h^2 d^2 = 2Rh + h^2

27. Standard distance (collision) check: d^2 = (x-a)^2 + (y-b)^2 + (z-c)^2

29. Great Arc distance between two points on a unit sphere: s=rcos^−1(cosθ1cosθ2 + sinθ1sinθ2cos(φ1−φ2)).

31. For a point (r, q, j)

32. For a point (r, q, j) j Provides a linear translation of distance, measured in radians.

33. For a point (r, q, j) j Provides a linear translation of distance, measured in radians. j IS the distance!

35. Our goal : find a simple rotational transformation which can be applied efficiently to all points, such that an arbitrary point moves to the North Pole. If successful, we can order all objects by f coordinate, to determine visibility by distance.

36. For a point (r, q, j)

37. For a point (r, q, j) q Provides a linear translation of distance, measured in radians.

38. For a point (r, q, j) q Provides a linear translation of distance, measured in radians. q IS the distance from prime meridian!

40. Rodrigues' rotation formula:

41. Rodrigues' rotation formula: 0

42. The Point of all this: Some concepts we’ve already learned could be giving us new and important insights into the problems we’re solving.