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Orbital Movement
There is an angle phi that is defined to rotate around z-axis [local system]. When it makes 360°, it will result in one complete rotation. It should be permanently increasing/decreasing, to simulate the motion.
The motion curve is described by 3 angles:
- alpha = yaw = rotation around x-axis [global system]
- beta = pitch = rotation around y-axis [global system]
- gamma = roll = rotation around z-axis [global system]
Global:
Global system is the world's normal axis system. It is constant, so x,y,z directions are always the same.
Local:
In this system the local system describes a 2D simple circle on its x-y-plane, meaning the z-coordinate is always 0.
Final Rotation + shift:
The final rotation is obtained by rotating the circle's local coordinate system around the global coordinate system. The shift from global origin is described by defined x/y/z center-coordinates.
Global system is the world's normal axis system. It is constant, so x,y,z directions are always the same.
Local:
In this system the local system describes a 2D simple circle on its x-y-plane, meaning the z-coordinate is always 0.
Final Rotation + shift:
The final rotation is obtained by rotating the circle's local coordinate system around the global coordinate system. The shift from global origin is described by defined x/y/z center-coordinates.
... in this system the actual axis rotations can be described by 2 things:
- Amplitude:
Describes the axis rotation, between 0° and 360°.
Technically, with only defining amplitudes you already can get all possible points on the sphere.
- Frequency Factor:
The frequency factor will result in pendeling the respective axis rotation between amplitude values.
Its actual value will always be somewhere from amplitude to -amplitude.- Factor = 0 → amplitude/axis rotation is constant
- Factor = 1 → amplitude/axis rotation equals phi_speed
- 0 < Factor < 1 → slower curves (with coming closer to 0 it gets slower)
- 1 < Factor → faster curves
Example:
We make alpha_amplitude 50° and make frequency factor 2.
Now the alpha rotation (x-axis) will go between 50° and -50°, back and forth, with factor 2, leading in 2x speed of a normal sinus curve.
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