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The correct way to interpolate between two points on a sphere is using slerp.
How would one interpolate between more than two points on a sphere? So summing a set of points with different weights on the surface of a sphere?
Simply summing the points multiplied by their weights and then normalising the result is not accurate enough when the angles are large. We need 'true' spherical interpolation.
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3 hours before bed: No more food or alcohol. 2 hours before bed: No more work. 1 hour before bed: No more screen time (shut off all phones, TVs and computers). 0: The number of times you'll need to hit snooze in the AM.
Your body temperature decreases, your eye movements stop, and your heart rate and muscles continue to relax. Your brain waves briefly spike then slow down. During a night of sleep, you spend the most time in stage 2.
Some people find that biphasic sleep feels natural and works great for them, while others feel better on a monophasic sleep schedule. There is historical evidence that humans used to naturally follow a biphasic sleep schedule. Research has also proven the benefits of a short, midday nap.
Completely exhale with a whoosh sound, then inhale through your nose to a mental count of four. Hold your breath for a seven count. Exhale through your mouth with a whoosh sound for a count of eight. Repeat this cycle three more times.
I asked this question on math.stackexchange.com, and someone found a paper that describes exactly this. Here it is: Spherical Averages and Applications to Spherical Splines and Interpolation
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