Slerp with more than two points

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 differen开发者_StackOverflow中文版t 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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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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The problem I see is:

Slerp gives constant velocity. That is, a given increment in your interpolation parameter gives you the same distance on the sphere, regardless of where you are on the [0,1] range.

Unfortunately, because the sphere is curved, you can't do this for more than one interpolation parameter. Either you need to give up constant velocity, or give up interpolating with more than one parameter.

You may be able to find an interpolation function that isn't constant velocity that nonetheless satisfies your requirements. But because of the above problem, I don't think it will correspond directly and symmetrically to the 1-D slerp.