I would like to know if it is feasible to carry out operations on very high (at least 50+, and optimally 100+) dimensional convex hulls and/or vector set. If so, what is the go-to tool for each operation.
The only tools I am aware of are Qhulls and MATLAB's convhulln, which still calls Qhull according to link. I am not familiar with computational geometry, and, after doing some online searching, operations in high dimension all seem to be too complex in terms of computation, memory, or simply does not have a definite solution.
My expected inputs is a set of n-D vector points, S.
The operations include:
- Find a convex hull from S.
- Find the intersecting vector set between two vector sets.
- Determine if a vector point exists in a vector set S.
- Find an inscribed/circumscribed n-sphere of the convex hull found from vector set S.
- Find the volume of a convex hull formed from S.
(Edit: I will describe what I hope to achieve for each aforementioned operation below.)
Purpose: Be able to distinguish vector points that are not on the surface of a convex hull. Since they can be considered as "contained" and thus not as "expressive" as points on the surface.
Output: Anything with the property of "boundary" that can be used to check if a point exists within the boundary or find the intersection between two boundaries.Purpose: Be able to retrieve anything with the property of boundary between two convex boundaries.
Purpose: Be able to determine if a given point is contained in the boundary formed by the set of vector points.
Purpose: Find alternative ways to represent the space formed by the boundary formed by the set of vector points.
Purpose: Determine the "volume" contained by the boundary (spread of vector points).
Do solutions generalized to n-dimensional convex hull exist? If not, what dimension is more suitable for modern technology to deal with (I will lower the dimension of my data points)?
PS. I understand my definition of an "operation" may be too vague. Please tell me if further clarification is needed.