Is there any study of intersections of hyper-ellipsoids, i.e. the condition of intersection of 4 surfaces embedded in four-dimensional Euclidean space and given by the equations $\sum_{a=1}^4 (x_a-t_a)^2/r_a^2=1$?
Very broad question. Topics: Generalizations of Bezout theorem . Warning: real version is different from the complex (or any closed field). Intersection numbers is broader topic.
Dear Svatopluk, thank you for your answer. My aim is very pragmatic. I have four hyper-ellipsoids with parallel axes, which are given by their algebraic equations. I want to know how they intersect. In fact, I want to have the criterium for that they intersect by exactly two points (call it minimal intersection).
This but add more dimensions: http://stackoverflow.com/questions/2945337/how-to-detect-if-an-ellipse-intersectscollides-with-a-circle
Dear Lucas, thanks for your contribution too. Here I am mainly concerned with analytic tools to solve the problem. However, your link was useful to see that I am on the right track.
- Badges
- Science topic
- Similar topics
- Medical Science Nursing
- Dissertations