# Questions tagged [ellipsoids]

An ellipsoid is a convex set defined by $\mathcal{E} := \left\{ x \in \mathbb R^n \mid (x - x_c)^T P^{-1} (x - x_c) \leq 1 \right\}$ where matrix $P$ is symmetric and positive definite.

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### Smallest N-dimensional ellipsoid containing a given ellipsoid and a point

Warning: I am not a mathematician, so excuse me if the problem at hand seems trivial or incomplete. So, I am working on the following problem: I have to find the smallest (i.e smallest volume) N-...
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I'm wondering whether equations like $x^2 + y^2 = 4$ can describe a function or not. The reason is that a function should normally link every input value to a single output value. However, in case of $... • 123 1 vote 1 answer 131 views ### Determine an ellipsoid from$3$perspective images of it There is an ellipsoid of unknown dimensions and unknown orientation hanging somewhere (also unknown) in$3$-dimensional space. You are given three perspective images of it from three distinct ... • 17.3k 1 vote 3 answers 114 views ### Equation of a cylinder with a profile / ellipsoid I have a geometry of a cylinder that is curved along both the lengths where there is generally a height of a cylinder. I am aware of the equation of a cylinder. I wanted to know what could the ... 1 vote 0 answers 29 views ### Immersed volume calculation Im trying to solve the following problem : Given the ellipsoid represented by the matrix$\widehat{A}$and knowing the coordinates of each point A,B,C,D,E,F,G,H, calculate the volume of intersection (... • 123 0 votes 1 answer 86 views ### An integral Identity about the Elliptic Integrals and Ellipsoids I was reading this article: https://webspace.science.uu.nl/~maas0131/files/MaasJCAM1994.pdf I came to the equation (24): The author says... "We thus find, by the same argument,":$$\int_0^1 ... • 7,805 1 vote 0 answers 151 views ### Geodesic curve on an ellipsoid I cannot find my mistake in the statement below, neither computational nor conceptual. I cannot prove that the velocity vector$\dot{x}$is constant along the acclaimed geodesic. Could you review it ... 0 votes 1 answer 112 views ### Simulation and fitting 3D ellipsoid I would like to simulate ellipsoid fitting. In the first step I had ellipsoid with centre in 0,0,0 with specific length of axes a, b, c described by eq.$\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{...
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I'm trying to figure out the smallest enlargement factor which I need to apply to one ellipsoid $E_1$ in order to fit another one $E_2$. Precisely, let $E(c, S) := \{x | (x-c)^T S (x-c) \leq 1\}$ be ...