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.
Questions tagged [ellipsoids]
202 questions
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Ellipsoid definition
One of the definitions of an ellipsoid in Boyd & Vandenberghe's Convex Optimization is
$$E = \{ x_c + A u : \| u \|_2 \leq 1\}$$
where $A$ is square and non-singular. It is also stated that if $A$ is singular, then we get a degenerate ellipsoid.
Can…
Cherryblossoms
- 917
2
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formula for segment of an ellipsoid
I'm an artist trying to sculpt shapes that I would describe as ellipsoids. I am wanting to sew together fabric to form these shapes, and although I know the dimensions of the ellipsoid I want to form, I don't know how to calculate the curvature of…
kris
- 21
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1 answer
Orientation of ellipsoid after a matrix $T$ act on a sphere described by all the unit vector $\vec{x}$?
I had this problem when I read this paper. It states that(around eq.(1)) for all the vectors $\vec{x}$ in the unit sphere, $T\vec{x}$ will lead the unit sphere into an ellipsoid if $T$ has full rank where $T$ stands for a $3\times 3$ matrix. And the…
narip
- 67
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1 answer
How to derive the parametric equations of the intersection curve of cylinder to ellipsoid
If person wants to derive the intersection curve of the rotated cylinder with offset to ellipsoid $x^2/a^2 + y^2/b^2 + z^2/c^2 = 1$.
The equations of rotated cylinder around $y$ with angle $\phi$ plus offset $x0$ as follows.
$x=r*\cos(\theta) +…
John Wang
- 19
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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. $\frac{x^2}{a^2} + \frac{y^2}{b^2} + \frac{z^2}{c^2} = 1$ and several vectors $v = (v_1, v_2,…
MaD
- 3
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2D projections of n-D hyper-ellipsoid in matrix representation
I have a hyper-ellipsoid defined as the transformation of the unit ball:
$$
\mathcal{E} = \left\{ T x + d \mid \left\Vert x \right\Vert_2 \leq 1 \right\}
$$
where $T \in \mathbb{R}^{n \times n}$ is symmetrical and positive definite and $d \in…
cedi123
- 11