# Questions tagged [projection]

This tag is for questions relating to "Projection", which is nothing but the shadow cast by an object. An everyday example of a projection is the casting of shadows onto a plane. Projection has many application in various areas of Mathematics (such as Euclidean geometry, linear algebra, topology, category theory, set theory etc.) as well as Physics.

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### If $A\subseteq B$, then $B^{\perp} \subseteq \Pi(B\mid A^{\perp})$

Suppose A, B are closed linear subspace of Hilbert space, I want to show if $A\subseteq B$, then $B^{\perp} \subseteq \Pi(B\mid A^{\perp})$, where $\Pi$ is the projection operator. I'm not sure how to ...
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### Proving that cylinder-to-sphere projection is area preserving.

I was going through the textbook Computer Graphics: Principles and Practice, and in the chapter for light, it talks about how the projection from a cylinder to sphere is area-preserving. I was trying ...
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### Shadow a Cube with body diagonal along y axis

We have a cube with its body diagonal (greatest diagonal joining two opposite vertices) aligned along the y axis. Thus, the cube stands on one vertex with the opposite vertex directly above it. The ...
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### Orthogonal Projection in an Enlarged Hilbert Space

Let $(H, \langle \cdot, \cdot \rangle_H)$ and $(U,\langle \cdot, \cdot \rangle_U )$ be Hilbert Spaces such that $H$ embeds into $U$. Let $M$ be a closed subspace of $U$, and define $\mathcal{P}$ to be ...
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### Orthogonal projection of a double-sided cone onto a plane

I would like to solve the following problem: a double cone with vertex at the origin of coordinates (0, 0, 0) is given (See fig. 1). The blue cone is symmetrical to the yellow one w.r.t. the origin; ...
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### Orthographic Projection and Concentric Circles [closed]

Let $C$ be the bounded set of concentric circles centered at the origin. Let $r_n = \sqrt{\frac{n}{\pi}}$ for any integer $n \in [1, k]$ be the radius of the circle $C_n \in C$. Assume $C$ is a ...
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### Determine if point can be projected on any segment in polyline

I am trying to implement a script that determines if a series of points can be projected on any segment of a polyline. The projection must be exactly on the segment, not in the rest of the line ...
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### sum of projected area and a generalization of Oppenheim's inequality

From this post: In $\mathbb R^4$, let $U$ be a 2D plane, let $\pi_1$ be the projection from $U$ onto $xy$-plane and $\pi_2$ be the projection from $U$ onto $zw$-plane, then $\det\pi_1+\det\pi_2\le1$, ...
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