# Tagged Questions

Projective geometry is closely related to perspective geometry. These types of geometry originated with artists around the 14th century.

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### Finding the Transform matrix from 4 projected points (with Javascript)

I'm working on a project using Chrome - JS and Webkit 3D CSS3 transform matrix. The final goal is to create a tool for artistic projects using projectors and animation - somewhat far away from using ...
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### The intersection of two parallel lines

My teacher told me that two parallel lines have a point of intersection, it is called Point at infinity. But I I can't understand how it can be true or how was it proved, can someone explain this to ...
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### Help understanding Algebraic Geometry

I while ago I started reading Hartshorne's Algebraic Geometry and it almost immediately felt like I hit a brick wall. I have some experience with category theory and abstract algebra but not with ...
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### Problem in Deducing Perspective Projection Matrix

I understand the traditional way(use similar triangle and make depth value linear) to deduce the perspective projection matrix. But I want to try another approach after I read this text: Fundamentals ...
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### Number of ways of coloring projected faces of any hypercube

EDIT: This is the concrete problem in its current state: How many ways are there of separating a figure consisting of $l$ layers of squares with connected vertices (as the one seen in Fig. 5, for ...
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### Analytically flavored book in projective geometry

I am looking for a book in projective geometry, using the apparatus of linear algebra, complex analysis, and, perhaps, modern algebra, in full. The counterexample is the Hartshorne's book on ...
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### Equation for non-orthogonal projection of a point onto two vectors representing the isometric axis?

Suppose I have two vectors that are not orthogonal (let's say, an isometric grid) representing the new axis. Suppose I want to project a point onto these two vectors, how would I do it? Dot product ...
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### The Process of Choosing Projective Axes to Put an Elliptic Curve into Weierstrass Normal Form

I'm reading the book "Rational Points on Elliptic Curves" and on page 23 the author takes an arbitrary (non-singular) elliptic curve in the projective plane and finds a rational point $O$, referring ...
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### Plucker's $\mu$

In Jürgen Richter-Gebert's book "Perspectives on Projective Geometry", he talks about Plucker’s $\mu$ in Section 6.3. He says that this trick was used by Plucker quite often. Plucker's trick involves ...
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### Manifold over a Finite Field

I'm trying to either associate a manifold with a finite field, or, ideally find a way of considering finite fields as manifolds, in a non-trivial manner. I hope to be able to use this to extend ...
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### Computing the properties of the 3D-projection of an ellipse.

I have an ellipse that is rotated around the white axis (see image below) in 3-dimensional space by an angle α. The axis passes through the perimeter and one of the ...
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### 4D to 3D projection

Im trying to calculate the position of 4D point in 3D world. I started with 2D and tried to extend it to the 3D and then to 4D. Firstly, I found out that its easy to calculate the projected position ...
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### Distinguished open sets in $\mathbb{P}^n$

I have given a homogenous polynomial $F\in\mathbb{C}[x_0,\ldots,x_n]$ of degree $d>0$ and consider the open set $U_F=\{p\in\mathbb{P}^n; F(p)\neq 0\}$. I'd like to prove that $U_F$ is isomorphic to ...