# Questions tagged [projective-geometry]

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

2,280 questions
Filter by
Sorted by
Tagged with
1 vote
29 views

• 25
36 views

18 views

### Geometric Configurations: Product identity

Wikipedia states that A configuration in the plane is denoted by $\left(p_{\gamma} \ell_{\pi}\right)$, where $p$ is the number of points, $\ell$ the number of lines, $\gamma$ the number of lines per ...
1 vote
94 views

### Projective Mapping of translated Quadric

Question I have an ellipsoid described by a covariance matrix $\Sigma \in \mathbb{R}^{3\times3}$ and its centroid location $\mu \in \mathbb{R}^{3}$ (yes; notation from statistics as I want to ...
• 69
1 vote
44 views

### Non-singular Conics are equivalent to some projective line.

The proof begins on pg.22. I am having trouble understanding why ${B|}_{W_y} \not\equiv 0$. Since I couldn't understand this part of the proof (on pg. 24 of the slides), I was trying to show it ...
• 1,240
1 vote
25 views

### A question regarding to the Wikipedia definition of homography (or projective transformation).

According to the section Definition and expression in homogeneous coordinates of this Wikipedia article, we get \begin{align} y_1 &= \frac{a_{1,0} + a_{1,1}x_1 +\dots + a_{1,n}x_n}{a_{0,0} + a_{0,...
• 1,240
27 views

18 views

• 1,072
27 views

### Find a rational parametrization of an affine conic section

Question: construct a rational parametrization of an affine conic $$-12x^2 - 44xy -65y^2+10y-1=0.$$ My ideas: say $y = t(x+1)$ and substitute into equation.
25 views

### Find fixed point of involution of complex projective line

Question: Find fixed points of involution g: $P_1(C) -> P_1(C)$, $g^2$ = Id, if g(2/3) = 3 and g(-2/3)= 1/4 My ideas: to use cross-ratio, maybe we can say g(3) = 2/3 and g(1/4) = -2/3 so we can ...
25 views

48 views

### Rigorously working with flat limits: lines meeting a curve by specialization

I am trying to get comfortable with flat limits. This question is motivated by Section 3.5.3 of Eisenbud and Harris's '3264 And All That' and Exercises 3.35 and 3.36. This section and the surrounding ...
• 2,742
47 views

### Rational Bézier Curves are projectively invariant

I want to prove that a Rational Bézier Curve is not only affine invariant but also a projective invariant. By affine invariance i mean that applying an affine map to the curve is the same as applying ...
28 views

### Calibrating a pinhole camera (finding $z_0$)

A pinhole camera is a very simple theoretical device for generating perspective images on a plane that a distance $z_0$ from the pinhole (a point) and whose normal vector is the direction vector at ...
• 10.1k