0
votes
1answer
18 views

When are two 3D Lines parallel in Plücker matrix form?

When are two lines in 3 dimensional space parallel, when the lines are both represented by Pl├╝cker matrices $L$ and $L'$. I'm trying to prove the solution to this question: ...
0
votes
0answers
31 views

Rotation plane on the sphere (quarternion)

I asked similar question on stackoverflow but still no answers.http://stackoverflow.com/questions/25185329/image-rotation-with-the-gyro-data-math I assume it is more math than programming problem. ...
0
votes
2answers
18 views

Projection matrix to project a point in a plane

How to determinate the 4x4 S matrix so that the P gets projected into Q, on the XZ (Y=0) plane? Q = S P
1
vote
2answers
134 views

Transformation matrix from quadrilateral to rectangle

There exists a rectangle somewhere in space with some orientation. A camera from the coordinate center point is looking along the z axis and is seeing the rectangle as a quadrilateral (due to ...
0
votes
1answer
55 views

Projection Matrix between two Vectors

Given a two normal vectors v1 = [a1;b1;c1] and v2 = [a2;b2;c2] as given in Fig1. How I can derive the projection matrix that ...
0
votes
1answer
57 views

Which 6x6 line-matrix corresponds to a 4x4 point/plane-matrix

In 3-dimensional projective geometry I have a point-point map (collineation) $c$ with matrix $A$. Then $A^{-1t}$ is the matrix for the plane-plane map for the same $c$. These matrices are 4x4 and ...
3
votes
2answers
115 views

Proving algebraically that $\mathbb RP ^3\cong SO(3,\mathbb R)$

I am giving a simple introductory course on algebraic geometry and I plan to mention that $$\mathbb RP ^3\cong SO(3,\mathbb R).$$ I know a rather simple proof of this using the fact that $\mathbb ...
2
votes
2answers
376 views

Matrix projection on a cone

How would you project a symmetric real matrix onto the cone of all positive semi-de finite matrices?
3
votes
1answer
54 views

Projection and direct sum

I want to show that for every projection $A^2=A$ we have that there exists a subspace $U_1 \subset ker(A)$ and $U_2$ such that $A|_{U_2} = id$ such that $V = U_1 \oplus U_2$. Does anybody here have a ...
1
vote
1answer
501 views

Projecting a point on a plane through a matrix

I need to render some shadows in opengl, one way to do this is to render your object twice, a first time multiplying it by a special "shadow matrix" that flat your object on a plane generating the ...
-1
votes
1answer
243 views

How to change XYZ axes system into another 'xy' system

I have $3D$ point set lying on a vertical plane. This plane is not parallel to either $X$ or $Y$ axis but makes an angle (say, $\theta$) to $X$ axis. And also it has some ($+$ or $-$) intercept to the ...
0
votes
1answer
86 views

Recovering a conic from a pole-polar pair

Consider a conic section $C$ in $\mathbb{R}^2$. Every point $P$ in the plane has a "dual" (pole-polar duality) line $L$ with respect to $C$ such that lines $PA$ and $PB$ are tangent to $C$, where $L ...
1
vote
1answer
121 views

Intuitive interpretation of the 3D to 2D mapping

Suppose a 3D configuration of points is given, $X\in\mathbb{R}^{n\times 3}$, and a non-zero matrix $Q\in\mathbb{3\times 2}$, with orthonormal columns. Now, suppose a mapping to 2D is obtained as ...
0
votes
1answer
159 views

Chain Rule and Homogenous Coordinates

I have a vector $\tilde{p} = (x,y,z)$ (homogenous coordinates). The corresponding non-homogenous vector is $p = (x/z, y/z)$. Now the $\tilde{p}$ is a result of some linear transform $R(\theta)$ of ...
10
votes
2answers
941 views

Augmented Reality Transformation Matrix Optimization

i am a software developer, i'm working on an Augmented Reality system. I'd like to receive some advice in order to optimize my math model. My program has to be slim and fast. Here's the situation: ...