0
votes
0answers
27 views

How to merge coordinates to learn position in space [closed]

I'm implementing an algorithm in which many different points move around in 3-dimensional space, learning their best positions. Each number in the coordinate must be between 0 and 100. For example, ...
0
votes
0answers
19 views

Mapping between two unknown 3D coordinate systems from common motion

Coordinate systems A and B are rigidly linked in an unknown way. The platform then moves and the motion vectors [RA|TA] and [RB|TB] are calculated in each coordinate system. They are parallel but not ...
0
votes
1answer
17 views

Rotation operator for a point in a coordinate system linearly derived from Cartesian coordinates

For some experimental and practical reason, I have created a new coordinate system in the form $$x^\prime_i=T_{ij}x_j$$ where $T_{ij}$ isn't a square matrix. $x_i$ is standard Cartesian coordinates, ...
0
votes
1answer
51 views

rotation matrix to axis angle

from wikipedia the above rotation matrix has a rotation of -74 degrees. What does it mean "around the axis (−1⁄3,2⁄3,2⁄3)"? How can I determine how many degrees is rotated on X axis, Y axis and Z ...
0
votes
0answers
25 views

How to move coordinate systems using rotation matrices.

I am having some trouble with this question. I understand that the rotation matrix will be 4x4 and that the first 3 columns will just be $u$, $v$ and $n$ transposed but I dont know what I am ...
0
votes
0answers
70 views

Converting Euler Angle z-y'-x'' sequence to heading

I'm trying to convert a set of Euler Angles to a heading $(0-360)$ degrees. The Euler Angles use the $\ x-y'-x''$ sequence headings, using $\ \psi, \theta, \phi$ as the rotation angles, respectively. ...
1
vote
0answers
82 views

Change of basis matrix notation confusion

I've got strange notation of change of basis matrix in my book and I'd like to have it explained a little bit. It says, if: $M _{\mathcal A}^{\mathcal B}(id) \cdot \vec{v} _{\mathcal B} = ...
1
vote
0answers
164 views

Reverse rotation back to original coordinates (Euler Angles)

so in the program I'm trying to write (still, it's a mathematical question) I have a set of coordinates and angles (Euler angles) which represent the place and orientation of an object in space, ...
2
votes
1answer
68 views

Coordinate System Rotation and Cross Term

If I have a conic equation $$ 5x^2 - 4xy + 8y^2 = 36 $$ and $ \left[\begin{array}{cc} 5 & -2\\ -2 & 8 \end{array}\right] $ in matrix form, whose eigenvalues are 4 and 9, how would I rotate ...
0
votes
0answers
20 views

Homogenous coordinates: are Wc and Z different?

In these two calculations: http://upload.wikimedia.org/math/b/2/3/b23832f1c400204a4011459712cd5603.png http://upload.wikimedia.org/math/f/5/f/f5f8c42659c83689fa35185403312899.png Is Wc essentially ...
0
votes
2answers
95 views

Can you transform any coordinate from any “space” to another “space” that's defined?

This question pertains to Matrix Transformations. So to provide an example, if I have 3D coordinates where $X = -1$ to $1$, $y = -1$ to $1$, $z = -1$ to $1$. They are "normalized" in my mind. Can I ...
1
vote
1answer
142 views

Perpendicular unit vectors

I have a known unit vector $p (a,b,c)$. First I want a unit vector $q$ which is perpendicular to $p$ and passing through a known point $V(X_0,Y_0,Z_0)$. Then a another unit vector $r$ which ...
0
votes
0answers
21 views

How to set dihedral values to null?

I have a protein with many residues, but I would like to set the phi and psi angles of residue 15 to value of null. I have a file containing all residues and Cartesian coordinates, and I have another ...
2
votes
2answers
44 views

Change of Coordinate Matrix question.

I have this question and the wording is very confusing, I dont understand how to answer it. Any help will be greatly appreciated. I have tried answering it and I just dont know where to begin. ...
1
vote
1answer
47 views

Can't figure out this transformation matrix

So basically I want to write a transformation matrix to take me out of one coordinate system and into another. The transformation has to be as follows: 1) The positive z axis normalized as ...
2
votes
1answer
119 views

Estimate for a rigid transform given a set of noisy measurements

I have a set of rigid transforms $\in \mathbb{R}^{4x4}$, where each transform is an approximation to some unknown, "correct" transform. I'm looking for an algorithm to estimate the correct transform ...
3
votes
0answers
73 views

How to solve a distance problem inside of a picture?

sorry for my bad english. I have the following problem: In the picture you can see 4 different positions. Every position is known to me (longitude, latitude with screen-x and screen-y). Now i want ...
1
vote
0answers
49 views

Linear 2D transform in the sense of geometric figures?

Consider tranformation which turns one aligned rectangle to another: This tranformation can be written in matrix form in the following way where ...
2
votes
1answer
280 views

How to get Euler angles with respect to initial Euler angle

I have a sensor which gives me Euler angles (roll,pitch,yaw). There is a baseline value of Euler angle (assume it is $5,10,15$) at the beginning.I want to calibrate from this baseline values all ...
0
votes
1answer
103 views

parabola in homogeneous coordinates

So if I have the parabola Y = X^2, how do I go about representing this homogeneously? I know I can parameterize it as F(t) = (t, t^2), but then what? The reason I ask is because I have a 3*3 matrix ...
1
vote
1answer
128 views

Derive Rigid Transform Matrix from Axes and Origin

I'm trying to derive the matrix of a rigid transform to map between two coordinate spaces. I have the origin and the axis directions of the target coordinate space in terms of the known coordinate ...
0
votes
0answers
72 views

Transform a point to a new space. How is it working?

Let us assume that you simply have a point: $(x_1, x_2).$ You also have a transformation $H,$ that maps this single point to a new point: $(y_1, y_2).$ So $y_1 = h_1(x_1, x_2),$ and $y_2 = h_2(x_1, ...
1
vote
1answer
114 views

determinant of matrix of transformation from Cartesian to orthogonal curvilinear

Let $(x_1, x_2)$ and $(y_1, y_1)$ be two orthogonal coordinate system with unit vectos $(\hat i_1, \hat i_2)$ and $(\hat e_1, \hat e_2)$ respectively defined by the $x_1 = x_1(y_1,y_2)$ and $x_2 = ...
0
votes
2answers
396 views

convert values from one coordinate system (x,y) to another coordinate system (x', y')

Following is a graph that contains both coordinate systems (x,y) and (x',y'). x, y, x', and y' are all axes ...
0
votes
2answers
53 views

Is there a simple way of arriving at this solution?

Suppose we are given the matrix $$\begin{pmatrix}x'\\y'\end{pmatrix}=\begin{pmatrix}\cos(\omega t)& -\sin(\omega t)\\\sin(\omega t)& \cos(\omega ...
2
votes
2answers
716 views

How to find a 2D basis within a 3D plane - direct matrix method?

I have a plane equation in 3D, in the form $Ax+By+Cz+D=0$ (or equivalently, $\textbf{x}\cdot\textbf{n} = \textbf{a}\cdot\textbf{n}$), where $\textbf{n}=\left[A\:B\:C\right]^T$ is the plane normal, and ...
1
vote
0answers
191 views

2D Cartesian Matrix / coordinate transformation.

I has initially asked this question in the programming site but did not get an answer that worked. This is my first question on this site so please bear with me. Consider a page with three distinct ...
1
vote
1answer
342 views

Jacobian matrix normalization

I have a problem with normalization of the Jacobian matrix. There seems to be no clear method for doing it: in some literature, it has been normalized by using some characteristic length, which is ...
2
votes
1answer
152 views

How to find the $P_2$ when $T_1P_1=T_2P_2$

$T_1$ and $T_2$ are $3 \times 3$ homogenous transform matrices. $P_1$ is the $3 \times 1$ matrix with $x, y$ coordinates of point $P_1$. What I am trying to do here is trying to get $x, y$ coordinate ...
3
votes
2answers
488 views

Plane and Matrix Question

I have this questions and it's really tough for me. Flat on a plane (with normal N through point P) sits a tank at point Q. The tank's local coordinate system is described by the 3x3 rotation ...