0
votes
0answers
11 views

New Axis calculation

I have a task whereby I use an accelerometer to calculate acceleration for a vehicle. The problem I am attempting to solve is to allow the accelerometer to be in any oriertaion. Basically I have a ...
0
votes
0answers
20 views

3D cartesian cordinates to 3D isometric cordinates

I am working on Isomer opensource project https://github.com/jdan/isomer and I need to convert 3D cartesian cordinates to 3D isometric cordinates. We already have 3D iso to 2D cartesian ...
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
34 views

How can I transform coordinate systems with quaternions?

I have a coordinate system 0 which I'd first like to rotate about its z-Axis which gives me system 1, and afterwards rotate system 1 about its y-axis which gives me system 2. See picture: Both ...
1
vote
1answer
59 views

Transfer Transformation from Physics to Vector Graphic

Upfront, I am not a professional in Maths and hope that the formulation of my question describes the problem well enough. I am creating a jump'n'run game, which uses a physics engine (Box2D) and SVG ...
0
votes
0answers
8 views

Given U,V<->X,Y trnslation formula explanation

Well in a text book (about numerical analysis methods to do a polynomial interpolation in bivariate functions). The following piece of text/functions is just given, without much explanation. The goal ...
1
vote
2answers
47 views

Coordinates rotation by $120$ degree

If I have a point on a standard grid with coordinates say: $A_1=(1000,0)$ $A_2=(707,707)$ Is there a easy way to transfer this points to $\pm 120$ degrees from the origin $(0,0)$, and ...
2
votes
0answers
77 views

Get 2D coordinate transformation matrix based on points in a system and their angles in the other?

I'd like to get the parameters (rotation angle,$\Theta$, and translation coefficients, $x_0$ and $y_0$)) of a transformation for translating and rotating points in a coordinate system to another. As ...
5
votes
1answer
162 views

Jacobian of Fourier Transformation

I am trying to calculate the Jacobian determinate of the Fourier transform which I stumbled upon when studying the Path Integral in Quantum Field Theory. I know the answer should be $1$ but I don't ...
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 ...
0
votes
1answer
131 views

How to project 3D plots on a 2D coordinate system without losing the metric scale?

I've been collection data of a river bank last week and I need to plot the cross sections of the data. The issue is, that the data taken consists of 3 coordinates: easting, northing and elevation. ...
3
votes
0answers
69 views

Changing coordinate system with non standard definitions

The standard coordinate transformation to polar coordinates is $$ \begin{cases} x=r\cos(\varphi)\\ y=r\sin(\varphi) \end{cases} $$ with $r\in[0,\infty), \ \varphi\in[0,2\pi)$ The question is whether I ...
1
vote
1answer
244 views

Which matrix transforms my vector field $F(r,\theta,\phi)$ from cylindrical to spherical coordinates

I am looking for the matrix that I have to apply my vector at the position $(r,\theta, z)$ to in order to get the appropriate vector in spherical coordinates. I am totally okay, if you could give me ...
0
votes
0answers
73 views

coordinate transformation and scaling

I have a global coordinate system that I need to transform to a local coordinate system. The new and old coordinate systems are shown below. Using transformation rules, I came with with the ...
0
votes
1answer
205 views

Transform between cartesian coordinate system and abstract coordinate system

I am trying to find a transformation that takes me between Cartesian coordinates and a pseudo-coordinate-system I have developed which is described as follows: Please first see the diagram below. ...
0
votes
1answer
152 views

Homothetic transformation

suppose that,we have Homothetic,in rectangular coordinate system,with center origin $(0,0)$ and $k$ ,and this homothetic send point $A(2,3)$ to point $B(2*x-1,x)$.aim is to find $k$,first i have ...
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 ...
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 ...
1
vote
1answer
126 views

Change of coordinate matrices

Find the change of coordinate matrices: Wherein B is the standard basis for P2 $$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1) $$ $$P_{B'B}$$ means the transformation for the ...
0
votes
1answer
126 views

Transformation of a matrix, change of basis

Find the change of coordinate matrices: Wherein B is the standard basis for P2 $$B' = (t^2+2,t+3,t^2+t+1) \\B" = (2t^2+t+1, t^2, 2t+1) \\ B= (t^2,t,1) $$ $$P_{B'B}$$ means the transformation for the ...
2
votes
2answers
110 views

question on transformation

If a $2$d coordinate transformation function is given by $f(x,y)= 3x+1$, then what does it mean? How do I calculate the transformed coordinates for the points say $(3,4)$ in the initial space?
0
votes
1answer
190 views

transformation between square and a polygon?

I have a square and a polygon. I want to transform all the points inside this square such that they are mapped inside the polygon. I was trying using scale and rotate matrices but I am not able to ...
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 ...
4
votes
2answers
350 views

How to solve an overdetermined system of point mappings via rotation and translation

I have a set of points in one coordinate system $P_1, \ldots, P_n$ and their corresponding points in another coordinate system $Q_1, \ldots , Q_n$. All points are in $\mathbb{R}^3$. I'm looking for a ...
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 = ...
2
votes
1answer
2k views

building transformation matrix from spherical to cartesian coordinate system

How to arrive at the following from given $ x = r\sin \theta \cos \phi, y = r\sin \theta \sin \phi, z=r\cos\theta $ $$ \begin{bmatrix} A_x\\ A_y\\ A_z \end{bmatrix} = \begin{bmatrix} \sin ...
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
1answer
6k views

Transformation of unit vectors from cartesian coordinate to cylindrical coordinate

Let $ (\hat i, \hat j, \hat k) $ be unit vectors in Cartesian coordinate and $ (\hat e_\rho, \hat e_\theta, \hat e_z)$ be on spherical coordinate. Using the relation, $$ \hat e_\rho = ...
3
votes
1answer
389 views

Coordinate transformation

I have some problems with a geometrical calculation. I want to know the coordinates of the point $P_2$ in my coordinate system $A \ (x,y,z)$ as shown in the following figure. Point $P_1$ (in $A \ ...
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 ...
0
votes
0answers
1k views

Unit vectors transformation from Cartesian to elliptic coordinates

I'm going to find a relation between Cartesian and elliptic unit vectors. For ellipse with major and minor semiaxes $a$ and $b$ Cartesian coordinates are: $$\begin{align*} x&=f ...