# Tagged Questions

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### Changing the length scale of the system of coordinates

Change the length scale on the axes of original system of coordinates, in which the equation $$y=x^3-px\qquad\text{(1)}$$ is plotted, i.e. introduce new coordinates $x_1$ and $y_1$ instead of ...
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### Coordinates rotation and function change

In the Cartesian coordinates $(x,y)$, I have a vector function $\bar{f}(x)=\hat{x}A\cos(yk)$, where $A$ and $k$ are constants. I make now a 45 degrees rotation (in the same plane) to the new set of ...
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### 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 ...
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### 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 ...
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### 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, ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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. ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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 ...
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### 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?
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### 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 ...
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### 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 ...
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### 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 ...
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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 $x_2 = ... 1answer 3k views ### building transformation matrix from spherical to cartesian coordinate system How to arrive at the following from given$ x = r\sin \theta \cos \phi, y = r\sin \theta \sin \phi, z=r\cos\theta $$$\begin{bmatrix} A_x\\ A_y\\ A_z \end{bmatrix} = \begin{bmatrix} \sin ... 2answers 403 views ### convert values from one coordinate system (x,y) to another coordinate system (x', y') Following is a graph that contains both coordinate systems (x,y) and (x',y'). x, y, x', and y' are all axes ... 1answer 6k views ### Transformation of unit vectors from cartesian coordinate to cylindrical coordinate Let (\hat i, \hat j, \hat k) be unit vectors in Cartesian coordinate and (\hat e_\rho, \hat e_\theta, \hat e_z) be on spherical coordinate. Using the relation,$$ \hat e_\rho = ... 1answer 396 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 \ ...
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 ...