Questions tagged [coordinate-systems]

This tag involves questions on various coordinate systems. The usual Cartesian coordinate system can be quite difficult to use in certain situations. Some of the most common situations when Cartesian coordinates are difficult to employ involve those in which circular, cylindrical, or spherical symmetry is present. For these situations it is often more convenient to use a different coordinate system.

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Phase Space Intersecting Hyperplane - Poincare Section/Map

I have a phase space and a hyperplane. I would like to know how I can find where the coordinates intersect the hyperplane. My plan is to create a Poincare Section/Map. The problem is I have no ...
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Find the Y Coordinate of a Right-Angled Triangle Vertex Given the X and Y Coordinates of the Two Other Vertices [closed]

Please help: given the coordinates of the vertex A (11; 2) and B (3; 8) of a right-angled triangle, find the Y coordinate of C given its X coordinate is 0 (without using trigonometric functions)
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Harmonic functions and coordinate transfomation

Related to a question about coordinates, I've been given the following comment to consider: "Local coordinate functions are given by suitable harmonic functions on subsets of the metric space, ...
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Transformation of line element in Minkowski space under infinitesimal coordinate variation

I'm trying to understand the following problem: We are looking at an infinitesimal coordinate transformation $$ x^\mu \rightarrow x^\mu + \epsilon u^\mu(x), \space \epsilon \rightarrow 0 $$ and we are ...
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How to solve different grid based combinatorics problems?

First of all, I apologize for this post being huge. With that being said, I am practising for mathematics olympiad. I have come across different problems that I have tried to solve. Recently, I have ...
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Need help with matrix transformation! [closed]

Given the transformation = [1 −2 3, 2 0 −3, 1 1 1][x1 x2 x3] . Find the co-ordinates (x1, x2, x3) corresponding to (2,3,0) in Y.
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Common normal for an ellipse and parabola

I came across the following question in a magazine with example problems for the JEE examination in India: Given are two curves $x^2/a^2 + y^2/63=1$ and $y^2=4x$. The maximum integral value of $a$ ...
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How are 3 coordinate frames related to each other?

Suppose we have three cartesian 3D-coordinate systems, each related to each other via some Euler angles. So for instance, if we have a vector $\vec v$ and its coordinates in the first frame, we get ...
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Why do Trigonometric functions _need_ to be negative?

The Trigonometric Unit Circle is a pretty common thing taught in High-School, yet it doesn't cover some questions I had. There have been questions in the past about why trigonometric functions can be ...
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Conic sections ( coordinates of the point of intersection of tangents with the curve )

I was told by my math teacher that equation of a pair of tangents drawn from the point is $T^2=SS_1$ This gives a second degree equation in $X$ and $Y$, which represents a pair of straight lines ...
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Polar equation of a shifted cardioid?

I am trying to find the equation (in polar form) of a cardioid shifted by an amount $x_0$ in the $x$ direction. I tried converting $r=1+\cos(\theta)$ in Cartesian coordinates, add $x_0$ to the $x$ ...
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3D rectangle coordinates knowing 2 coordinates , and the elevation of the 2 others

I have this simple 3D geometry problem that I need to solve in order to go to the next step with a python script. Please check the attached image. here is what I know : A, B coordinates (X,Y, Z) A ...
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Defeated by coordinate spaces and transformations; need help figuring out what questions to ask

I'm trying to write a toy app that generates "procedural art" by rolling circles around inside each other. I have been banging my head against the math for months now, repeatedly thinking I'...
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System coordinate rotation, using a vector's value [closed]

Say I have two 3d cartesian coordinate systems, with one being a rotated version of the other. And say I have a vector A, and know its coordinates in both systems, can I get the rotation that was ...
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Is it matrix vector multiplication or matrix coordinate multiplication?

Recently I got confused about the difference between a vector and a coordinate and here is what I concluded. Given a vector space $V$ over a field $F$, a vector in the vector space $\vec{w}$ and a ...
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3D points backprojected onto a 2D plane.

In a Cartesian 3D coordinate system defined by XYZ, there is a known point $\textbf{P}$ defined with it coordinates $(x_0, y_0, z_0)$ in X-Y plane. Following is the diagram: $P$ in X-Y plane is ...
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Rigorously defining coordinate systems on physical space

I just started reading about manifolds and learned of coordinate charts. I am trying to mentally piece together my intuitional understanding of coordinates in our physical space (PS) vs the definition ...
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What steps would you follow to change coordinate systems for this Lagrangian? (Cartesian to Spherical)

I'm self-teaching my way through "Lagrangian and Hamiltonian Dynamics" by Peter Mann and find myself stumbling on the following basic transformation. Consider the following Lagrangian (for a ...
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Can I calculate this coordinate with the given?

I studying about the total station. This time, I want to know how the total station calculate the coordinate of its point with two known points. Their coordinates in the global coordinate system are $$...
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Is it possible to calculate a coordinate with these conditions?

enter image description hereI'm studying about algorithms for GPS or several surveying problems. I want to know is it possible to solve the problem below. We know Global coordinates of two points. ...
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Point of intersection with a Plane [closed]

Please consider the image below i need to get the X,Y,Z coordinates of the blue point ( the intersection with the plane (P2). Things i know are : Coordinates of B Coordinates of B1 Beta Angle Plane ...
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A basis with constant metric tensor

Let's consider a plane which coordinates are $x^1,x^2$. Then, consider the basis given by ${\partial \vec P/\partial x^i}$. Accordingly to this choice of coordinates and basis there will be a metric ...
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How to convert screen coordinates (+depth) to other coordinates

I am creating software related to motion capture that captures human motion from a camera. And in the motion capture library I am trying to use, I can only get the screen coordinates (...
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2answers
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Why is this (image) function transformation not logical?

I am taking MIT 6.003 course from OCW and came upon the following problem from lecture 1: For the above image $f(x, y)$, does the below image represent the transformation $f(-x-250, y)$? The correct ...
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periodic Euclidean tiling functions with counting, and ordinal to cartesian functions. (here floret pentagonal tiling)

The floret pentagonal tiling, also known as the snub trihexagonal tiling, is pictured below. Given a specific horizontal/vertical range (the grey box is an example (9,14) in the image) starting at the ...
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Given two distinct intersecting circles, length of that chord of larger circle which is bisected by the smaller circle is equal to?

Two circles whose centres lie on the x axis, whose radii are $\sqrt2cm$ and $1cm$ and whose centres are 2 cm apart intersect at a point A.The chord AC of the larger circle cuts the smaller circle at ...
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Calculating centre of rotation of a line based on endpoint coordinates in 3D where line translation may also occur.

DISCLAIMER I am not a mathematician, I am a biomechanist. So please excuse any poor terminology. I would like to know how to calculate the centre of rotation of a line with endpoints A1 and B1, to a ...
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Given multiple coordinates (x,y) of a vehicle, how to determine the angle at which the vehicle turns?

Around 20 coordinates of a vehicle's location are mentioned. Everytime the car turns, at what angle does it turn? How to determine the angle? Is there any particular formula to get the angle using ...
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Why does matrix notation imply working in a cartesian coordinate system?

I am reviewing my notes from a course in fluid dynamics and noticed that the lecturer put a remark stating that we are implicity choosing to work in cartesian coordinates since we are representing ...
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What is correct representation of homogenous coordinates?

I read from this answer and understand that the homogenous coordinates is of the form $[x, y, z]$ which represents by square bracket. Also read from this answer the homogenous coordinates is of the ...
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Calculate rotation of a point set

I am trying to solve the following problem: I have a set of 2D coordinates of fingers on the screen (e.g. $x_1$;$y_1$, $x_2$;$y_2$ etc) before the rotation was done. Fingers are moved to the new ...
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General formula of coordinates of a point on an arc given the centre of the arc, radius and the starting and ending angle of arc wrt horizontal.

I am given the centre of an arc, the starting and ending angles of the arc wrt the horizontal and the radius of the arc. I want a general formula that I can use to get the coordinates of points on the ...
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1answer
65 views

Ball with diameter collision with inclined wall/plane in 2D Coordinate System

Given the position of a ball, the diameter, a direction/target position and the 4 edges of a rectangle(2:1 ratio) how can I find the end position (coordinates of a point) of a ball if it collides with ...
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1answer
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Can I extract yaw, pitch and roll from XYZ and/or latitude, longitude and altitude information

I have a problem regarding my programming project and I'm stuck on the mathematical side of the problem. I am parsing geometrical data from a provider and from their side every information is provided,...
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Gradient in integral transformation

I have a question on the handling of gradients in coordinate transformations: For a coordinate transformation in form of a rotation defined by the mapping $\Phi: \Omega \mapsto \Omega'$, $\psi \mapsto ...
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1answer
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Why am I not able to find the equation of this straight line in my way?

I want to find the equation of the straight line EB. My attempt: $$D\equiv\left(\frac{2+6}{2}, \frac{1+3}{2}\right)$$ $$\equiv(4,2)$$ Now, the slope of AD, $$\frac{2-5}{4-3}$$ $$=-3$$ Now, let $k$ is ...
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1answer
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Different bin sizes in a Cartesian coordinate system

What is the name of a Cartesian coordinate system where the X- and Y-axis have different bin sizes?, i.e. the unit in both axis do not have the same length, so the grid is formed by rectangles, not ...
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1answer
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Can we make a coordinate system with two imaginary axes?

As question suggests, can we make a coordinate system with two imaginary axes instead of one real and one imaginary (as usual for a complex plane)? Is it possible? And if yes does it have any meaning ...
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How to transform PDE for moving coordinate system and perspective?

I have a nonlinear PDE that I'm trying to transform to a very confusing coordinate system. The exact wording of the coordinate system is The origin of the coordinate system is taken to be ...
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Conventions for naming functions that represent scalar and vector fields in different coordinates

I am looking for some sensible convention for naming functions that represent scalar and vector fields in different coordinates systems. Currently I am saying something like this: Let $f$ be the ...
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2answers
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Inside /outside test of the point on 2D plane

Suppose I have one plane $Ax+By+Cz+D=0.$ I want to test $(x, y, z)$ is inside of this plane or outside. My attempt:1 Then draw normal N on that plane which point away from the observer Image1. If $Ax+...
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1answer
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Shifting of origin

Find the equation of straight line joining the point $(2,2)$ to the points in which the straight line $y=mx+c$ cuts the circle, $x^2 + y^2 =2ax+2ay$. Hence find the condition that these points may ...
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Mapping points between an intermediate coordinate system to a global coordinate system

Problem Statement Let's say I have 3 orthogonal coordinate systems in 3d space c1, c2, c3, with c1 being the "global" coordinate system, and c2 and c3 being the "local" coordinate ...
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Spinning polygon at plane

Given a polygon $P$ and some line $l$, Crossing the polygon with some angel $θ$ relative to the $x$ axis, I am Intrested In spinning the polygon, And the line $l$ In such way that the line will be ...
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1answer
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Orthonormal coordinate coframe in arbitrary Riemannian manifold - question on published paper

In Miranda Jr, Pallara, Paronetto and Preunkert's Heat semigroup and functions of bounded variation on Riemannian manifolds (p.106, property (4)), the authors state that for an $n\ge 2$-dimensional ...
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How to calculate distances on a 2D relative cordinate system?

By relative coordinate system I am refering to a specific system where each coordinate is given only as its distance away from other points (if this kind of system has a more accurate name then please ...
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"chained" spherical coordinates

I'm having a bit of trouble understanding how to solve my problem. I have tried searching online but i'm not sure i'm using the correct terminology. In essence my problem is this. I have three spheres,...
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Transformation of tensor depending on another tensor

I have a tensor $\mathbb{T} = T_{xx} \mathbf{e}_x \otimes \mathbf{e}_x + T_{xy} \mathbf{e}_x \otimes \mathbf{e}_y + T_{xz} \mathbf{e}_x \otimes \mathbf{e}_z + \dots$ in cartesian coordinates that I ...
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Can anyone explain this? Why the derivative with $x$ don't have lambda?

I have difficulty in understanding the chain rule given in the picture. The derivative with $x$ do not have lambda, while $y$ term have. Why is it so?
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Show that the change of variables transforms a linear system

Show that the change of variables $x=2u+v$, $y=3u+v$ transforms the linear system $$ \left\{ \begin{aligned} x'(t) &= \phantom{3}x-2y \\ y'(t) &= 3x-4y \end{aligned} \right. $$ into $$ \left\{...

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