Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

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2
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1answer
602 views

Triangle and parametric coordinates

I'm studying on a book where it says: "A triangle is the set of points where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
0
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1answer
25 views

Formula to map any given point on circumference of circle with given radius

I am working on a project where I need this. Mathematically : I need a formula to map any given point P(x,y) on circumference of a circle of given radius r and center c in 2D space. Insights of ...
0
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0answers
35 views

Challenging calculation of a Jacobian for an unusual matrix coordinate transformation

I am studying a random matrix ensemble and I am having trouble performing a coordinate transformation. My question is very straightforward, but perhaps a bit technical. I have the following integral--...
0
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0answers
25 views

tangent space in a moving coordinate frame

I've got a problem in some geometry of flow. For the sake of completeness I will give the complete derivation of the equation of interest, but I will seperate it into derivation part and question ...
1
vote
1answer
42 views

coordinate geometry high level problems

If the lines $aX^2 + 2hXY + bY^2 =0$ form two sides of a parallelogram and the line $lX + mY =1$ is one diagonal, prove that the equation of other diagonal is $Y(bl – lm) = X(am – hl)$
0
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0answers
24 views

transform Gaussian ring from cylindrical coordinate system to Cartesian coordinate system

I have Gaussian vortex ring with the equation in cylindrical coordinate system as enter image description here with enter image description here $x_c$, $y_c$, $z_c$, $R$, $\pi$, $\gamma$ are known. ...
0
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1answer
22 views

Given points P (2,3),Q (4,-2),R (a,0) what should be the value of a if |PR-RQ| Is maximum?

Given points P (2,3),Q (4,-2),R (a,0) what should be the value of a if |PR-RQ| Is maximum ? I tried that maybe the points are collinear but I'm getting wrong answer applying collinearity condition i....
-1
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1answer
20 views

how to get the angle of arc ??

dart game board is divided into sectors by 30 degrees like pizza slice. the given is (x, y) coordinates, and I need to find where coordinates are lying on. how can I get the angle just with ...
1
vote
1answer
2k views

Extrinsic and intrinsic Euler angles to rotation matrix and back

currently I'm working on the visualization of coordinate systems in space to understand rotation matrices better. Until now I thought everything would be ok, but there is a thing that does not get ...
-1
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0answers
34 views

Lorentz manifolds - Change of co-ordinates

Let $(M,g)$ be a lorentz 4-dimensional manifold. Let $p\in M$ and $(U,\psi=(x^1,x^2,x^3,x^4))$ a local chart around $p$ such that $x^i(0)=0$ for all $i$. Let new coordinates $\bar x^i$ that verify: $$...
1
vote
1answer
32 views

Linear Transformation Basis Exercise

I have tried to solve the following exercise. Is it right? Consider the linear transformation L: ℝ⁴→ ℝ³. Knowing that: $$ L \begin{pmatrix}2\\0\\0\\0\end{pmatrix} = \begin{pmatrix}2\\2\\2\end{...
0
votes
1answer
23 views

Linear transformation explanation

I have the following exercise: Consider the linear transformation L: ℝ³→ ℝ². Knowing that: $$ L \begin{pmatrix}1\\1\\0\end{pmatrix} = \begin{pmatrix}1\\2\end{pmatrix} \space\space\space\space\...
0
votes
2answers
30 views

Find the nearest point

How can I find the nearest point of the set(M) to the point (A) in GENERAL(with different set or in 3D space )?
1
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2answers
27 views

notation of a real coordinate system of n dimension

I observe that books write a bold faced R, But the professors write R preceded by a bar. Is that I, denoting infinitism? I am not sure if it is I, its more of a vertical bar. Is it universal, or ...
1
vote
2answers
467 views

New x coordinate of a rotated line

I need help finding the equation to find $x$ I work in GIS and I'm working on a script that uses the new x coordinate of a rotated line. I havent work with trigonometry in a long long time so I ...
0
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0answers
12 views

Oblate Spheroidal Coordinates, Confocal Ellipsoidal Coordinates and Geodesy

What is the name of the orthogonal coordinate system that is most commonly used in modern geodesy\geomatics engineering to model the reference ellipsoid? I suspect it is either oblate spheroidal ...
1
vote
0answers
20 views

Cartesian and Polar Coordinates, proving the same number-pair

The question states: Prove that a necessary and sufficient condition for a point to be represented by the same number-pair (a,b) both cartesian and polar coordinates is that it lies on the initial ...
0
votes
1answer
48 views

Algorithm for getting consecutive line segment edge points from midpoints

So I have a rectilinear grid that can be described with 2 vectors. 1 for the x-coordinates of the cell centres and one for the y-coordinates. These are just points with spacing like x spacing is 50 ...
0
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1answer
33 views

intersection of lines and circle in coordinate geometry

If line $y=kx$ divides two chords drawn from point $(\sqrt{3},1)$ on the circle $x^2+y^2=4$ in $1:2$ . Then range of values of $k$ $\bf{My\; Try::}$ Equation of chord $(1)$ which passess ...
1
vote
1answer
33 views

Help needed understanding this explanation for the Jacobian

In this Quora Answer, a very intuitive explanation for the Jacobian is provided, there is however a step I don't understand: He takes this square: And via a polar coordinates transformation ...
0
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0answers
36 views

Avoiding the spherical polar coordinate singularity on $S^2$ by using a double cover?

Is it possible to avoid the spherical polar coordinate singularity on $S^2$ by taking the coordinates as they originally are on $T^2$, i.e. ranging from $0$ to $2\pi$ mod $2\pi$? How would one ...
0
votes
1answer
30 views

Coordinate transform a triangle

There is a triangle with points P1(x1,y1),P2(x2,y2),P3(x3,y3) on an XY plane. The final ...
0
votes
1answer
14 views

Polar angle of a given point

How to find out polar angle of a given point $A(x_1,y_1)$ relative to another point $B(x_2,y_2)$ in a 2D space?
10
votes
1answer
3k views

Rotating a point in spherical coordinates around Cartesian axis

If I have a point in spherical coordinates, and I rotate it around one of the Cartesian axes, what will be the new spherical coordinates for the point? Both spherical and Cartesian coordinate systems ...
1
vote
1answer
23 views

Definition of a cubic coordinate system

I'm looking at "Foundations of Differentiable Manifolds" by Frank Warner, and have a question about one of the basic definitions at the beginning of the book. He writes: A coordinate system $(U,\phi)$...
0
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0answers
18 views

Calculating x and y coordinates from curvilinear orthogonal coordinates.

We have a curvilinear orthogonal coordinate system defined with $u=xy$, $v=\frac{x^2 - y^2}{2}$, $z=z$. First, calculate x and y. For them, I got $x=\sqrt{\frac{-2v\pm2\sqrt{v^2-u^2}}{2}}$ and $y=u/x$...
0
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0answers
18 views

Adding Pitch/Yaw to Spherical Coordinates

Im running a program on a simulator where I have a stationary camera at global position $(0, 0, 0.48)$ with a pitch $=-28$ and yaw $=0$ rotation. The reference for this pitch and yaw are the global ...
2
votes
1answer
20 views

The meaning of spacecraft attitude represented in quaternion

I am reading the following paper about the attitude control of aircraft: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1271671 The quaternion represents the relative orientation of two ...
0
votes
2answers
28 views

Find the volume defined by $ 0 \leq z^2 \leq 2$ and $x^2 + 4y^2 - (2-z)^2 \leq 0$

I am asked to find the volume defined by $$ 0 \leq z^2 \leq 2\\ x^2 + 4y^2 - (2-z)^2 \leq 0 $$ How can I do that using cylindrical coordinates? Is that minus sign before $(2-z)$ really supposed to ...
1
vote
1answer
31 views

Induced metric on a one-sheet hyperboloid

I am trying to find the induced metric on a one-sheet hyperboloid. Suppose we use cylindrical coordinates $(r, \theta, z)$ for the ambient space in which the hyperboloid is embedded. The hyperboloid ...
0
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0answers
31 views

Triangulation with two camera setup - Result in world or camera coordinate system?

I have some problems to understand how I can triangulate a 3D-point using a two camera setup. Let's assume I'm using a right handed coordinate system and the camera is looking in positive z-...
1
vote
1answer
16 views

Derive the length of the longest line segment that can be enclosed inside the region A.

Q. Let A be the region in the xy-plane given by A={(x,y): x=u+v, y=v, u^2+v^2≤1}. Derive the length of the longest line segment that can be enclosed inside region A. My attempt: I found the equation ...
3
votes
1answer
380 views

Change in neumann boundary conditions through coordinate transformation of elliptic PDE, weak formulation

The standard weak formulation of the Neumann problem for the Poisson equation is to find $u \in H^1 ( \Omega)$ such that for every $v \in H^1 ( \Omega)$: $$ \int_{\Omega} \nabla u \nabla v d x = \...
0
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0answers
19 views

Converting coordinates

I am having huge trouble converting between cartesian to polar and to spherical. I need these methods for my limits of integration in most cases but using the formulas never seem to work, I just ...
1
vote
2answers
31 views

parametric polar equation of a circle

I discovered that Mac's Grapher has a parametric polar mode, i.e. where $r$ and $\theta$ can be specified in terms of a parameter, usually $t$. I am attempting to convert the generic equation for a ...
0
votes
1answer
27 views

Cone under similarity transformation

Suppose we have a cone passing through the origin of $xyz$ coordinate system. Now, the question is that whether we can find an invertible transformation on this coordinate system that turns the cone ...
0
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0answers
10 views

Linear equation scale transform

I have a linear equation in the general form: Ax + By = C in the standard coordination (Cartesian Coordinate System). I would like to scale this linear's coordination to a custom ratio (for example x =...
1
vote
1answer
26 views

Triple integral $\int_{0}^{2\pi} \int_{0}^{2\cos(\theta)} \int_{0}^{\sqrt{2r\cos(\theta)}} r \ dzdrd\theta$ to find volume of a solid

On evaluating the volume between $$x^2+y^2 = 2x\\z^2=2x$$ I set up the triple integral $$\int_{0}^{2\pi} \int_{0}^{2\cos(\theta)} \int_{0}^{\sqrt{2r\cos(\theta)}} r \ dzdrd\theta$$ for which ...
0
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0answers
17 views

Using GPS coordinates in trillateration

for a project we need to find a certain position. The info we have : 3 surrounding positions and the distance between those positions and the point we are looking for. We've got a setup like this ...
0
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0answers
17 views

coordinate transformation of operators

I recently came across a youtube video (https://www.youtube.com/watch?v=6O6iZug6e6Y) on transformation electromagnetism (yes this is physics) and some of the math equations that was postulated did not ...
-1
votes
1answer
19 views

Find coordinates of point C in a equilateral triangle [closed]

How to find the coordinates of point C in a equilateral triangle, where $A=(-2,2)$ and $B=(6,2)$. http://i.stack.imgur.com/TXjjG.png Thanks in advance
0
votes
1answer
16 views

How to find coordinates of $D$

How can I find the coordinates $D$ if I have the other coordinates of a parallelogram $A(-3/-2)$, $B(4/1)$, $C(6/5)$, $D(?/?)$. Thanks in advance
1
vote
1answer
16 views

how to find the pivot/axis and angle that move one coordinates space to another?

I am writing a plugin for a 3d modeler, and I am stuck. For my plugin, I need to get the axis and the angle used for rotating a 3d object. But I only get the coordinates (~ 3dmatrices) of the objects ...
0
votes
1answer
28 views

Can point in 3D space be represented as vector?

If yes, then such vector is just displacement from origin in coordinate system? Also, I have another(optional) question, how to name variable that represnts particular point using vector? Position or ...
2
votes
0answers
39 views

Faster Alternative than Calculating Euclidian Distance to determine which Coordinate has Max Distance from a fixed coordinate (eg (0,0))

I am developing a program that needs me to determine which coordinate in a $2$-D figure has maximum distance from a fixed coordinate. Let me demonstrate: $3$ points: $(1,3), (2,2), (5,0) $; Fixed ...
0
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0answers
11 views

determine lat/lng coordinate by adding distance in one direction from another coordinate

How can I calculate the coordinate of a latitude/longitude point that is X feet in one direction (North, South, East, or West). For example, how do I get the point 1000ft North of 45,-100? 500ft East ...
13
votes
4answers
6k views

Simple proof of integration in polar coordinates?

In every example I saw of integration in polar coordinates the Jacobian determinant is used, not that I have a problem with the Jacobian, but I wondered if there's a simpler way to show this which ...
4
votes
0answers
47 views

Flea on the coordinate system

We drop a flea on a point of the coordinate system(with integer coordinates). Due to the dimensions of the flea we can not see it. The flea jumps away every second by one unit (always in the same ...
0
votes
2answers
25 views

Volume of paraboloid $z = x^2+y^2$ with heigth $h$

I am asked to find the Volume of paraboloid $z = x^2+y^2$ with heigth $h$. How would be the best way to approach that problem (cartesian/cylindrical)? My reasoning using cylindrical coordinates doesn'...