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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Translate and Rotate mesh

I have a mesh constituted of some vertices in 3d space, let's call them $(x_1,y_1,z_1),(x_2,y_2,z_2),\cdots,(x_n,y_n,z_n)$. The mesh's central point is $(0,0,0)$. How to find out the new coordinates ...
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3answers
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New coordinates after clockwise rotation of triangle?

The figure below represents a triangle $PQR$ with initial coordinates of the vertices as $P(1,3)$, $Q(4,5)$ and $R(5,3.5)$. The triangle is rotated in the $X-Y$ plane about the vertex $P$ by angle ...
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Coordinates change movement problem

yesterday I asked a related question that was a specific case of my problem. It was solved here: Geometry/ Triangles problem but I would want to know if its possible to get a generic universal ...
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1answer
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+100

Trigonometric position function and intersection

I have the following position function for a point: $x(t) := C_x - (S_x-C_x) \cdot \cos(t\cdot\theta) + (S_y-C_y) \cdot \sin(t\cdot\theta) + t \cdot v_x$ $y(t) := C_y - (S_x-C_x) \cdot ...
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How to perform statistical test for two sets of points?

(I have asked this question originally on Cross Validated; however, no good answer and someone suggested me to ask the question here). Thanks a lot in advance if anyone can help. We know that we can ...
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$A: \mathbb R^3 \to \mathbb R^3$ what is the representation of $A$ under coordinate change? (Tensor)

For our initial homework on Tensor Calculus we have to do the following: Consider a map $A: \mathbb R^3 \to \mathbb R^3$, where we use local coordinates $\mathbf{x}$ given by $x^1,x^2$ and $x^3$. ...
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How to detect how clustered coordinates are in a graph? [closed]

Assuming we have a 2D graph with n points, I want to detect how clustered are the points. By clustered I don't mean only how close they are in general, but a very clustered graph can be one with m ...
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30 views

How does one determine whether a coordinate basis is orthogonal or not?

Apologies for what is perhaps a very basic question, but I have been studying differential geometry with a view to gain a deeper understanding of general relativity and I have hit a stumbling block. ...
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0answers
14 views

How to determine changing scale factors when performing coordinate transfomations?

To explain: I have two coordinate systems. One (x,y) and the other (x',y') as seen in this photo. Coordinate systems I am trying to convert the coordinate in the (x,y) system to the rotated red ...
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1answer
16 views

Get coordinates in a scaled and translated canvas

I'm drawing an image to a scaled and translated HTML5 canvas. It's zoomed to a certain point on the image to be more specific, so only a smaller partition is visible. In this smaller part, I want to ...
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4answers
24 views

Feynman lectures, Volume I, chapter 13-4

While reading Feynman lectures on Physics, volume I, Chapter 13-4, I found following assumption, which I don't understand: Then, since $r^2 = \rho^2 + a^2$, $\rho\,d\rho = r\,dr$. Therefore ... ...
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2answers
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Finding the equation of a circle from the equation of its tangents

Given the equation of a pair of lines : $36x² - 63xy + 20y² + 54x - 17y - 10 =0.$ If the circle touches one of the lines at (-3,-1) and the other at some point then find the equation of the ...
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0answers
20 views

Calculating the sun position fails

could you help me find the mistake(s) in my calculation of the sun position today on hawaii at 16:00? I'm following this Wikipedia article. Number of days since 2000/01/01 (2016/01/29): $$n ...
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0answers
13 views

Relations between unit vectors in polar and curvilinear coordinates

I'm a bit confused about the relations between unit vectors in curvilinear and polar coordinates in a plane. Let $u_{R}$ be the radial unit vector in polar coordinates and $u_{N}$ the normal unit ...
2
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1answer
33 views

Rational points on a line

This question is quite unique. Does there exist some point in the coordinate system such that any line passing through it has at most 2 rational points lying on it?
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0answers
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Trying to develop a formula for relative angle relationships in fixed space

Fixed space is defined relative to origin $(0,0,0)$. Fixed space has an origin with angles $(0,0,0)$ as well. A particle $P$ has $(x,y,z)$ coordinates relative to the origin: $P_x$, $P_y$, and ...
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1answer
11 views

Rectangular to polar conversion angle error

I am trying to determine the polar form of the following rectangular vector: -105 + 140j The polar form is $\sqrt(-105)^2+140^2$ = 175 and the angle is ...
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2answers
24 views

If $x=r\cos(\theta)$ then in $?=r\cos(\theta+a)$ what is $?$ equal to?

What I mean by $r\cos(\theta+a)$ is that it's the same function $r\cos(\theta)$ but it's translated by $a$ units, if this makes any sense. I just want to know what it means in terms of $x$.
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0answers
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What does it mean for a polar coordinate system to have basis vectors?

So I understand that every element of a vector space can be represented uniquely by a linear combination of the basis vectors: $v=\alpha_1v_1+\cdots+\alpha_nv_n$ Then coordinates to those basis ...
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1answer
26 views

Change of Variables in Laplacian

I know how to prove $$\nabla^2(\frac{1}{r}) = -4\pi\delta^3(\textbf{r}),$$ where in Spherical coordinates, $$ \nabla^2 = {\frac{1}{r^2} \, \frac{\partial}{\partial r} \left( r^2 \, ...
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1answer
25 views

Rotating a 3 coordinate point

Im having trouble figuring out how to rotate the z axis 90 degrees. For a programming im making example new_x = y; // For a 90 degree clockwise rotation, the new x is the original y, new_y = ...
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1answer
68 views

How to change between these two coordinate systems?

I have a problem with the coordinate system change between two 3D rotation sensors A and B. The coordinate systems have the same origin and are (mostly) perpendicular. I tested a somewhat pure ...
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2answers
35 views

How to get coordinates with a new basis?

I have this exercise. Consider the following vectors of ℝ²: $$ u_1 = \begin{pmatrix}1\\2\end{pmatrix}, \space\space\space u_2 = \begin{pmatrix}2\\1\end{pmatrix} $$ Determine the ...
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5answers
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Basic understanding of a metric.

What is a metric ? Do a metric depend on the system of coordinates I use ? Does it depend on surfaces (or higher dimensional manifolds. Correct me if I'm wrong using the word) the coordinate frames ...
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1answer
21 views

Position of a point$\ \ C(x|y)\ \ $ on a line between $\ \ A(1|1)\ \ $ and $\ \ B(5|2)\ \ $ when $x (i.e. 1)$ away from $A$

How to calculate the position of a point on a line when the start end endpoint of the line and the distance of the point from the start are given$?$ Example: $A(1|1)$ $B(5|2)$ Distance of point ...
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5answers
49 views

Two points are given (-2,0) and (0,4/3) we can easily find the equation of …

Two points are given (-2,0) and (0,4/3) we can easily find the equation of straight line joining these two points Let A(-2,0) and B(0,4/3) Equation of straight line joining these two points ...
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1answer
11 views

Finding the second point of intersection from a normal on a hyperbola

The question is phrased as follows: "A rectangular hyperbola, W, has equation xy = 12" a) Show that the gradient of the normal, N, to W at the point P(2,6), is 1/3. b) Hence find an equation for ...
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1answer
38 views

Transformation matrix in polar coordinates

I'm trying to write a software widget that allows the user to resize the component, so I can write a transformation matrix $\mathbf T_\text{xy}$ that will map $(x,y)$ to a transformed $(x',y')$, that ...
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0answers
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Diagonal of parallelepiped circumscribed around ellipsoid is constant

There are many rectangular parallelepipeds that can be circumscribed around a given ellipsoid in $\mathbb R^n$. Prove that the length of the main diagonal does not depend on the choice of such ...
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2answers
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Parabola having focus $(1,2)$ touches both axes. Find the equation of directrix.

Parabola having focus $(1,2)$ touches both axes. Find the equation of directrix. As perpendicular tangents meet at directrix, the directrix passes through origin. So the directrix has equation of the ...
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1answer
48 views

Contravariant vector example with polar coordinates

My book gives me this definition for contravariant vector: Let an n-tuple of real numbers $a^1,a^2, \dots, a^n$ be associated with a point P of an n-dimensional Riemannian space with coordinates ...
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3answers
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What is the general equation of lines going through 'a' particular point?

I want to know the general equation of lines going through a single point where there will be arbitary constants which will change and cause the line to rotate in a circle and consequently the center ...
0
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1answer
21 views

Why aren't the derivatives of this transformation and its inverse reciprocals of each other?

Consider the coordinate transformation under rotation that \begin{align} y' & = y\cos\phi + z\sin\phi \\ z' & = -y\sin\phi + z\cos\phi , \end{align} we can get \begin{equation} \frac{\partial ...
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1answer
30 views

Changing variables: partial derivatives of a tensor

Given is the tensor $T$ in Cartesian coordinates $T=\operatorname{diag}\{T_{xx},T_{yy},T_{zz}\}$ in cylindrical coordinates $T=\operatorname{diag}\{T_{rr},T_{\theta\theta},T_{zz}\}$ How does one ...
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2answers
54 views

Finding the number of normals to a parabola

Find the number of normals to the parabola $y^2=8x$ through (2,1) $$$$ I tried as follows: Any normal to the parabola will be of the form $$y=mx-am^3-2am$$ Since the point (2,1) lies on the ...
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0answers
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Prolate spheroidal coordinates and spheroidal harmonics expansion

I recently started to study problems with prolate spheroidal geometries, for which prolate spheroidal coordinates are most suited. In particular I have the advantage that the problem is axisymmetric ...
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0answers
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Cylindrical coordinate derivative of a vector field.

Considering the following identity transformation in cylindrical coordinate: $$\mathbf{v}(R,\theta,z)=R\;\mathbf{e}_{R}+\theta\;\mathbf{e}_{\theta}+z\;\mathbf{e}_{z} $$ Taking its derivative ...
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1answer
43 views

Where can I learn about other types of coordinate systems?

As a junior math major the only coordinate systems I've thus far been exposed to are Cartesian and polar (including cylindrical and spherical) coordinates. But of course these aren't the only ones. ...
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World To Screen Game math

I have a Coordinate system, I have my XYZ, pX,pY,pZ and the other player, eX, eY, eZ and I want the Pitch and YAW First the YAW: I first take VectorX = eX - pX VectorZ = eZ - pZ then I ...
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Trying to get 2D X angle through 3D

Im trying to make an aimbot for Call of duty 4 for educational purpose I tried this: I declared a few variables enemy coords = eX, eY, eZ Player = pX, pY, pZ Vector length for X, Z I have 4 ...
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1answer
36 views

World to screen

I tried this: I have 2 players in a game (Cod 4). I read X, Y, Z and store them in: ...
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2answers
24 views

coordinates format to GPS

I was wondering if someone could help me figure out how to go about converting the coordinates on a map I was sent from abroad from the format I see to the usual latitude/longitude I'm used to. (I'm ...
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1answer
16 views

Create unique identifier from close coordinates

Suppose that I have the following list of coordinates: ...
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1answer
25 views

Projection of a plane on coordinate planes

$$\left|\begin{matrix} x & y & z & 1 \\ x_1 & y_1 & z_1 & 1 \\ x_2 & y_2 & z_2 & 1 \\ x_3 & y_3 & z_3 & 1 \end{matrix}\right|=0$$ This is the equation ...
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1answer
23 views

How can vector functions define coordinate systems?

I was watching a lecture in which the professor states that by taking the derivative of a vector function, one can find the basis of the coordinate system being studied. My question is, how can a ...
2
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1answer
52 views

Spherical distance between two points in terms of latitude and longitude

I have seen the answer to this question - Great arc distance between two points on a unit sphere However in a fortran program that I have this is the code to calculate spherical distance between two ...
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0answers
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Equal areas of segments in the lazy caterer problem?

In the book "Build Your Brain Power" by Wootton and Horne, they mention the lazy caterer's problem, asking for a way to cut a circular cake into 8 equally sized pieces with 3 cuts. Clearly since the ...
2
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1answer
35 views

Actual convention for the term Sinusoidal Phase “Shift” or “Offset”

I have seen the convention for a sinusoid appear as: $x(\theta) = A \cdot \sin( B \cdot (\theta - \phi) \ ) + D$ $y(\theta) = A \cdot \sin( B \cdot (\theta + \phi) \ ) + D$ Is "offset": $\phi$ ...
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1answer
31 views

Forming a line from two points

In the book Multiple View Geometry in Computer Vision, it says "a line is defined by the join of two points" in section 3.2.2 Later on it goes to say there is a point $P^+x$ (the point that projects ...
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1answer
33 views

Do you know the formula?

I have three data: coordinates $(x,y)$ angle in degrees ($\gamma^\circ$) distance in meters (m) How should I calculate in general a new position $(a_1,b_1)$? For example, assume the following ...