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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how do you find the distance between 2 points with known distances between other points

link to diagram for explanation: http://i.imgur.com/8cmuWib.png I am trying to determine the distance between i and j. These nodes are all placed in a coordinate system. things I know: ...
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1answer
30 views

Find the end points of a line segment in 3D space

I have a line segment in 3 dimensional space (x,y,z), and I want to find the 2 endpoints of this line segment. Is there a systematic way of doing this? To be specific, I have the line described by ...
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1answer
29 views

Azimuth angle limit in Spherical co-ordinate system

In spherical co-ordinate system (r, θ, φ), θ can range from 0 to 2pi, but φ only varies from 0 to pi. Why is that?
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3answers
53 views

Calculate the divergence of the polar coordinate vector field $\partial_\phi$ [closed]

I have to solve this problem: $v=\partial_\phi$ on $M=\mathbb{R}^2\backslash{0}$ where the components of $v$ are in polar coordinates. Calculate the divergence of $v$. Even with the help of ...
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2answers
52 views

Calculate area of “hand-drawn” polygon

I have a series of coordinates that represent a hand-drawn polygon. At the intersection, the lines slightly "overshoot," e.g.: ...
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2answers
36 views

Find the Equations of the straight line with the help of the given information.

Suppose two straight lines 3x+4y=5 & 4x-3y=15 cut each other at the point A. Take 2 points B & C on those 2 lines, such that AB=AC. If line BC passes through the point (1,2), then find the ...
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How to estimate the world position of origin of a coordinate system based on its members global position?

I have n points of interests (POIs). I have a local coordinate system. For all these n POIs I know there position in this system, that is there x, y, z translation (local position) from origin of ...
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1answer
29 views

Equation of line in hyperbolic space

After a slightly peculiar dream the other night, I find myself suddenly inspired to do numerical simulations in three-dimensional hyperbolic space. For this to work, I need an equation of line in ...
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19 views

Nonlinear-Variation of Helmholtz Equation

I was wondering on the solution of the equation $$\nabla^2P(\vec r)=v(\vec r)P(\vec r)^2\phantom{.......}(1)$$ Or more simply, if there exists a coordinate system where: $$\nabla^2P(\vec r)=P^2(\vec ...
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3answers
71 views

Figure out the component of a value in X and Y coordinates using trigonometry.

Alright. It's been long that I studied trigonometry and did Laws of Motion and Free Body Diagrams, and I was decent good at them, but somehow I am having trouble in understanding the following. Note ...
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4answers
114 views

I have discovered a way to calculate the absolute value (area,volume, etc) of a n-dimentional shape, using it's coordinates only, how do I publish it?

Firstly, I want to preface by saying that I am no experience with the maths community at all, however I did take Maths and Further Maths for my A-Levels. What I have discovered is a way of using ...
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10 views

Transforming matrices using tensor transformations?

Let us say I started with the matrix $$ A= \begin{pmatrix} x & -y\\ y & x \\ \end{pmatrix} $$ And I wanted to use the tensor transformation: $$ \bar ...
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33 views

How to scale x- and y- axes equally in Maple?

I have the ellipse $\frac{25}{36}x^2+\frac{5}{36}y^2=1$. Maple draws it as a circle: How can I change the coordinates, to make it look like an actual ellipse?
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1answer
38 views

Parametrizations and coordinates in differential geometry - what's the difference?

From what I've read one can introduce the notion of a tangent vector to a point on a manifold in terms of an equivalence class of curves passing through that point (the equivalence relation being that ...
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13 views

Representation of a cone in 3D

I need to find the representation of a cone in the 3D space with the following criteria: It's tip is located at the origin. It opens in the positive direction of the axis (it’s one-sided). The ...
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1answer
48 views

How to find intersection of two hypotenuses

I am a web developer who is bad with mathematics. I have never needed some math/geometry formulas before. But now I realize it is needed for more advanced design tecniques. I decided to learn math but ...
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3answers
49 views

Given I know the coordinates of a rectangle, how can I find the coordinates of an enlarged rectangle?

I have a rectangle, and know the dimensions, coordinates of the 4 corner points and therefore the centre point. If I scaled it up e.g. scalefactor * height, from its centre, how can I find the new ...
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24 views

Solve for 'y' for elipse rotated at an angle

How solve for y if we have set of x coordinates for elipse rotated at an angle 'A' ,has the origin at (h,k) and height as a and b
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1answer
58 views

Find coordinates of bounding box corners of rotated rectangle

I have a rotated rectangle inside a bounding box. It can be rotated to any angle. I know the coordinates of the "top left" corner of the inside rectangle (and I am able to work out the other 3 ...
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0answers
30 views

Local parametrizations and coordinate charts on manifolds

I have recently had discussions on related questions about coordinate charts on here which has started to clear up some issues in my understanding of manifolds. Apologies in advance for the ...
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1answer
146 views

Graham scan with collinear points

I'm having some trouble understanding the Graham scan algorithm as described in Wikipedia. Particularly, I don't understand how to handle collinear points. Consider these points as a simple example: ...
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1answer
20 views

Rearranging coordinate equation

I am looking to rearrange the following equation, given that I already know the distance and one set of coordinates (I need to find the coordinates of the second point basically) $$d = ...
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34 views

Smart coordinates for six-dimensional integral

I have a (hopefully) simple question: I am dealing with a definite (on all of $\mathbb{R}^6$) six-dimensional integral $$\int_{\mathbb{R}^6} F(\vec{x}_1,\vec{x}_2)d^3x_1d^3x_2$$ where the function ...
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1answer
29 views

How to find the position on a circle that satisfies two constraints?

Say I'm given an point P1 at coordinates $(x_1,y_1)$, and another point $P_2$ at coordinates $(x_2,y_2)$. Then I have a point $P_0$ that needs to be at coordinates $(x,y)$ such that it is a fixed ...
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3answers
43 views

2-Sphere surface coordinate dimension

Ordinary sphere in $\mathbb{R}^3$ is two-dimensional object (2-sphere), i.e. it requires at least two coordinates to define point on a surface. As I notice, however, there is a catch. If we use ...
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1answer
17 views

Other abscissa than $y = 0$?

Circle contains three vertices whose coordinates are (0,6) , (0,10) and (8,0). Abscissa of second vertex in which given circle passes through x-axis, is equal to? I do not even understand the text of ...
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39 views

Finding coordinates of position given three coordinates and distances: 3D

I'm hoping to determine the x, y, z coordinates of a 4th position (D) given the coordinates of three other positions and their distances: $A(0.25, 0.25, 0.25), B(0.4663, 0, 0.25)$, and $C (0.3912, ...
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1answer
157 views

Definition of a Cartesian coordinate system

Apologies if this is a basic question, but I'd really like to clarify the exact meaning of what a Cartesian coordinate system is. Heuristically, is it correct to say that a Cartesian coordinate system ...
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1answer
67 views

Meaning of “locally homeomorphic to $\mathbb{R}^{n}$”

I am fairly new to differential geometry and approaching it with a physics background (in the study of general relativity), as a result I'm having a few struggles with terminology etc, so please bear ...
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49 views

Constructing coordinate maps on manifolds

I've been studying differential geometry for a little while now, but I've never properly justified to myself rigorously the need to consider other more general coordinate maps, other than Cartesian on ...
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3answers
73 views

How to “rotate” points through 90 degree?

I am trying to do some intersection tests and so the math gets weird if two certain points have the same $x$ coordinate and so infinite slope. The points can be anywhere in any quadrant. I want to ...
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2answers
48 views

calculate the volume

There is a triangular prism with infinite height. It has three edges parallel to z-axis, each passing through points $(0, 0, 0)$, $(3, 0, 0)$ and $(2, 1, 0)$ respectively. Calculate the volume within ...
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24 views

Converting vector in cartesian to cylindrical coordinates

This seems like a trivial question, and I'm just not sure if I'm doing it right. I have vector in cartesian coordinate system: a⃗ =xi⃗ −2xj⃗ + yk⃗ And I need to represent it in cylindrical coord. ...
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28 views

Looking for a formula to map a 2d pixel coordinate to a region within a grid.

I am given a pixel bounding box of the form: (x1, y1), (x2, y2) Where (x1, y1) is the bottom left coordinate and (x2, y2) is the top right coordinate of the ...
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2answers
45 views

How do I calculate the angles between a point on a sphere and each unit vector in $\Bbb R ^3$?

Given the Cartesian coordinates of any point $p$ on the surface of a sphere in $\Bbb R ^3$, how do I calculate the angles between each axis $(x, y, z)$ and the vector $n$ defined by origin $o$ and ...
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1answer
82 views

Coordinate systems on manifolds

I am fairly new to differential geometry and something I can't get my head around is, if an $n$-dimensional manifold is locally homeomorphic to $\mathbb{R}^{n}$, i.e. Euclidean space, then isn't it ...
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2answers
108 views

Geometry: What is being calculated here?

Context: I am a computer graphics programmer looking at a code-implementation. I need help understanding a function that has neither been documented properly nor commented. Given a circle with ...
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0answers
17 views

Bipolar toroidal coordinates - position vector, velocity and acceleration

Bipolar toroidal coordinates: $x = a \frac{\sinh\tau \cos\phi}{\cosh\tau-\cos\sigma}$ $y = a \frac{\sinh\tau \sin\phi}{\cosh\tau-\cos\sigma}$ $z=a \frac{\sin\sigma}{\cosh\tau-\cos\sigma}$ Would ...
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26 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 point: ...
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2answers
19 views

Getting the coordinates of a point on section [duplicate]

What is the endpoint $P(x,y)$ of a line segment , if I know its starting point: $C(x(1), y(1))$, the gradient $G$, and its length $L$?
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4answers
127 views

Notation of a function in coordinates

I have a question about some notation which puzzles me a lot. Consider a function $f:\mathbb{R}^n\rightarrow \mathbb{R}^m$. Then people often write or say that if we choose coordinates $x=(x^1,…,x^n)$ ...
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1answer
49 views

Coordinates on the sphere not global?

I'm reading a book on differential geometry and some part of the introduction I do not understand but I'm curious to understand it. Maybe someone can try to explain those parts to me. "Each point on ...
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2answers
24 views

unique number from 3D coordinates

Is it possible to get a unique real number from $(x,y,z)$ coordinates? I need to sort a list of coordinates so i am looking for a simple function that generates one unique number with which to sort. ...
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0answers
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How can we express $(\hat{r}, \hat{\phi})$ in respect of $(\hat{i}, \hat{j})$ ? [closed]

We have the following: How can we express $(\hat{r}, \hat{\phi})$ in respect of $(\hat{i}, \hat{j})$ ??
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1answer
40 views

Formal name for the coordinate values of the pushforward of the inverse metric on an embedded manifold?

What is the formal name of the following object: \begin{align}\tag{4} \Delta^{\alpha \beta} = \dfrac{\partial y^\alpha}{\partial x^m} g^{mn} \dfrac{\partial y^\beta}{\partial x^n} \end{align} where ...
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26 views

How to find the location of a point in a global coordinate system from a local coordinate system

I was wondering if you would be able to help guide me on a solution involving rotation matrices. In-terms of data, I have the global coordinate system a $3\times 3$ matrix, the local coordinate ...
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1answer
55 views

Is there an equation to describe translation and rotation?

Suppose a free rod, $l=2r$, is hit on a tip T and translates with $v= 1r/s$ and at the same time rotates with angular velocity $\omega= 1rad/s$. Is there an equation that can determine the position of ...
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3answers
109 views

Why do we assume the complex plane is curvey at infinity?

In at least a few areas (i.e., those that I have happened across) when we have a need to capture a half-plane we do so by taking a semi-circle of radius $r$ in that half, and taking the limit as ...
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1answer
50 views

rectangular coordinate system vs Cartesian coordinate system?

Is there any difference between a rectangular coordinate system and a Cartesian coordinate system? Is one of them a subtype of the other? My book mentions a rectangular Cartesian coordinate system. ...
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30 views

Parametrization of surfaces for vector integration

I'm having some trouble calculating vector fields through surfaces. After attempting a few and being dissapointed with a wrong answer multiple times I figured I must be doing something wrong in the ...