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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0answers
6 views

Divergence free part of laplacian operator in cylindrical coord. (Curl Curl operator)

I want to derive $\nabla \times \nabla \times \mathbf{V}$ in cylindrical coordinates. My variables are $(u,v,w)$ in $(z,r, \theta)$ (axissymetric, radial and azimuthal directions). I computed first ...
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4answers
49 views

Points on 3d line

Say we have $2$ points on a 3d line, point $A(x,y,z)$ and point $B(x,y,z)$. If we want to get the coordinates of a third point, beyond point $B$ but a certain distance from point $A$, how would we do ...
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1answer
18 views

new plane equation after transformation of coordinates

I have a plane equation $ax + by + cz + d = 0$ w.r.t to a particular coordinate frame. this coordinate frame w.r.t to the world coordinate frame is $$\begin{vmatrix} r_1 & r_2 & r_3 & ...
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1answer
15 views

Finding the equation for the tangent plane to earth given latitude and longtiude

I'm creating a program where I need to calculate the equation of the plane tangent to the earth at a given latitude and longitude. I used Projecting an Arbitrary Latitude and Longitude onto a Tangent ...
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0answers
2 views

Transformation from unknown orientation representation to DCM

I'm working with some really strange software which has some sort of custom orientation representation, and I'm trying to get it into a standardized format (direction cosine matrix). However, that's ...
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3answers
18 views

How to move the position of a curve $x,y$ coordinates?

I have some silly problem. I want to know how to move the curve in $x,y$ coordinates which I have some curve. For example, $f(x) = x^2$ and this is originally start at $(0,0)$. But I want to this ...
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1answer
10 views

Angle of Elevation in Earth Coordinate Systems

Does a calculated angle of elevation differ between earth centered earth fixed (ECEF) coordinates and geodetic coordinates? I've computed an angle of elevation from one object to another in 3D space ...
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0answers
18 views

How can I obtain a unit vector of a shifted spherical system?

I hope that I can explain myself clear enough, Assuming I have a sphere that has been moved down in the $Z$-axis. I know that r unit vector when the sphere is not shifted can be expressed as: ...
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0answers
4 views

How can I obtain a unit vector of a shifted spherical system?

I hope that I can explain myself clear enough, Assuming i have a sphere that has been moved down in the Z-axis. I know that the radial unit vector when the sphere is not shifted can be expressed as: ...
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0answers
16 views

Given the perimeter of an equilateral triangle, and a fraction of the perimeter, how would i find the (x,y) coordinates of the triangle.

Given the perimeter of an equilateral triangle, and a fraction of the perimeter, how would I: Create a formula for finding the x coordinate Create a formula for finding the y coordinate of the ...
2
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3answers
224 views

Parametric coordinates of parabola?

Can $(a(\sin(t))^2 , 2a \sin(t))$ be the parametric coordinates of the parabola $y^2 = 4ax$ ? I found that these coordinates satisfy the equation of the parabola but my friend says that although ...
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0answers
17 views

Coordinate Systems Transformation(Rectangular to Cylindrical)

I am new to this subject: Cartesian, Cylindrical and Spherical coordinate system. Coordinate System Transformation I have this example problem that I cant get the right answer. Transform to ...
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3answers
46 views

Do these points make a straight line?

I'm trying to prepare for my calculus 3 class coming up this fall and doing some practice problems. I'm having a hard time visualizing some of these 3D coordinates. $D(0,-5,5)$ $E(1,-2,4)$ ...
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0answers
6 views

Finding the 3D coordinates of an object with cameras

I'm working on a project where I need to find the coordinates of an object. I used this paper for now http://dsc.ijs.si/files/papers/S101%20Mrovlje.pdf . It describes how with two cameras facing the ...
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0answers
37 views

Provide solution to geometrical problem [closed]

Given points belonging to great circles (within an error: ±0.5⁰show): A- Which belong to the same circle? B- Which circles intersect? C- Prove the points of intersection are unique. With the data ...
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1answer
32 views

Interpolating Random Points

I have a list of (x,y) co-ordinates that need to be interpolated. The co-ordinates are not necessarily part of a function. Therefore, polynomial interpolation will not work. Is there a way to use some ...
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0answers
10 views

lat/lon spherical coordinates to equidistant spherical coordinates

How to transform spherical data expressed in latitude/longitude pairs (parallels/meridians) in a new set of pair expressed just in parallels pairs? In other words, I need to transform data expressed ...
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0answers
22 views

Converting longitude and latitude to altitude and azimuth

I am interested in a problem where a camera is mounted on the Earth that has a mechanism for altitude and azimuth adjustments. The longitude, latitude and altitude of the camera are known, and the ...
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1answer
19 views

Cross product in spherical coordinate

Hello I have a question: Is the formula for the cross product the same in spherical coordinates as in cartesian coordinates? I have found conflicting answers on the internet.
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1answer
22 views

Coordinates of regular octagon

There are coordinates of two vertices in a regular octagon $$\{A_0,A_1,...,A_7\}$$ with Cartesian coordinates $A_0 = (2,-4)$, $A_2 = (0,0)$. The task is to find coordinates of all other vertices. ...
2
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1answer
46 views

Conversion between coordinate systems

I am trying to convert between two coordinate systems and think I've come up with the answer but would like to make sure my assumptions are correct and to help with some of the math. The problem is ...
2
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0answers
23 views

Multiple objects triangulation in 3D, intersecting the right vectors (rays)

I am working on a project in which I should be able to triangulate the position of multiple objects when they are seen by (at least) two cameras. Single object Currently I am able to triangulate a ...
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1answer
9 views

Gradient in cylindrical coordinates

This is more of a maths question, but several sources point at different expressions for the gradient in cylindrical coordiantes. Sometimes I see the radial component for the gradient of a scalar ...
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0answers
37 views

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 ...
1
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1answer
23 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
51 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
48 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
32 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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0answers
13 views

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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0answers
18 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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0answers
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
63 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
105 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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0answers
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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0answers
30 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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0answers
12 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
46 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
28 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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0answers
23 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
36 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
25 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
137 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
19 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 = ...
2
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0answers
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
27 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
16 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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0answers
38 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, ...