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Questions tagged [coordinate-systems]

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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Skew coordinate system transformation matrix

I am currently working through problems in Susan Lea's Mathematics for Physicists. However I am stuck on a problem and the book is not known to errata. The problem is: A Skew (non orthogonal) ...
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2answers
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How to find the auxiliary circle of a non-standard ellipse?

Given the equation of conic C is $5x^2 + 6xy + 5y^2 = 8$, find the equation S of its auxiliary circle? Now, I know that the equation C is an ellipse. Since $\Delta = 5*5(-8) - (-8)(3^2) \neq 0$ And,...
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1answer
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Finding the faces of a shape from coordinates

I have shapes, both regular and irregular that are defined by a set of 3D xyz coordinates i.e. 100 coordinates that define a cube. Some of there coordinates make up the faces of the cube and some of ...
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1answer
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Rigorous version of “spatial infinity is a point and not a sphere”

This is a question on differential geometry/topology of Lorentzian manifolds. It is motivated by Physics, but since I want a mathematicaly rigorous formulation I think the correct place to ask is here....
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Riddle Based Question [closed]

On a plane are two points A and B at a distance of 5 Apart. The number of straight lines in this plane which are at a distance of 2 from A and at a distance of 3 from B.
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1answer
31 views

Finding third point coordinates knowing start & end point coordinates

In my timeline i know the position of the first & last date: 1914-02-10 = (79.5, 0) 2018-08-12 = (823.5, 0) How can i calculate the position(x-coordinate) ...
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Defining a coordinate system for a ray

My doubt comes from the following problem in the book "Geometry from an advanced standpoint". Given a ray $\overrightarrow{AB}$, there is a coordinate system $f$ on the line $\overleftrightarrow{AB}$...
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How does Z-order curve preserve locality?

I recently came across Z-order curve which maps multidimensional data points to one dimension preserving locality. It uses bit-interleaving of coordinate values. Intuitively I can see from diagram ...
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1answer
33 views

Finding point coordinates that have been reflected.

I'm just working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have ...
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2answers
71 views

How can there be a position vector?

I'm studying curvilinear coordinate systems in $\mathbb{R^3}$, and after thinking about it for some days I still don't understand this. When we have, say, cylindrical coordinates, we have a different ...
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2answers
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Finding components of lines intersecting at a point.

I'm just working on some summer problems so that I can be more prepared when I go into my class in the fall. I found a website full of problems of the content we will be learning but it doesn't have ...
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1answer
28 views

If (-x,-y) is in 4th quadrant, then which option or options are true? [closed]

If $(-x,-y)$ is in 4th quadrant, then which option or options are true? A) $1/x<1/y$ B) $(1/x)+(1/y)>0$ C) $(1/x)-(1/y)>0$ D) $(1/x)-(1/y)<0$ E) $(1/x)+(1/y)<0$
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4answers
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Why do we start measuring angle from positive direction of X axis only?

Why do measure the angle from positive X axis in coordinate geometry? Further we also say clockwise rotation would produce negative angles? How can angles be negative? I mean, how much is $-30°$? Does ...
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0answers
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Prove that the semi Latus rectum of an ellipse is the harmonic mean of the segments of focal chord.

I am a 12th student. I found this property in a reference book, without its proof. So i tried to prove this myself but got stuck. Here's my attempt at the problem: Basically the question is to prove $$...
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4answers
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Why complex plane is defined? [duplicate]

I am not getting the motivation behind defining Complex plane. I mean why defining such plane helps to understand $i$? So if I want, can I replace any other number in place of $i$( suppose, I replace ...
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1answer
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Distance between co-ordinates in a plane

A and B are two points on a co-ordinate plane. All the points, in the same plane as A and B, whose distance from B is twice that from A lie on a a straight line intersecting AB at a point O such that ...
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1answer
21 views

Finding a transformation between a positional and an acceleration vectors

I'm trying to solve the following problem. I have two sensors sticked together. The first one gives its positional data (x, y, z) in meters in a custom coordinate system with its a certain origin in a ...
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0answers
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How Euler angles change when we reverse direction of some axes

I looked at the other questions but couldn't find an answer for this particular question: I have measured Euler angles of an object in one coordinate system and I need to use these data in another ...
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1answer
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New coordinates after rotation of axis around origin.

I have a point $(-24.75665066,0.61535793,34.60714434)\in\mathbb{R}^3$ I would like to find the new coordinate after a $3\times3$ rotation matrix is applied to the axis, around the origin. Matrix ...
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0answers
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Find the area of triangle having equations {x+2y-5=0}, {2x+y-7=0} and {x-y+1=0} [duplicate]

I was just studying the coordinate system and came through a problem in which I was supposed to find area of triangle without finding it's coordinates!.! It's equations were given. It is totally a new ...
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1answer
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translate linear coordinates to circular space

I have $5$ points ($P_0 \rightarrow P_4$) on a straight line, and $4$ control points ($C_1 \rightarrow C_4$) that I use to connect the points with quadratic bezier curves (as seen in the top part of ...
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1answer
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2nd Point of Sector that lies on Circle on a 2D coordinate plane?

Hey can anyone help in finding the second coordinate of sector that lies on circle. I have a circle of radius 10 units, centred at (0,0). I am parting a sector of angle theta(sector can be minor or ...
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1answer
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mapping a cube into a tetrahedron

I have a cube with vertex at (0,0,0),(0,0,1),(0,1,0),(1,0,0),(0,1,1),(1,1,0),(1,0,1),(1,1,1), and a tetrahedron with vertex at (0,0,0),(0,0,1),(0,1,0),(1,0,0). How do I map the cube's coordinates to ...
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1answer
61 views

Finding coordinate points of corners of a triangle [closed]

Assuming one of the corners is at (0,0), and you know the lengths of all sides, is it possible to find the coordinate points of the other two corners? I can find the values of each angle using the Law ...
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1answer
65 views

Pull Constant from Atan2 Function

I am trying to calculate intersection Latitude value based on given coordinates and intersect Longitude. $\begin {align} b &= \text {is bearing in radians} \\ Lat_1 &= \text {is Latitude 1} \\...
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1answer
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Gradient of vector field using differential forms

I have been reading about differential forms from various sources. The usual vector-calculus operations of gradient, divergence, curl are nicely represented by the exterior derivative operator $d$ ...
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1answer
27 views

Generalised change of spherical coordinates

I have a set of points in an equatorial coordinate system specified by a longitude, $0^{\circ}\leq\alpha < 360^{\circ}$ and a latitude, $-90^{\circ}\leq \delta \leq +90^{\circ}$ I want to take a ...
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1answer
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Parameterizations of the unit simplex in $\mathbb{R}^3$

The unit simplex in $\mathbb{R}^3$ is $$\Delta^3 = \left\{(t_1,t_2,t_3)\in\mathbb{R}^{3}\mid t_1+t_2+t_3 = 1 \mbox{ and } t_i \ge 0 \mbox{ for all } i\right\}$$ When trying to describe it ...
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1answer
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Point in Coordinate System A, how to find its location in Coordinate System B?

SHORTEST POSSIBLE WAY TO ASK MY QUESTION (edit) I have a 3D point (x,y,z) and two coordinate systems. The rotation and translation between the coordinate systems is known, as I have a quaternion ...
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2answers
39 views

Correct way to find the area of a concave quadrilateral in co-ordinate geometry using triangles.

A lot of textbooks where I live teach students to calculate the area of a quadrilateral using its coordinates by considering it to be made up of two triangles. We calculate the area of each triangle ...
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1answer
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New coordinate system

I have an exercise where if $\Sigma=(0,E)$ is a orthogonal coordinate system, then the line $r$ is such that: $$r\colon X=A+\lambda\vec{AB}$$ where $A(1,2,1)_{\Sigma},B(2,1,2)_{\Sigma}$ and $C(3,1,2)_{...
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1answer
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coordinates of a car given its trajectory.

I have some straight and curve pieces that I use to build tracks for a car (robot), so every time the shape of the track where the car will move is known but I don't have its equation (I think getting ...
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1answer
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I don't know how to find coordinate systems for a question. [closed]

MST is $3 \times 3$ homogeneous matrix that transform points from coordinate system $S$ to coordinate system $T$. 1- What are the coordinates of $P$ in coordinate system $O$? 2- What are the ...
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Given the speed of an object expressed in NED, how can i plot its position relative to a fixed starting point?

Firstly, sorry in advanced for my convoluted description, I think it's always a sign of not understanding the subject when one find its hard to even explain the question in the right terms, hopefully ...
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1answer
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Problem of coordinate transformation $x^\alpha$

This is intuitively very simple problem but I am unable to complete it with Mathematical rigor. Here is the deal: A coordinate system $(u,v,w,p)$ in which the metric tensor has the following non-...
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1answer
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Plotting XYZ coordinates, given an array of distances to n 3D vertices.

I believe this is more of a mathematical topic than a gaming one, hence the post here. For the sake of context: In a game called Subnautica, the player has the ability to move about in an underwater ...
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1answer
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Partial Derivatives of Cartesian and Polar Coordinate Systems

Plane polar coordinates, $r$ and $\phi$, and Cartesian coordinates, $x$ and $y$, are related by $$x=r\cos\phi,\ y=r\sin\phi,$$ and $$r^2=x^2+y^2,\ \phi=\tan^{-1}({y \over x}).$$ To try to find the ...
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Lines and Points

Let $S_1$ and $S_2$ be the set of points in x-y plane (where $x>0$ and $y$ is real) defined as: $$S_1 = \{(x,y) : | x + |x|| + |y + |y|| < 2\}$$ $$S_2 = \{(x,y) : | x - |x|| + |y - |y|| < 2\}$...
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1answer
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Cylindrical Coordinates example

I am trying to describe the surface given by the equation $\theta = \pi/4$. Now, since $x$ and $r$ can be anything, doesn't this describe a vertical plane through the origin, given by $y=x$? I am told ...
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How to create a point behind another point given an angle?

I have a point A and a radian angle value R (image below describes this heading system) that represents a heading from point A. How do I create a point B that is a small, fixed distance (like 1.0 ...
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3answers
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How to get the transform the coordinates of a 3D point from the standard basis to another basis?

Suppose I have the coordinates of a point in the standard $\mathbb{R}^3$ basis $B_0 = (\vec{e_0}, \vec{e_1}, \vec{e_2})$, with $\vec{e_0} = (1,0,0)$, $\vec{e_1} = (0,1,0)$ and $\vec{e_2} = (0,0,1)$. ...
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1answer
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Finding 3rd point coordinates of rectangular triangle [closed]

I have to calculate coordinates of 3rd point of rotated image in programming language. This are images, so coordinates are always positive, where left top corner is ...
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3answers
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Shortest distance from ellipse to line

What is the shortest distance between the ellipse $$\frac{x^2}{4}+y^2=1$$ and the line $y=\frac{-\sqrt{3}}{2}x+8?$ I tried solving it by using a line that is tangent to the ellipse and parallel to ...
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2answers
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Position of Point with respect to a Triangle

Consider a triangle formed by three sides, equations of which are as follows - a1x + b1y + c1=0 a2x + b2y + c2=0 a3x + b3y + c3=0 Is there a nice method to figure out whether a point P(h,k) lies ...
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2answers
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Is the aircraft flying inside the safe zone?

I have the latitude and longitude say $(x_i, y_i), i = 1, 2, \ldots n$ ordered ooints on the boundary of the the safe flying zone. I also have the coordinates of the current location of an aircraft $(...
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1answer
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How can I define the relationship (something similar to correlation) between 2 sets of points?

I have 2 sets of points with different number, namely $Blue=\{(x_1,y_1),(x_2,y_2),...(x_n,y_n)\}$ and $Yellow=\{(x_1,y_1),(x_2,y_2),...(x_m,y_m)\}$, how can I define some indicator to reflect the ...
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0answers
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How to determine scale factor of x-values in a grid that have been both moved and scaled?

I'm converting vector file types and during the conversion, the $x$-values are both moved and scaled. In the image below, the left-hand blue point had an $x$-coordinate at $0$ while the right-hand ...
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1answer
28 views

Find the equation of the circle(s) touching $u$ and $S$.

Given line $ u : 2x + y - 4 =0$ and circle $ S : x^2 + y^2 -16x -20y + 159 = 0$. Find the equation of the circle touching $u$ and $S$ externally and has radius $2\sqrt5$.What I have done is that I ...
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1answer
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What is this comma notation for the definition of position vectors? (basis vectors)

In Wikipedia, this formula is used to show the definition of position vectors in all three coordinate systems: position vectors. In spherical coordinates, the position vector is defined as: $\vec{r}(...