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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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Relative coordinates

Hey I have a question related to relative coordinates. Say I consider a pendulum. First I have a global coordinate system. At some position a pendulum is fixed. I use a position vector $\mathbf{r}_{...
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1answer
30 views

Finding Where on a Circle a Line Segment will Intercept

Assume the following: A known point in space. A line segment beginning at the above point. The length of the segment is known, but the slope is not. A circle with a known center point and radius. ...
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Plane rotated about line of intersection to another plane?

The plane ax+by=0 is rotated about its line of intersection with the plane z=0 through an angle n. What is the equation of the plane in its new position? I saw a question in stack exchange relating to ...
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1answer
38 views

Telling the greatest angle of the triangle when slopes are given

When coordinates or position vectors (2D or 3D) of vertices A,B,C of a triangle ABC or its side vectors AB, BC, CA are given we can find the largest angle of $\Delta$ ABC by finding the angle ...
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Coordinate transformation in ODE's with a unit step function

Consider the following general set of 2 ODE's $$\dot{x}=\Theta(\dot{x} )f_1(x,y)+(1-\Theta(\dot{x}))f_2(x,y)$$ $$\dot{y}=(1-\Theta(\dot{y}))g_1(x,y)+\Theta(\dot{y})g_2(x,y)$$ where $\Theta(x)$ is ...
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1answer
15 views

How do I calculate the coordinates of the centers of the faces of a truncated icosahedron?

I'd like to draw a truncated icosahedron in 3-space. Wikipedia gives formulas for the cartesian coordinates of all the vertices, but I'd like just the center coordinates to use as local coordinate ...
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1answer
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Translate point after rotation relative to different origin

I have 200x380 input image and coordinates (63,146) where (0,0) is top-left: I rotate about the centre some amount of degrees and expand the "canvas" to avoid cropping resulting in larger output ...
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2answers
29 views

Find the coordinate if slope, distance and one coordinate is known.

I have got a coordinate $(x_1,y_1)$ say, $(10,12)$ and a slope of $3$. Now I need to find a coordinate $(x_2,y_2)$ such that is $4$ units away from $(x_1,y_1)$. I know the formula $d = \sqrt{(y_2-y_1)...
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2answers
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Relation between Vectors and Coordinates [closed]

My teacher said that Vector Algebra and Coordinates are same thing but only difference is sense of direction. $Question$: Do we use vectors just for definiting direction or there is any other purpose ...
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1answer
7 views

Coordinate transformations

I have two scalar functions of $x$ and $y$ that I can define: $$f(x,y)=x^2+y^2\qquad \text{and}\qquad g(x,y)=x^2 + \sin^2(x) y^2.$$ Is it true that there is literally no coordinate change that will ...
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1answer
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GRE Coordinate Geometry Question

Question: In the xy-plane, the point with coordinates (−6,−7) is the center of circle C. The point with coordinates (−6, 5) lies inside C, and the point with coordinates (8,−7) lies outside C. If m is ...
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Determining circle-line intersection on sphere

There are two sets of coordinates (latitude/longitude) that form a line along the surface area of the Earth. There is a third coordinate, along with a radius, that denotes a circular region somewhere ...
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0answers
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Pure pursuit algorithm - Transform Global to vehicle coordinates?

project: autonomous driving car I have a small RC car, a Raspberry Pi and a camera which are fixed on the car. Now I want to let the car drive autonomous with image processing. So far I can detect ...
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0answers
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Equivalence relation for homogeneous coordinates

My geometry textbook states that the vectors $(a, b, c)^T$ and $k(a, b, c)^T$ represent the same line for any non-zero $k$; in other words, two such vectors related by an overall scaling are ...
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3answers
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Finding the position where a picture was taken

Assuming I have a photo where a few significant points are visible, and I can point them out on a map. How many points would I have to identify, in order to find the precise position? Would I also ...
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1answer
23 views

Scalar relationships between the coordinates of two rotated coordinate systems

I'm wondering how come between the coordinate system $\xi \eta$, rotated -45° with respect to $x y$ coordinate system, and the $xy$ coordinate system there are the following relationships: $$x = \...
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1answer
67 views

Evaluating Area Under a Curve [closed]

Consider the curves: $$\displaystyle f: \Big(\frac{x-c}{a}\Big)^{2k+1} + \Big(\frac{y-d}{b}\Big)^{2k+1}=1$$ $$\displaystyle g: y = -\frac{b}{a}x +d+ \frac{bc}{a}$$ Where $a$,$b$,$c$,$d$,$k$ $...
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1answer
37 views

Finding plane equation from an orthonormal basis

I have a $3$-dimensional data set, $\textbf{X}$, from which I have found the singular value decomposition $\textbf{X}$=$\textbf{U}$$\textbf{S}$$\textbf{W}^T$. As I understand, the vectors $\left\{...
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4answers
29 views

Coordinate change in $n$-dimensional space

I have a unit vector in an $n$-dimensional space, $V = [v_1, v_2, ..., v_n]$. I am looking for a transformation $R$, $\;W = R * V$, which could give me back $\;W = [1, 0, ..., 0]$. Any idea?
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0answers
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How can i draw a rectangle through two points on a spherical coordinate system?

So I have two points, as an example: x1 = (49.233381, 28.483318); x2 = (49.233366, 28.483529); Using this points i need to draw rectangle. Which have a=200m ...
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Problem with Graphing Transformation of Cartesian coordinate into Polar coordinate.

I was trying to map Rectangle from cartesian to polar coordinates. I started by making a rectangle in a Cartesian Plane. From the x and y coordinates of the rectangle, I calculate the radius and angle ...
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1answer
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Finding equation of the parabola from tangent information

Two lines drawn through $T$ at $(-1,-2)$ are tangent to a parabola at $P$ $(2,3)$ and $Q$ $(3,-1)$, respectively. Find the equation of the parabola. I tried using similarity of triangles to find the ...
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Maximum number of common chords that are existent between two Conics

The maximum no. Of common chords between a circle and a parabola is 6. this is because they can have at most Four Points of intersection. However I have doubt regarding other combination of conics. ...
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2answers
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What will be the equation of an annulus? [closed]

Let us consider a circle with radius 4 and a concentric circle with a radius 2. Now if the annular region is shaded, what will be the equation of the shaded annular region?
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3answers
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What branch of mathematics does coordinate systems belong to? [closed]

I'm a high school student and I'm new to mathematics involving coordinates, especially polar coordinate systems and cartesian coordinate systems.
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0answers
37 views

Triple Integral: Coordinate change from polar to spherical $(dx\wedge dy\wedge dz)\rightarrow(d\rho\wedge d\phi\wedge d\theta)$

Let $x=\rho \sin(\phi)\cos(\theta), y=\rho \sin(\phi)\sin(\theta), z=\rho \cos(\phi)$. Then $$dx=d(\rho \sin(\phi)\cos(\theta))=\sin(\phi)\cos(\theta)d\rho-\rho \sin(\phi)\sin(\theta)d\theta+\rho \cos(...
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Is there an appropriate transformation of weights?

Background Sometime back I managed to conjecture an interesting formula: $$ \lim_{k \to \infty} \lim_{n \to \infty}\ \sum_{r=1}^n \lambda_r \left( f(\frac{k}{n}r)\frac{k}{n} \right) = \lim_{s \to ...
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4answers
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If $p$ is the length of the perpendicular from the origin of a line $ \frac{x}{a}+\frac{y}{b}=1 $, what can be it's property? [closed]

If $p$ is the length of the perpendicular from the origin of a line $ \frac{x}{a}+\frac{y}{b}=1 $, what can be it's property? The options were: A) $ p^2=a^2+b^2 $ B) $ \frac{1}{p^2}=a^2+b^2 $ C) $ ...
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Integer coordiantes problems [duplicate]

A point $A$ is called "be seen" from $O$ iff there is no integer point on $OA$ (except $O$ and $A$). (Sorry for my translation because i don't know exactly this definition in English). The problem ...
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2answers
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From $dxdy$ to $\rho d\rho d\phi$. Where am I doing wrong?

A small area element in the xy plane reads $da=dxdy$. In plane polar coordinates, it reads $da=\rho d\rho d\phi$. We also know, $$x=\rho\cos\phi,~ y=\rho\sin\phi.$$ So using partial derivative formula,...
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0answers
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Local polar coordinate system to global polar coordinate system

Let's have a point located in the local polar coordinate system at $(r,\phi)$. The origin of this local system is located at $(R_0,\Phi_0)$ in a global coordinate system. I would like to express $(r,\...
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Questions on coordinate representation of a map between smooth manifolds (sphere with stereographic projections)

On the sphere $S^n$, consider the atlas given by the stereographic projection: $\{(U_1, \phi_1), (U_2, \phi_2)\}$, where $U_1 = S^n \backslash \{N\}$, $U_2 = S^n \backslash \{S\}$, $N$ and $S$ are ...
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Questions about the basics of coordinate systems and their basis

Since I think I am missing some basic understanding about coordinate systems and their basis, I would really appreciate your help answering my questions. Also if something isn't written mathematically ...
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1answer
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Change of base matrix between displaced and rotated coordinate systems

I have a function that solves a problem when a specific angle equals $0$. The same function can be used with non-zero angles if you compute the problem from other coordinate system. The scheme of the ...
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1answer
25 views

Coordinates of 3D vector in rotated coordinate system (without using a matrix)

The problem: There is a vector with coordinates X,Y,Z. This vector is in a coordinate sytem that has been rotated by A degrees along the X axis and B degrees along the Y axis. I would like to know ...
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4answers
33 views

Is it possible to know the equation of a line by only knowing the slope and where the line intercepts the x axis?

I do not know where my line intercepts the $y-$axis. I know it intercepts the x axis at coordinate $(10, 0)$. At an angle of $30^{\circ}$. So would $$y = mx + b = (10\tan(30)) + b$$ be correct? ...
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1answer
21 views

I have 3 objects in the real world that I want to mark on a x y graph, I know where to plot 2 of them but how to mark the third point?

In the real world I have 3 points of interest ABC. A B and C are each 20 cm apart and are placed in a equilateral triangle formation. A coordinates are (-10, 0) and C coordinates are (10, 0). I'm ...
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1answer
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Given a set of points, find maximum area of triangle

Given a finite set of 2-d points, I need to find the maximum area of triangle formed. My solution steps : Take mean of points , lets call it (x_m, y_m). Take 3 most distant points from (x_m, y_m). ...
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1answer
31 views

1 Coordinate Geometry [closed]

In a Quadrilateral ABCD ,if the bisectors of angle A and angle C meet on BD ,prove that the bisectors of B and D meet on AC. Can someone please help me with a coordinate geometry proof .
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0answers
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Geodesics under coordinate transformation

Consider components of metric tensor $g'$ in a coordinate system $$g'= \begin{pmatrix} xy & 1 \\ 1 & xy \\ \end{pmatrix} $$ We can transformation rule which brings $g'$ to euclidean metric $...
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1answer
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How to designate a coordinate system

Imagine I have a coordinate system where the coordinates are $a$ and $b$ How to designate this system? $a-b$ $ab$ $a,b$ $aOb$ (where $O$ stands for origin). Is there an accepted standard? I have ...
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Relation between Normal coordinates and Cartesian coordinates in flat space

Let $\gamma_v$ be the unique maximal geodesic with initial conditions $\gamma_v(0)=p$ and $\gamma_v'(0)=v$ then the exponential map is defined by $$exp_p(v)=\gamma_v(1)$$ If we pick any orthonormal ...
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1answer
43 views

Help a robot avoid computing the matrix inverse using the Gram-Schmidt process

Imagine you have a robot whose position is recorded as $t_1, t_2, t_3, \dots$ in its coordinate frame. Check the visualization here. We can write down the robot's basis in our 2D image plane, i.e. ...
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0answers
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Vectors and Coordinate planes with non-perpendicular axis

Given two vectors $A$ and $B$ with $|\theta_A-\theta_B|=\frac{\pi}{2}$ and $r_a$ and $r_b$ are any real numbers, can every possible vector be represented by $A+B$ with some constant $r_a$ and $r_b$? ...
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0answers
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How to fill a rectangle with smaller specific rectangles that have cardinal information about their adjacent neighbours

Lets say its 6x6 grid that is represented by top left(0,0) and bottom right(1,1) in coordinate system. Next, I have set of objects with their cardinal directional information about each of their ...
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2answers
39 views

How can I apply a sign to a calculated angle?

apologies in advance as I'm a software engineer and not a mathematician so I will probably explain this very poorly. Thanks for muddling through it. I have a system with three points in three-...
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How do I use a set of orthogonal vectors as a new coordinate system?

I'm dealing with a problem where I need to apply a coordinate transformation to a set of data, but am not sure how. This is probably very simple, but I want to make sure I do it right. Suppose that ...
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1answer
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Find the grid number of a X,Y coordinate

Let's say we have a grid separated in chunks. Each chunk contains multiple points. Grid and chunks Each chunk has a number : Chunks numbers Let's say we have a point X,Y, how do we find its grid ...
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1answer
18 views

About the definition of divergence

The divergence is defined as: $\nabla . \mathbf{A}=\lim \limits_{V \to 0} \dfrac{ \unicode{x222F}_{\partial V} \mathbf{A}.d\mathbf{S}}{V}$ My question is of two parts: $(1)$ If we are using ...
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1answer
13 views

Calculating projected coordinates for rotations on a Cartesian plane

There are four points Blue (4,1), Purple (6,3), Red (9,3) and Green (4,5) plotted on a 1 cm Cartesian grid. I want to rotate the diagram about the Blue point anticlockwise (2nd layout) and clockwise (...