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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Avoiding the spherical polar coordinate singularity on $S^2$ by using a double cover?

Is it possible to avoid the spherical polar coordinate singularity on $S^2$ by taking the coordinates as they originally are on $T^2$, i.e. ranging from $0$ to $2\pi$ mod $2\pi$? How would one ...
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1answer
30 views

Coordinate transform a triangle

There is a triangle with points P1(x1,y1),P2(x2,y2),P3(x3,y3) on an XY plane. The final ...
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1answer
16 views

Polar angle of a given point

How to find out polar angle of a given point $A(x_1,y_1)$ relative to another point $B(x_2,y_2)$ in a 2D space?
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1answer
25 views

Definition of a cubic coordinate system

I'm looking at "Foundations of Differentiable Manifolds" by Frank Warner, and have a question about one of the basic definitions at the beginning of the book. He writes: A coordinate system $(U,\phi)$...
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18 views

Calculating x and y coordinates from curvilinear orthogonal coordinates.

We have a curvilinear orthogonal coordinate system defined with $u=xy$, $v=\frac{x^2 - y^2}{2}$, $z=z$. First, calculate x and y. For them, I got $x=\sqrt{\frac{-2v\pm2\sqrt{v^2-u^2}}{2}}$ and $y=u/x$...
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0answers
24 views

Adding Pitch/Yaw to Spherical Coordinates

Im running a program on a simulator where I have a stationary camera at global position $(0, 0, 0.48)$ with a pitch $=-28$ and yaw $=0$ rotation. The reference for this pitch and yaw are the global ...
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1answer
23 views

The meaning of spacecraft attitude represented in quaternion

I am reading the following paper about the attitude control of aircraft: http://ieeexplore.ieee.org/stamp/stamp.jsp?arnumber=1271671 The quaternion represents the relative orientation of two ...
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2answers
28 views

Find the volume defined by $ 0 \leq z^2 \leq 2$ and $x^2 + 4y^2 - (2-z)^2 \leq 0$

I am asked to find the volume defined by $$ 0 \leq z^2 \leq 2\\ x^2 + 4y^2 - (2-z)^2 \leq 0 $$ How can I do that using cylindrical coordinates? Is that minus sign before $(2-z)$ really supposed to ...
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1answer
33 views

Induced metric on a one-sheet hyperboloid

I am trying to find the induced metric on a one-sheet hyperboloid. Suppose we use cylindrical coordinates $(r, \theta, z)$ for the ambient space in which the hyperboloid is embedded. The hyperboloid ...
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0answers
39 views

Triangulation with two camera setup - Result in world or camera coordinate system?

I have some problems to understand how I can triangulate a 3D-point using a two camera setup. Let's assume I'm using a right handed coordinate system and the camera is looking in positive z-...
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1answer
17 views

Derive the length of the longest line segment that can be enclosed inside the region A.

Q. Let A be the region in the xy-plane given by A={(x,y): x=u+v, y=v, u^2+v^2≤1}. Derive the length of the longest line segment that can be enclosed inside region A. My attempt: I found the equation ...
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1answer
26 views

Converting coordinates

I am having huge trouble converting between cartesian to polar and to spherical. I need these methods for my limits of integration in most cases but using the formulas never seem to work, I just ...
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2answers
33 views

parametric polar equation of a circle

I discovered that Mac's Grapher has a parametric polar mode, i.e. where $r$ and $\theta$ can be specified in terms of a parameter, usually $t$. I am attempting to convert the generic equation for a ...
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0answers
10 views

Linear equation scale transform

I have a linear equation in the general form: Ax + By = C in the standard coordination (Cartesian Coordinate System). I would like to scale this linear's coordination to a custom ratio (for example x =...
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1answer
26 views

Triple integral $\int_{0}^{2\pi} \int_{0}^{2\cos(\theta)} \int_{0}^{\sqrt{2r\cos(\theta)}} r \ dzdrd\theta$ to find volume of a solid

On evaluating the volume between $$x^2+y^2 = 2x\\z^2=2x$$ I set up the triple integral $$\int_{0}^{2\pi} \int_{0}^{2\cos(\theta)} \int_{0}^{\sqrt{2r\cos(\theta)}} r \ dzdrd\theta$$ for which ...
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0answers
19 views

Using GPS coordinates in trillateration

for a project we need to find a certain position. The info we have : 3 surrounding positions and the distance between those positions and the point we are looking for. We've got a setup like this ...
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0answers
17 views

coordinate transformation of operators

I recently came across a youtube video (https://www.youtube.com/watch?v=6O6iZug6e6Y) on transformation electromagnetism (yes this is physics) and some of the math equations that was postulated did not ...
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1answer
19 views

Find coordinates of point C in a equilateral triangle [closed]

How to find the coordinates of point C in a equilateral triangle, where $A=(-2,2)$ and $B=(6,2)$. http://i.stack.imgur.com/TXjjG.png Thanks in advance
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1answer
16 views

How to find coordinates of $D$

How can I find the coordinates $D$ if I have the other coordinates of a parallelogram $A(-3/-2)$, $B(4/1)$, $C(6/5)$, $D(?/?)$. Thanks in advance
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1answer
27 views

Cone under similarity transformation

Suppose we have a cone passing through the origin of $xyz$ coordinate system. Now, the question is that whether we can find an invertible transformation on this coordinate system that turns the cone ...
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1answer
19 views

how to find the pivot/axis and angle that move one coordinates space to another?

I am writing a plugin for a 3d modeler, and I am stuck. For my plugin, I need to get the axis and the angle used for rotating a 3d object. But I only get the coordinates (~ 3dmatrices) of the objects ...
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1answer
28 views

Can point in 3D space be represented as vector?

If yes, then such vector is just displacement from origin in coordinate system? Also, I have another(optional) question, how to name variable that represnts particular point using vector? Position or ...
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0answers
11 views

determine lat/lng coordinate by adding distance in one direction from another coordinate

How can I calculate the coordinate of a latitude/longitude point that is X feet in one direction (North, South, East, or West). For example, how do I get the point 1000ft North of 45,-100? 500ft East ...
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0answers
47 views

Flea on the coordinate system

We drop a flea on a point of the coordinate system(with integer coordinates). Due to the dimensions of the flea we can not see it. The flea jumps away every second by one unit (always in the same ...
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2answers
25 views

Volume of paraboloid $z = x^2+y^2$ with heigth $h$

I am asked to find the Volume of paraboloid $z = x^2+y^2$ with heigth $h$. How would be the best way to approach that problem (cartesian/cylindrical)? My reasoning using cylindrical coordinates doesn'...
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0answers
18 views

Evaluate the integral $f(x,y,z) = x$ within $x^2+4y^2+9z^2 \leq 1$ and $x \geq 0$ and also $y \geq 0$

I am asked to evaluate the integral $f(x,y,z) = x$ within $x^2+4y^2+9z^2 \leq 1$ and $x \geq 0$ and also $y \geq 0$ using a change of variables. Should I proceed with spherical coordinates? If so, is ...
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2answers
38 views

Evaluating the integral of $f(x,y,z) = \frac{y}{\sqrt{z}}$ on $y \geq 0$ and $0 \leq z \leq x^2$ and $(x-2)^2+y^2 \leq 4$

I am asked to evaluate the integral of $f(x,y,z) = \frac{y}{\sqrt{z}}$ on $$ y \geq 0\\ 0 \leq z \leq x^2\\ (x-2)^2+y^2 \leq 4 $$ What I have so far (and it seems a little off) is $$ \int_{0}^{\pi}...
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3answers
54 views

Converting into rectangular form

I have 2 related questions: First: Let $z_1 = 2+2i$ and $z_2 = 2-2i$. Find $z_1z_2 $ in rectangular form. I have no idea... I'm also clueless about this question: Change the following to ...
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0answers
26 views

Using cylindrical coordinates evaluate $\int_{0}^{2} dx \int_{0}^{\sqrt{2x-x^2}} dy \int_{0}^{a} z \sqrt{x^2+y^2} dz$

I am asked to solve the following problem: Using cylindrical coordinates evaluate $\int_{0}^{2} dx \int_{0}^{\sqrt{2x-x^2}} dy \int_{0}^{a} z \sqrt{x^2+y^2} dz$ Before doing that long ...
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1answer
29 views

What's the name of the two diagonals in a 2D plot? [duplicate]

In a 2D plot (with x and y), what's the correct name of the diagonal lines, i.e. the line at 45° and that at 135°?
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44 views

There is a square that vertices are (0,0) (0,2) (2,0) (2,2) [duplicate]

A point P satisfies following condition : The straight line passing through P and dividing the area of the square by 1:3 does not exist. Can we know the locus of P and the area of the locus ? I ...
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1answer
29 views

Co-ordinate transformation of metric

In a past exam paper that I am using to prepare for my upcoming finals, I have encountered the following question (paraphrased): Given the metric: $$\mathrm{d}s^{2} = -c^{2}\:\mathrm{d}t^{2}+\left(...
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2answers
18 views

Find limits of integration for region under sphere $x^2+y^2+z^2=a^2$ inside cone $x^2+y^2=z^2$ and above $0xy$

I am asked to find the limits of integration for region under sphere $x^2+y^2+z^2=a^2$ inside cone $x^2+y^2=z^2$ and above $0xy$. Should I use spherical coordinates or cylindrical coordinates? Is it ...
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1answer
54 views

Find limits of integration for the interior region of sphere with center $(a,0,0)$ and radius $a$ using spherical coordinates

I am asked to find limits of integration for the interior region of sphere with center $(a,0,0)$ and radius $a$ using spherical coordinates. How can one do that? I know that one may use $$ x = r \...
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3answers
77 views

There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$

There is a square $Q$ consisting of $(0,0), (2,0), (0,2), (2,2)$. A point $P$ satisfies following condition: The straight line passing through $P$ and dividing the area of square $Q$ in the ...
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0answers
38 views

Project (lat,lng) GPS point to a line segment (road segment) [closed]

Is there a way to project a point A to a B,C line segment and find a point D ? The points ...
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0answers
19 views

Good way to plot coordinate system in computer?

I want to plot a coordinate system rotation in my paper, I want to know what would be a good way to make the plot? The plot would look like:
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1answer
55 views

Coordinate charts vs. coordinates on manifolds

I just realised that I'm confused what coordinates really means in the context of manifolds. For example, say $M=S^2$. Then we can define smooth charts as follows: Let the open sets be $U = S^2$ ...
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1answer
33 views

Evaluate the volume of the solid defined by $x^2+y^2+z^2 \leq 9$ and $x^2+y^2 \leq 3y$

I am asked to solve the following problem: Evaluate the volume of the solid defined by $x^2+y^2+z^2 \leq 9$ and $x^2+y^2 \leq 3y$. I thought about using spherical coordinates: $$ 0 \leq \rho \...
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1answer
20 views

Evaluate $f(x,y,z) = z^3$ on the region defined by $z \geq 0 \ x^2+y^2 \leq 1 \ x^2+y^2+z^2 \leq 2$

I am asked to solve the following problem: Changing the variables, evaluate the integral of the function $f(x,y,z) = z^3$ on the region defined by $z \geq 0 \quad x^2+y^2 \leq 1 \quad x^2+y^2+z^...
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1answer
16 views

What is the intuitive meaning of the partial derivate in coordinate transforms?

We learned that when changing coordinate system from $u^i$ to $u'^i$, a contravariant vector transforms like this (using the Einstein-convencion): $v'^i = \frac{\partial x'^i}{\partial x^j}v^j$, And ...
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0answers
8 views

Why describe basis multipliers as barycentric coordinates?

So a disclaimer up front: I'm from a EECS background as opposed to pure math, so if possible keep that in mind for your answers. I've been reading a paper on 2D-3D triangulation and came across the ...
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1answer
19 views

Formula to move N units along a slope in cartesian system, based upon an angle, which will calculate final point as an x,y location in grid

I need a formula which will calculate my final x,y location in a cartesian coorindate system. First, let me set this up. An Easy Example To Explain What I'm Looking For Start at point 20, 20 in a ...
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2answers
28 views

Set up the triple integral for region between cylinders $x^2 + y^2 = 9 \quad x^2 + y^2 = 16 \quad z = 4+x^2$ and $0xy$ plane

I ran into a problem that I am not sure about the correct answer. The question is: Set up the triple integral for region between $x^2 + y^2 = 9 \quad x^2 + y^2 = 16 \quad z = 4+x^2$ and $0xy$ ...
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1answer
33 views

How do you check if a coordinate $(x,y)$ is inside or on the perimeter of a cross

$1.$ How do you check if a $(x,y)$ coordinate is inside a cross? $2.$ How do you check if a $(x,y)$ coordinate is on the perimeter of a cross? The cross is like a medical sign. The cross will have $...
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0answers
35 views

Visualizing Nash Equilibria of a 4 dimensional matrix

Are there any good ways to visualize Nash equilibria of a 4-d matrix? I have created an game theory model which consists of of four players (P1; P2; P3; P4) who can all choose between a set of 27 ...
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0answers
19 views

Change directly between spherical coordinate systems, without intermediate Cartesian coordinate system.

Is there a practical way to change from one spherical coordinate system to another spherical coordinate system without changing to an intermediate Cartesian coordinate system? The Stack Exchange-...
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1answer
35 views

Find the area of the square using co-ordinates

Given a square $ABCD$ such that the vertex $A$ is on the $x$-axis and the vertex $B$ is on the $y$-axis. The coordinates of vertex $C$ are $(u,v)$. Find the area of square in terms of $u$ and $v$ only....
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0answers
23 views

Change of coordinates using the wedge product?

I while back (over a year ago) I was told about wedge products (or something very similar) and how they can be used to change e.g. the curl in Cartesian coordinates to in spherical coordinates. ...
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1answer
22 views

Defining a region in $\mathbb{R}^2$

I was trying to do this exercise but my answer doesn't match with the solution and I'm wondering why: Consider the coordinates transformation defined by $x=2u+v$ and $y=u^2-v$. Being $T$ the ...