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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2
votes
1answer
141 views

How to get new orientation on a sphere?

This is my first question here, hopefully it fits. Imagine all people on the northern hemisphere are looking North to the Pole. Now I want them to look towards a new location given by latitude, ...
3
votes
2answers
890 views

How to find a 2D basis within a 3D plane - direct matrix method?

I have a plane equation in 3D, in the form $Ax+By+Cz+D=0$ (or equivalently, $\textbf{x}\cdot\textbf{n} = \textbf{a}\cdot\textbf{n}$), where $\textbf{n}=\left[A\:B\:C\right]^T$ is the plane normal, and ...
3
votes
1answer
425 views

Coordinate transformation

I have some problems with a geometrical calculation. I want to know the coordinates of the point $P_2$ in my coordinate system $A \ (x,y,z)$ as shown in the following figure. Point $P_1$ (in $A \ ...
2
votes
1answer
723 views

Finding points relating to the edge of a circle in an x,y coordinate system

My question is a bit hard for me to express, so please bear with me. I never got far in trig, and haven't done much on the subject in years; trying to get back into it as it's a pretty major part of ...
0
votes
1answer
211 views

Coordinates on diamond

I got a couple of diamond put side by side like on the image below The only coordinates I know on the image are the top corners (green text). I need to know which diamond does a dot belong. ...
9
votes
4answers
4k views

Simple proof of integration in polar coordinates?

In every example I saw of integration in polar coordinates the Jacobian determinant is used, not that i have a problem with the Jacobian, but I wondered if there's a simpler way to show this which ...
1
vote
1answer
170 views

Curves and first fundamental form

Would I be right to think that if I have a coordinate system $(x,y)$ so that the lines/curves where one coordinate is fixed, so something like $x=a$ and $y=b$, always intersect at the same angle, then ...
2
votes
1answer
75 views

Changing coordinates in a grid

I'm a developer very bad in math, and I got a problem that I'm not able to solve. I got a grid each cell got a position X and Y like shown in the picture below Actually I got the red coordinates, ...
1
vote
0answers
196 views

2D Cartesian Matrix / coordinate transformation.

I has initially asked this question in the programming site but did not get an answer that worked. This is my first question on this site so please bear with me. Consider a page with three distinct ...
1
vote
0answers
165 views

Relative spherical coordinates of 2 points.

I have 2 points in space, defined by their spherical coordinates. I'd like to know the spherical coordinates of the second point in a reference system centered on the first point (I know the unit ...
2
votes
2answers
14k views

How to find the equation of a graph with given coordinates? [duplicate]

Possible Duplicate: Writing a function $f$ when $x$ and $f(x)$ are known If I am given 9 co-ordinates of a random graph say for e.g ...
0
votes
1answer
170 views

Calculating Travel Direction of two coordinates

Maths isn't my strong point and i've been stuck here for hours trying to figure out how do to this (it's probably gona be very easy to do now as well) but it's driving me crazy so i'm going to ask for ...
0
votes
1answer
219 views

Help needed with volume integral in Cylinder coordinates

Problem (more here and the problem XIV.6:6 here on page 976) Integrate $\int_A z dx dy dz$ in cylinder-coordinates when $$A=\{(x,y,z)\in\mathbb R^3 | x^2+y^2 \leq z \leq ...
1
vote
1answer
84 views

Coordinates translation in space

First of all sorry if the title is somewhat opaque, the problem I am trying to solve is already hard to explain properly in my first language. So, let's consider we have a plane, rectangle target in ...
0
votes
1answer
37 views

Counting ways on the coordinate system

What is the number of ways in which you can reach a point (2,2) from the origin, taking unit steps at a time , in not more than 7 steps?
0
votes
1answer
426 views

Evenly distributed normal distribution on surface of a unit sphere

Hello I am using Mathematica code to to generate NPoints of randomly generated points normally distributed around one point on the surface of a sphere using Return[Table[ ...
1
vote
1answer
277 views

What do the parameters skewX and skewY mean in the transform specified by Flash's motion XML?

Flash has the ability to export animations into a format they call motion XML. Its specification is here I am trying to write a python renderer for these animations using pyglet. I understand ...
2
votes
1answer
618 views

Given an arbitrary number of points, how do you find an equidistant center?

Given an arbitrary set of points on a Cartesian coordinate plane, is there a generalized formula to find the closest point that is equidistant from all the given points? My first guess was finding ...
0
votes
1answer
3k views

Finding an equation of a sphere for a specific plane

I am not sure how to proceed with this question from Stewart's SV Calculus text: Find equations of the sphere's with center $(2, -3, 6)$ that touch (a) the $xy$-plane, (b) the $yz$-plane, (c) ...
2
votes
2answers
656 views

What is an effective way to teach children the Cartesian coordinates?

My nephew is preparing for a $4$-th grade state test. They need to learn topics like reflection about $x$ or $y$-axis of a point( say $(3,5)$ reflected about the $y$-axis). I tried to explain but ...
0
votes
1answer
52 views

Why direction of axes of coordinate often not indicated in diagram?

Is there any case/reason of not showing the directions (from negative to positive) of axes in coordinate diagrams? Sometimes I see the direction not specified, even though the discussion using that ...
0
votes
0answers
118 views

How to convert coordinates between a base image and a projected/distorted version?

(Sorry, I meant to provide images, but can't due to low reputation. Please click the links.) I have tried reading some papers on orthorectifiation (like A Comprehensive Study on the Rational Function ...
0
votes
2answers
237 views

Help me with Cylinder -coordinates problem, back to Cartesian or not? How to do it fast?

Source of the problem, 3b here. Problem Question Electricity density in cylinder coordinates is $\bar{J}=e^{-r^2}\bar{e}_z$. Current creates magnetic field of the form ...
1
vote
0answers
2k views

Direction ratio of a vector in 3d?

Suppose I have a vector whose starting end is the origin & the other end can be in any of the 8 quadrants (in 3d). I can easily get direction ratios for the vector & also know in which ...
2
votes
1answer
3k views

Transforming the Laplace operator from Polar to Cartesian coordinates

I'm trying to find the error in my logic here. Let's say we are given the Laplace operator in polar coordinates: $$ \frac{\partial^2}{\partial r^2} + \frac{1}{r}\frac{\partial}{\partial r} + ...
0
votes
1answer
386 views

Query about Cartesian vector notation.

I'm just starting to teach myself about covariant and contravariant vectors. With the little knowledge I've acquired so far I'm wondering if, for an ordinary Cartesian vector $\mathbf{V}$, it's OK to ...
3
votes
2answers
1k views

How are 3D coordinates transformed to 2D coordinates that can be displayed on the screen? What is the formula for this?

The title asks it all, and could someone please also explain the formula as well? Thanks.
11
votes
1answer
854 views

Can someone please explain the cube to sphere mapping formula to me?

I am wondering if anyone could explain how the following formula works, it is supposed to take the input as a point on a cube then map that to points on a sphere, please go gentle on me, I'm in 9th ...
1
vote
1answer
400 views

Jacobian matrix normalization

I have a problem with normalization of the Jacobian matrix. There seems to be no clear method for doing it: in some literature, it has been normalized by using some characteristic length, which is ...
1
vote
0answers
958 views

Conversion of motion equation from Cartesian to Polar coordinates: Is covariant differentiation necessary?

Say I have the following equation of motion in the Cartesian coordinate system for a typical mass spring damper system: $$M \; \ddot{x} + C \; \dot{x} + K \; x = ...
1
vote
1answer
46 views

Defining a set of axes.

I was reading up a little on reference frames and am confused about a certain detail. Is it correct to say that the positive $x$-axis, for example, can be defined as follows? $$ X^+ = \lim_{C ...
1
vote
1answer
309 views

Complex numbers as coordinates

Is it possible to have an n-dimensional geometry where each coordinate can be a complex number, or would it make no sense, i.e. lead to contradictions? Spacetime, can be described as having 4 ...
1
vote
0answers
52 views

Altering the shape of a Gaussian curve

I just posted this on Stack Overflow but then I found out about this forum. I hope I'm not breaking any policies by posting the same question here. I am not allowed to post images here yet, so please ...
0
votes
2answers
375 views

Finding X and Y Intersections of “Ray D1” and “RayD2”

I have two different line on a coordinate plane and I'm looking for the intersection point of those lines which is shown on third quadrant of the plane. Here are the values for each two lines: d1: (0, ...
1
vote
2answers
2k views

Vector Projection XY plane

How do I find orthogonal projection of a vector $\vec V_1=(2,3,4)^T$ formed with the points $A(0,0,5)$ and $B(2,3,9)$ on $xy$ plane?
0
votes
0answers
52 views

General Coordinates property proof

In my problem sheet I need to show: Let $\textbf{r} = \textbf{r} \left( t , \{ q_{j} \} \right)$ Then: $$\frac{\partial \dot{\textbf{r}}}{\partial \dot{\textbf{q}_{j}}}=\dfrac{\partial ...
0
votes
1answer
174 views

finding a point in a cylinder

I am trying to build a basic color approximation model for a website. I think the HSL would be the most efficient model to use. I remember from school the formulae for a cylinder is $$\pi ...
0
votes
1answer
372 views

Finding the sign of $\phi$ in spherical coordinates

I know its a little silly, but I got the wrong sign several times. Just to be clear, $z=r\cos(\phi), -\frac{\pi}{2}\leq\phi\leq\frac{\pi}{2}$ when converting from cartesian to spherical. So, how do I ...
0
votes
1answer
826 views

transformation of 3D coordinate system

how to transform a cylinder from a coordinate system having orthogonal basis vectors $v_1$, $v_2$ and $v_3$ into another a coordinate system having orthogonal basis vectors ...
0
votes
1answer
399 views

Bitwise Operations: Collapsing two values into one.

Alright, so I'm having a hard time thinking of a way to do this. Perhaps someone here can help! Here is the problem: I need to figure out a way to use bitwise operations (or any sort of equation) to ...
0
votes
1answer
934 views

Bearing from one point to another on 2D number plane

Title says it all, I'm looking for the formula to get the bearing from one point to another on a number plane. I have found examples of this for lat/lon around the earth but that's not exactly what i ...
1
vote
1answer
113 views

What is the maximum point for which number of way to reach is given

Previous question: link Say there are two points $P_1(a_1,b_1)$ and $P_2(a_2,b_2)$, the number of ways of reaching $P_1$ from the origin is $w_1$ and $P_2$ from $P_1$ is $w_2$. (Here $a_1<a_2$ and ...
0
votes
2answers
2k views

Number of ways of reaching a point from origin [duplicate]

Possible Duplicate: How can I find the number of the shortest paths between two points on a 2D lattice grid? If we have a point p(x,y) in coordinate system [x>=0, y>=0; i.e 1st quadrant] ...
0
votes
1answer
276 views

Rigid motion in curvilinear coordinates

I would like someone to clarify this since it has bedazzled me and can't seem to get a grip on it. Consider a 3D real space and Euclidean coordinates ($x_1,x_2,x_3$), with an associated standard basis ...
0
votes
1answer
340 views

Inverse function theorem and invertibility of coordinate transforms.

Suppose $x'_i = h_i(x_1, \ldots, x_n)$ for $i = 1,...,n$. To apply the inverse function theorem, let $f: R^{n} \rightarrow R^n $ with $f^i(x_1,...,x_n) = h_i(x_1,...,x_n)$. Assume that the ...
1
vote
1answer
190 views

Bijections of the plane

I recently had to deal with polar coordinates and thus wondered: "Polar coordinates" is just a special name for some bijection from $\mathbb{R}^2$ to $\mathbb{R}^2$ that can be very easily visualized ...
1
vote
1answer
4k views

Converting global to local coordinate systems

I have been given equations for converting from a global to local coordinate system in 2 dimensions, however with no explanation/proof as to how the equation is obtained. I realise that on occasion ...
-2
votes
2answers
3k views

How to get the (X,Y) point with a given angle?

To be more exact.. If i have an angle of 1.42 radians or 81 degrees, with the radius of an ellipse: x = 300 and y = 75. What is the X-Y point for that angle and how would I get that? Thanks in ...
0
votes
2answers
195 views

Vector Geometry - relation between a point and a line with angle and one known point on it

I have two problems I will be very grateful if somebody helps me about them. If I have a line $L_1$ with a known point $(x_1, y_1)$ on it and has slope $\theta_1$, how do I know if a point $P=(x, y)$ ...
1
vote
1answer
3k views

Transforming from one spherical coordinate system to another

I have a set of points on the surface of a sphere specified in one coordinate system (specifically, the equatorial coordinate system), and for each point I need to work on all its neighbouring points ...