Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.

learn more… | top users | synonyms

0
votes
0answers
2 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: ...
0
votes
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 ...
0
votes
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 ...
0
votes
1answer
9 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 ...
0
votes
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: ...
-4
votes
0answers
33 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 ...
-2
votes
0answers
15 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
votes
3answers
221 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 ...
1
vote
1answer
345 views

Triangle and parametric coordinates

I'm studying on a book where it says: "A triangle is the set of points where for some point po, where u and v range over the parametric coordinates (we are talking about barycentric coordinates ...
0
votes
2answers
383 views

converting kph and heading to xyz velocity vector

I am writing software (in C++) that is required to send out messages from our simulation system to another simulation system. Problem is we track the simulation object's current speed (kph) and ...
0
votes
0answers
11 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 ...
14
votes
4answers
25k views

finding out the area of a triangle if the coordinates of the three vertices are given

What is the simplest way to find out the area of a triangle if the coordinates of the three vertices are given in x-y plane? One approach is to find the length of each side from the coordinates given ...
0
votes
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. $D(0,-5,5)$ $E(1,-2,4)$ ...
1
vote
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 ...
1
vote
1answer
30 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 ...
1
vote
1answer
165 views

Extrinsic and intrinsic Euler angles to rotation matrix and back

currently I'm working on the visualization of coordinate systems in space to understand rotation matrices better. Until now I thought everything would be ok, but there is a thing that does not get ...
3
votes
4answers
370 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
1
vote
1answer
307 views

New x coordinate of a rotated line

I need help finding the equation to find $x$ I work in GIS and I'm working on a script that uses the new x coordinate of a rotated line. I havent work with trigonometry in a long long time so I ...
1
vote
1answer
2k views

How to find coordinates of 3rd vertex of a right angled triangle when everything else is known?

I want to locate precisely the 3rd coordinate of a right angled triangle. I have: the length of three sides The three angles The other two coordinates of the triangle The triangle can lie in any ...
0
votes
0answers
9 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 ...
0
votes
1answer
18 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.
0
votes
1answer
7 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 ...
0
votes
0answers
19 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 ...
1
vote
1answer
534 views

How can I transform coordinate systems with quaternions?

I have a coordinate system $0$ which I'd first like to rotate about its $z$-axis which gives me system $1$, and afterwards rotate system $1$ about its $y$-axis which gives me system $2$. See picture: ...
0
votes
2answers
1k views

How to find center of a circle given 2 points on the circle and the radius?

I would like to find an equation that I can put into excel to calculate the coordinates for the center of the circle. Given $P_1\equiv (a=33855.05, b=21129.55)$ $P_2\equiv (c=33745.04, ...
0
votes
1answer
21 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
votes
1answer
45 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
votes
0answers
20 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 ...
0
votes
1answer
101 views

Perpendicular at a defined distance from point on line intersects another line in coordinates?

It approximately looks like the following picture The figure may be rotated at any angle. I know the coordinates of points $A$, $B$, $C$, $D$ and the length of $BF$. $\angle ABD$ and $\angle CBD$ ...
1
vote
2answers
30 views

Given 4 coordinates from the perimiter of a square, can the square be constructed?

I have a square, tilted at an unknown angle. I am given 4 coordinates of the square. They lie on the perimeter, one per side. With these 4, and nothing else, am I able to determine the vertices of ...
0
votes
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: ...
0
votes
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 ...
2
votes
1answer
1k views

Rotating a point in spherical coordinates around Cartesian axis

If I have a point in spherical coordinates, and I rotate it around one of the Cartesian axes, what will be the new spherical coordinates for the point? Both spherical and Cartesian coordinate systems ...
1
vote
1answer
29 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
vote
1answer
20 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?
1
vote
3answers
62 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 ...
0
votes
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 ...
1
vote
1answer
524 views

How to show that a line pass through a point?

How to show that a line pass through a point? Two fixed straight line $OX$ and $OY$ are cut by a variable line at the points $A$ and $B$ respectively and $P$ and $Q$ are the feet of the ...
1
vote
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.: ...
0
votes
2answers
29 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 ...
0
votes
0answers
12 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 ...
0
votes
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 ...
0
votes
1answer
142 views

parabola in homogeneous coordinates

So if I have the parabola $Y = X^2$, how do I go about representing this homogeneously? I know I can parameterize it as $F(t) = (t, t^2)$, but then what? The reason I ask is because I have a ...
-1
votes
1answer
275 views

Finding the angle between lines represented by a homogenous equation

I am trying to find angle between two lines represented by the following homogeneous equation: $$ 7x^2 + 4xy + 4y^2 = 0.$$ I tried to use the standard formula $$ \theta = \arctan \left(\frac{2 \sqrt ...
1
vote
2answers
101 views

Calculating coordinates

OK, I have a picture which will hopefully make my explanation a bit clearer. I have a line $(a, b)$ to $(x, y)$ and all I know is the end points of the line. I am trying to draw a line from the ...
0
votes
1answer
874 views

Find the coordinates of a point on a circle given 2 points and an angle

I have a circle with $A$ as a center, $B$ and $C$ two points on the circle. I have the coordinates of $A$ (the center) and $B$ (the point on the circle). How can I find the coordinates of $C$ (another ...
0
votes
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 ...
1
vote
1answer
739 views

coordinate geometry - find point in right-angled triangle

I'm making a map. I've come across a geometry problem, and I'm not so knowledgeable about maths! Let me illustrate with pictures. I am trying to plot flightpaths with a curved line, using a ...
0
votes
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 ...
2
votes
2answers
332 views

Find parametric expression of an arc given its start point, end point and central angle in 3D cartesian coordinate system

In a 3D cartesian coordinate system, the coordinates of start point and end point have been given as $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$. If the central angle of the two points (the one smaller ...