# 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.

2,341 questions
1answer
9 views

2answers
15 views

### 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 ...
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 ...
1answer
21 views

### 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 ...
2answers
23 views

### 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 ...
0answers
17 views

### 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 ...
0answers
35 views

### 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 ...
3answers
166 views

### 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 ...
1answer
23 views

0answers
11 views

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. ...
0answers
11 views

### 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 $r_b$? ...
0answers
27 views

### 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 ...
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-...
0answers
13 views

### 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 ...
1answer
30 views

### 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 ...
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 ...
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 (...