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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0answers
14 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 ...
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0answers
11 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 ...
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0answers
17 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 ...
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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 ...
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1answer
270 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 ...
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2answers
99 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 ...
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1answer
872 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 ...
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2answers
28 views

Coordinate Perpendicular and Parallel lines [on hold]

The line $y=2x+7$ is parallel to the line $y=2x-3$. The line $y=-0.5x+7$ is perpendicular to the line $y= 2x-3$. Calculate the perpendicular distance between the pair of parallel lines.
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8 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 ...
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1answer
710 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 ...
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4answers
99 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 ...
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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 ...
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2answers
3k views

building transformation matrix from spherical to cartesian coordinate system

How to arrive at the following from given $ x = r\sin \theta \cos \phi, y = r\sin \theta \sin \phi, z=r\cos\theta $ $$ \begin{bmatrix} A_x\\ A_y\\ A_z \end{bmatrix} = \begin{bmatrix} \sin ...
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0answers
26 views

How to scale x- and y- axes equally in Maple?

I have the ellipse $\frac{25}{36}x^2+\frac{5}{36}y^2=1$. Maple draws it as a circle: How can I change the coordinates, to make it look like an actual ellipse?
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1answer
477 views

Lines in coordinate system of Hyperbolic Plane

An orthogonal coordinate system of the hyperbolic plane can be set up by fixing an orgio $O$, an $x$-axis, a $y$-axis (intersecting each other at $O$ in angle $90^\circ$), and, from any point $P$ ...
4
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1answer
38 views

Parametrizations and coordinates in differential geometry - what's the difference?

From what I've read one can introduce the notion of a tangent vector to a point on a manifold in terms of an equivalence class of curves passing through that point (the equivalence relation being that ...
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5answers
2k views

How do I determine if a point is within a rhombus?

I know the coordinates of the 4 rhombus' vertices. I also have the coordinates of another arbitrary point (the result of a click on the screen). How do I determine if that point is within the ...
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2answers
147 views

What is the number of integer coordinates on a line segment?

What is the number of integer coordinates(end points included) on a line segment with integer end coordinates (x1,y1) and (x2,y2)? Integer coordinate means that both abscissa and ordinate are ...
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1answer
22 views

Find the volume of the solid obtained by rotating the region [closed]

Find the volume of the solid obtained by rotating the region in the $xy$ -plane enclosed by the parabola $y^2=x$ and the line $x=10$ around the $x$-axis.
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0answers
12 views

Representation of a cone in 3D

I need to find the representation of a cone in the 3D space with the following criteria: It's tip is located at the origin. It opens in the positive direction of the axis (it’s one-sided). The ...
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1answer
44 views

How to find intersection of two hypotenuses

I am a web developer who is bad with mathematics. I have never needed some math/geometry formulas before. But now I realize it is needed for more advanced design tecniques. I decided to learn math but ...
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3answers
17 views

Given I know the coordinates of a rectangle, how can I find the coordinates of an enlarged rectangle?

I have a rectangle, and know the dimensions, coordinates of the 4 corner points and therefore the centre point. If I scaled it up e.g. scalefactor * height, from its centre, how can I find the new ...
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0answers
23 views

Solve for 'y' for elipse rotated at an angle

How solve for y if we have set of x coordinates for elipse rotated at an angle 'A' ,has the origin at (h,k) and height as a and b
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1answer
128 views

Graham scan with collinear points

I'm having some trouble understanding the Graham scan algorithm as described in Wikipedia. Particularly, I don't understand how to handle collinear points. Consider these points as a simple example: ...
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1answer
20 views

Find coordinates of bounding box corners of rotated rectangle

I have a rotated rectangle inside a bounding box. It can be rotated to any angle. I know the coordinates of the "top left" corner of the inside rectangle (and I am able to work out the other 3 ...
2
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0answers
22 views

Local parametrizations and coordinate charts on manifolds

I have recently had discussions on related questions about coordinate charts on here which has started to clear up some issues in my understanding of manifolds. Apologies in advance for the ...
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1answer
19 views

Rearranging coordinate equation

I am looking to rearrange the following equation, given that I already know the distance and one set of coordinates (I need to find the coordinates of the second point basically) $$d = ...
2
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0answers
34 views

Smart coordinates for six-dimensional integral

I have a (hopefully) simple question: I am dealing with a definite (on all of $\mathbb{R}^6$) six-dimensional integral $$\int_{\mathbb{R}^6} F(\vec{x}_1,\vec{x}_2)d^3x_1d^3x_2$$ where the function ...
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0answers
36 views

Finding coordinates of position given three coordinates and distances: 3D

I'm hoping to determine the x, y, z coordinates of a 4th position (D) given the coordinates of three other positions and their distances: $A(0.25, 0.25, 0.25), B(0.4663, 0, 0.25)$, and $C (0.3912, ...
0
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1answer
27 views

How to find the position on a circle that satisfies two constraints?

Say I'm given an point P1 at coordinates $(x_1,y_1)$, and another point $P_2$ at coordinates $(x_2,y_2)$. Then I have a point $P_0$ that needs to be at coordinates $(x,y)$ such that it is a fixed ...
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3answers
36 views

2-Sphere surface coordinate dimension

Ordinary sphere in $\mathbb{R}^3$ is two-dimensional object (2-sphere), i.e. it requires at least two coordinates to define point on a surface. As I notice, however, there is a catch. If we use ...
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1answer
9k views

Transformation of unit vectors from cartesian coordinate to cylindrical coordinate

Let $ (\hat i, \hat j, \hat k) $ be unit vectors in Cartesian coordinate and $ (\hat e_\rho, \hat e_\theta, \hat e_z)$ be on spherical coordinate. Using the relation, $$ \hat e_\rho = ...
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1answer
16 views

Other abscissa than $y = 0$?

Circle contains three vertices whose coordinates are (0,6) , (0,10) and (8,0). Abscissa of second vertex in which given circle passes through x-axis, is equal to? I do not even understand the text of ...
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1answer
339 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 ...
5
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1answer
132 views

Definition of a Cartesian coordinate system

Apologies if this is a basic question, but I'd really like to clarify the exact meaning of what a Cartesian coordinate system is. Heuristically, is it correct to say that a Cartesian coordinate system ...
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1answer
63 views

Meaning of “locally homeomorphic to $\mathbb{R}^{n}$”

I am fairly new to differential geometry and approaching it with a physics background (in the study of general relativity), as a result I'm having a few struggles with terminology etc, so please bear ...
2
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1answer
189 views

How to translated a scaled figure so that a marked point remains fixed?

I've got a bit of a mathematical problem. Basically I have a square, and the width and height are multiplied by $1.02$. Now in the square is a point, which we'll refer to as $(c, d)$, and the origin ...
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1answer
793 views

how to find the area of rhombus if there is only 3 coordinate of the rhombus is given?

This is the question: Find the area of the rhombus $PQRS$ if the coordinates of point $P$, $Q$ and $R$ are $(6, 4)$, $(8, 7)$ & $(-6, 3)$ respectively. Does any one know how to solve this? ...
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0answers
45 views

Constructing coordinate maps on manifolds

I've been studying differential geometry for a little while now, but I've never properly justified to myself rigorously the need to consider other more general coordinate maps, other than Cartesian on ...
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3answers
63 views

How to “rotate” points through 90 degree?

I am trying to do some intersection tests and so the math gets weird if two certain points have the same $x$ coordinate and so infinite slope. The points can be anywhere in any quadrant. I want to ...
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2answers
45 views

calculate the volume

There is a triangular prism with infinite height. It has three edges parallel to z-axis, each passing through points $(0, 0, 0)$, $(3, 0, 0)$ and $(2, 1, 0)$ respectively. Calculate the volume within ...
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0answers
18 views

Converting vector in cartesian to cylindrical coordinates

This seems like a trivial question, and I'm just not sure if I'm doing it right. I have vector in cartesian coordinate system: a⃗ =xi⃗ −2xj⃗ + yk⃗ And I need to represent it in cylindrical coord. ...
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1answer
469 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: Both ...
4
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2answers
368 views

What is the difference between coordinates transformation and change of coordinates?

In the context on 3D computer graphics, what is the difference between coordinates transformation and change of coordinates? It can just be a matter of notation, but my book makes a clear distinction ...
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2answers
349 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 ...
3
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1answer
53 views

Is there an equation to describe translation and rotation?

Suppose a free rod, $l=2r$, is hit on a tip T and translates with $v= 1r/s$ and at the same time rotates with angular velocity $\omega= 1rad/s$. Is there an equation that can determine the position of ...
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0answers
23 views

Looking for a formula to map a 2d pixel coordinate to a region within a grid.

I am given a pixel bounding box of the form: (x1, y1), (x2, y2) Where (x1, y1) is the bottom left coordinate and (x2, y2) is the top right coordinate of the ...
3
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1answer
59 views

Coordinate systems on manifolds

I am fairly new to differential geometry and something I can't get my head around is, if an $n$-dimensional manifold is locally homeomorphic to $\mathbb{R}^{n}$, i.e. Euclidean space, then isn't it ...
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2answers
32 views

How do I calculate the angles between a point on a sphere and each unit vector in $\Bbb R ^3$?

Given the Cartesian coordinates of any point $p$ on the surface of a sphere in $\Bbb R ^3$, how do I calculate the angles between each axis $(x, y, z)$ and the vector $n$ defined by origin $o$ and ...
4
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2answers
107 views

Geometry: What is being calculated here?

Context: I am a computer graphics programmer looking at a code-implementation. I need help understanding a function that has neither been documented properly nor commented. Given a circle with ...