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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1answer
35 views

Formula to convert Cartesian coordinates to spherical coordinates? [on hold]

I have this formula: x, y, z = cos(vertical)*sin(horizontal), sin(vertical), cos(vertical)*cos(horizontal) Which maps a spherical coordinates (horizontal and ...
1
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1answer
51 views

The ant is moving through the coordinate system, Started at $(0,0)$ to $(4,4)$. What is the probability that the ant will find food at $(3,2)$?

The path to the $(3,2)$ is $3+2 \choose 3$ or $3+2 \choose 2$. Total path is $4+4 \choose 4$ And the probability is : $ \frac{3+2 \choose 3}{4+4 \choose 4}$ = $ \frac{5 \choose 3}{8 \choose 4}$ = ...
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1answer
15 views

Given the end-vertices of two line segments, how do you calculate the point at which they intersect?

Given only the vertices of each line segment, and it's assumed they intersect, how do I calculate the point at which they intersect (in two and additionally three dimensions)?
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3answers
21 views
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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 ...
-1
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0answers
40 views

Three line segments made by intersection in harmonic progression [on hold]

I'm learning coordinate geometry in high school and have this question as a doubt. The equations of three lines are $7x + y = 16$ , $5x - y - 8 = 0$ and $x - 5y + 8 = 0$. A variable line through ...
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1answer
23 views

How to transform the quadratic form of an ellipse to a circle

Consider the ellipse $x^TPx\le a$. I would like to transform (the quadratic form of) this ellipse into a circle $y^T\begin{pmatrix}1&0\\0&1\end{pmatrix}y\le b$ via a coordinate transform ...
18
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6answers
29k 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 ...
3
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0answers
25 views

Get the largest rectangle in a quadrilateral

So I have coordinates for a few shapes with 4 sides of varying angles. I need to find the largest rectangle in them, even if the rectangle is rotated. Is there an algorithm for this? In the example ...
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2answers
420 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 ...
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1answer
44 views

Finding all intersecting circles of one circle.

I have one circle $C_0(x_0,y_0,R_0)$ in a plane (which moves around here and there). There are many other circles on the same plane $C_1(x_1,y_1,R_1),C_2(x_2,y_2,R_2).....,C_n(x_n,y_n,R_n)$ where ...
1
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1answer
363 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 ...
6
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1answer
62 views

Is this GRE math problem wrong?

I'm working out of the Manhattan GRE test prep book and I've come across a question that I can't figure out why they chose the answer they did. "Perpendicular lines m and n intersect at point (a,b), ...
4
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1answer
44 views

Determining the angle of a photograph containing known parallel objects/lines.

I have a photograph of a house and a window taken at an angle. I'm trying to determine the angle at which the photograph was taken. The house has wooden siding that can be safely assumed to be ...
2
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3answers
163 views

Average of points on an xy plane

I was at a family reunion yesterday which required a bit of travel. Most of that part of the family lives near one another, so I am the outlier. I can't reasonably expect them to have the next reunion ...
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0answers
14 views

Spherical coordinate system remain the same if the origin is changed and each point make the same translation?

Now I have a spherical coordinate system whose origin is located at (a,b,c)[cartesian], and I have another point whose location is (r, theta, tho) in this spherical system, and P's cartesian ...
0
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1answer
11 views

Write the co-ordinates of E such that the parallelogram ABCE is a rhombus.

I'm unsure how to do this and it's always in my exams. (The original shape was a triangle and E was originally not a point) A:(1,0) B:(0,8) C(7,4) Gradient of AC:2/3 AC equation:2x - 3y - 2 = 0 ...
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2answers
16 views

Finding coordinates of points $P, Q$ given $A, P, Q$ are collinear. [closed]

In the $x,y$-plane, point $P$ lies on the line $y=2x-5$ and point $Q$ lies in the line $y=12-x$. A point $A(1,2)$ is such that $A, P, Q$ are collinear and $AQ=3AP$. Find th coordinates of $P$ and $Q$. ...
0
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1answer
36 views

intersect area of two polygons in cartesian plan [closed]

is possible to calculate the overlapping polygons area of two polygons in cartesian plan coordinate: polygon 1: $(1,1) - (2,2) - (3,3) - (4,2)$ polygon 2: $(1,0) - (2,3) - (3,2) - (4,1)$ ...
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0answers
88 views

Convert geodetic coordinates to cartesian coordinates

I am working on some simulation software that will represent a number of entities in a defined geographic area in the world. The part of the software that I am currently working on is to implement ...
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4answers
2k views

How do I map a 3D triangle into 2D?

The problem I'm having is mapping a 3D triangle into 2 dimensions. I have three points in $(x,y,z)$ form, and want to map them onto the plane described by the normal of the triangle, such that I end ...
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0answers
5 views

How to match the time for given points in two different 3D Cartesian coordinate system?

I have two machine to record a men's motion (what we actually record are the 3D coordinates of the men's 14 different body parts). machine 1 record the coordinates 100 times per second, and machine 2 ...
1
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1answer
319 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 ...
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1answer
85 views

Getting coordinate between two coordinates knowing the distance and latitude

That is my wall: I know the coordinates of the lower points (left and right). (X1,Y1,Z) and (X2,Y2,Z) where X is the latitude, Y longitude and Z the altitude. I want to know the another point of ...
2
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1answer
58 views

Pair of tangents to a hyperbola

How do I find the joint equation of the pair of tangents drawn to the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$ from an external point $(x_1, y_1)$. My book says that the answer is $SS_1 = ...
0
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0answers
239 views

Calculating 3D points corrds from 2D image

The current scenario I have is that I have an image of a rectangular board from an angle and I need to calculate the 4 coordinates of the 4 corners of the rectangle. Currently I have gone through the ...
0
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0answers
29 views

The gradient in $n$-dimensional spherical coordinates

I am in the middle of a computation where I need to work with the formula of the gradient in spherical coordinates in $\Bbb R ^n$ (no preferred convention for the angles). I could patiently and ...
0
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0answers
16 views

Formula for a involute

Given the graph of the function in Cartesian coordinates, $f(x)$, what is $g(x)$ such that $g(f(x))$ is the involute of $f(x)$? In polar?
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2answers
37 views

Please help me solve this problem on Coordinate Geometry

Problem: A rod of length 2 units moves so that its ends are on the positive X-axis and on the line $x+y=0$ which lies in the second quadrant. Find the locus of the midpoint of the rod. I've ...
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1answer
15 views

Co-ordinate analysis

Coordinates $ (\alpha, \beta, R) $ with $ -1 \ge \alpha,\space \beta \le1,\space R \lt 1 $ are related to Cartesian co-ordinates $ (x, y, z) $ via $ x= R \alpha, \space y= r \beta $ and $ \space ...
4
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1answer
2k 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 ...
0
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1answer
16 views

Graph the area of the surface in Spherical Coordinate System

I would like to know how to graph a surface area in spherical given the value of the area. It is because I would to calculate the surface area and I dont know how to visualize which side of the sphere ...
2
votes
2answers
337 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 ...
2
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1answer
53 views

conversion of laplacian from cartesian to spherical coordinates

In cartesian coordinates, the Laplacian is $$\nabla^2 = \frac{\partial^2}{\partial x^2}+\frac{\partial^2}{\partial y^2}+\frac{\partial^2}{\partial z^2}\qquad(1)$$ If it's converted to spherical ...
1
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1answer
29 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
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1answer
12 views

Converting a point from Rectangular to Cylindrical Coordinate Systems

I am solving this problem and I am stuck on converting a point from rectangular to cylindrical coordinates. The answer is from $B(0,5,0)$ to $B\left(5,\frac\pi 2,0\right)$. The problem is when I ...
1
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1answer
548 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 ...
0
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1answer
24 views

The shape of the hyperbolic curves coordinates

Any one has an idea about hyperbolic coordinates ? and how to imagine it ? Indeed I am trying to find the shape of the coordinate curves far away from origin ! and what is the shape of them at $u=0 ...
0
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2answers
38 views

Calculating distance between 2 points - confused about radians

Let me start by saying math is NOT my strong point - by a long shot. I was asked to write a program calculating which locations from a given list (the co-ordinates given in degrees) are within 100km ...
2
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1answer
21 views

Conversion of spherical coordinates to cartesian

For the flow $A = \frac{c}{r}$ with $r=\sqrt{x^2+y^2+z^2}$ I wanted to calculate the velocity field with $\nabla A$ As a result I get $(-\frac{c}{r^2},0,0)$. So far so good. When I tried converting it ...
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2answers
4k views

How to calculate the middle of a line?

My question is following. I have a line with a given (X1, Y1) and (X2, Y2) coordinates (see figure below). I need to calculate ...
0
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0answers
29 views

Cartesian transformation

I am led to believe a Cartesian Transformation is what I need, but I am not sure. Here is my problem. I have two coordinate systems one Global x,y,z another local i,j,k that exists inside of x,y,z I ...
4
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1answer
35 views

Square inside a Polar coordinate system

I have a square lying on a polar coordinate. Is there any general relationship between radius and angle, which may be derived along the side of square. More generally put, given the coordinates of the ...
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1answer
71 views

Evaluate integral with gaussian curvature

I thought evaluating it in the following way: $$\begin{align} \int_0^{2\pi}\int_0^{\pi}K(x,y)\sqrt{\det(g_{ij})} \, dy\,dx &= \int_0^{2\pi}\int_0^\pi \sqrt{\det L_{ij}}\cdot \sqrt{{\frac{\det ...
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0answers
22 views

Divergence free part of laplacian operator in cylindrical coord. (Curl Curl operator)

I want to derive $\nabla \times \nabla \times \mathbf{V}$ in cylindrical coordinates. My variables are $(u,v,w)$ in $(z,r, \theta)$ (axissymetric, radial and azimuthal directions). I computed first ...
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2answers
95 views

A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate…

Problem : A straight line L with negative slope passes through the point (8,2) and cuts the positive coordinate axes on points P and Q . As L varies find the absolute minimum value of OP + OQ ( O ...
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2answers
2k views

Finding a line perpendicular to a line and passing through the intersection of other two lines

So here is the question as in my text book Find the equation of the line through the intersection of $2x - 3y + 4 = 0 $ and $3x + 4y - 5 = 0$ and perpendicular to $6x - 7y + c = 0$ so I ...
0
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4answers
51 views

Points on 3d line

Say we have $2$ points on a 3d line, point $A(x,y,z)$ and point $B(x,y,z)$. If we want to get the coordinates of a third point, beyond point $B$ but a certain distance from point $A$, how would we do ...
1
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1answer
23 views

new plane equation after transformation of coordinates

I have a plane equation $ax + by + cz + d = 0$ w.r.t to a particular coordinate frame. this coordinate frame w.r.t to the world coordinate frame is $$\begin{vmatrix} r_1 & r_2 & r_3 & ...
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1answer
20 views

Finding the equation for the tangent plane to earth given latitude and longtiude

I'm creating a program where I need to calculate the equation of the plane tangent to the earth at a given latitude and longitude. I used Projecting an Arbitrary Latitude and Longitude onto a Tangent ...