Questions on coordinate systems, a geometric method where a point in n-dimensions is assigned a corresponding n-tuple of numbers.
3
votes
1answer
135 views
Given known reference points, how do I calculate the approximate height of a point from a photograph
I have a photo with three towers. I know that the base of all three towers are at the same elevation, and at the top they each comes to a point. Two of the towers are the same height, though they ...
9
votes
2answers
131 views
Is there any way to find the equation for this situation?
$\mathbb N = \{1,2,3,4\dots\}$
Let us suppose we are starting at a point with coordinates $(0,0)$. Now draw a line from $(0,0)$ to $(1,0)$ and from $(1,0)$ to $(1,2)$. Now by the Pythagorean theorem, ...
0
votes
2answers
151 views
Gram-Schmidt Orthogonalization - does it distort?
I am writing a 3D solar panel positioning programme and have a section of code where I use the Gram-Schmidt Orthogonalization process to go from 3D to 2D for easier calculations.
(For reference, here ...
0
votes
1answer
100 views
how to get rotation component of quaternion form using 3d coordinates
I have a series of 3d coordinates distributed in a 3d space according to a root point. I can determine the x, y , z component using reducing the vectors. but I am not clear how to get rotation ...
0
votes
0answers
71 views
Circle-Circle intersection coordinate system
Consider two points in the 2D Euclidean plane, the origin $0$ and $x$. One can define a co-ordinate system such that for any point $y$ in the plane, $y$ is parametrized by its distance from $0$, call ...
1
vote
1answer
78 views
find $a$ for which figure's area is maximum
suppose that we have following interval $(-5,2)$,we should find such $a$, which takes all possible values from this interval,creates following inequality systems
$$5+a-|2y|\ge 0$$
$$|x|\leq ...
0
votes
0answers
83 views
Calculate a tilt between two points in a geographic coordinate system?
This is an extension of the question here and for context, I'm writing a script for Google Earth that generates a tour, and aims the camera in the current direction of the velocity vector.
Heading ...
1
vote
2answers
98 views
Are there derivations of equations of non-degenerate real quadric surfaces
Take the ellipsoid for example
$$(x^2/a^2)+(y^2/b^2)+(z^2/c^2)=1$$
in the x-y plane you have an ellipse described by $$(x^2/a^2)+(y^2/b^2)=1$$ (suppose z=constant)
in the y-z plane you have an ellipse ...
0
votes
1answer
230 views
Find the coordinates of a point on a circle given 2 points and an angle
I have a circle with A as a center, B and C 2 points on the circle.
I have the coordinates of A (the center) and B (the point on the circle). How can I find the coordinates of C (another point on the ...
0
votes
1answer
73 views
Z-index of an arbitrary point on a flattened 3-dimensional triangle
I have a triangle in a 3-dimensional coordinate system that I want to draw to a screen. I'm able to flatten the triangle to 2 dimensions and determine whether an arbitrary point on the screen falls ...
0
votes
0answers
65 views
Transform a point to a new space. How is it working?
Let us assume that you simply have a point: $(x_1, x_2).$ You also have a transformation $H,$ that maps this single point to a new point: $(y_1, y_2).$ So $y_1 = h_1(x_1, x_2),$ and $y_2 = h_2(x_1, ...
1
vote
0answers
96 views
Gradient when changing coordinate system
A change of variables from $\vec{r_1}$, $\vec{r_2}$ to $\vec{r}$, $\vec{R}$ is given by:
$$
\vec{r} = \vec{r_1}-\vec{r_2}\text{ , }\vec{R}=c_1 \vec{r_1} + c_2 \vec{r_2}
$$
I'm supposed to find ...
1
vote
4answers
100 views
How to determine the position of neighbor points?
I have two points (red points represented on the image below), they form a line that have a specific formula (y = mx + n), I need to determine the coordinates of 4 other points (blue points) that are ...
0
votes
2answers
117 views
How to place rectangle so it envelopes two circles, one circle in the very right end of the rectangle and one in the other end.
How can i place a rectangle so it envelopes two circles, one circle in the very right end of the rectangle and one in the other end.
Say i have two circles with the xy coordinates and a radius:
...
2
votes
2answers
504 views
How to get upper-left, upper-right, lower-left and lower-right corners XY coordinates from a rectangle shape.
How can i get the get upper-left, upper-right, lower-left and lower-right corners XY coordinates from a rectangle shape when i have the following data available to me?
...
0
votes
0answers
57 views
How To Calculate 10 KM coords in Google Maps
Well actually i've latitude and longitute $23.061389$, $76.37222199999997$
I want to create $10$ KM triangle in $120$ degree
How can I calculate other $2$ coords ??
1
vote
3answers
106 views
How do I calculate a change of coordinates given two lines as new axis?
Suppose we have an old coordinate system using the variables $x$ and $y$. We are given two equations for lines to form the axis for new coordinates. e.g. The line $z=0$ is given by the equation $y = ...
2
votes
1answer
317 views
invariance of cross product under coordinates rotation
Question goes as
If $\vec A$ and $\vec B$ are invariant under rotation, the prove that $ \vec A \times \vec B $ is also invariant.
However solution of on the other page is not given. Says ...
1
vote
1answer
127 views
divide triangle into ratio 1:2
I have a problem related to triangles. Please give me some hint to progress.
Suppose we have the following coordinates $A(-2,3)$,$B(1,-1)$,$C(-1,-1)$.
From point $A$, draw a line which divides ...
0
votes
1answer
82 views
Find the number of common normals to both these curves.
Find the number of common normals to the curves $ x^2 + (y-1)^2 =1 $ and $y^2=4x$.
My take :
I formed a cubic in $m$ i.e. slope, so there'll be 3 normals.
Please help.
2
votes
1answer
104 views
How to find the eccentricity of this conic?
How to find the eccentricity of this conic?
4(2y-x-3)² - 9(2x+y-1)²=80
My approach :
I rearranged the terms and by comparing it with general equation of 2nd degree, I found that its a hyperbola. ...
1
vote
1answer
331 views
unit vector transformation in rotation of coordinate system
The transformation of coordinate from $(x, y, z)$ to $(x', y', z')$ is given by
$$ x' = a_{11}x + a_{12}y + a_{13}z\\
y' = a_{21}x + a_{22}y + a_{23}z\\
z' = a_{31}x + a_{32}y + a_{33}z$$
If $(\hat i ...
1
vote
5answers
1k views
Find out the differential equation of the following families of curves.
Find out the differential equation of the following two families of curves :
Straight lines having slope and $x$-intercept equal in magnitude.
Straight lines at a fixed distance $p$ from the origin.
...
0
votes
1answer
102 views
Produce function of curve, given some coordinates
I tried asking something similar to this before, but I guess I didn't explain it very well. Hopefully this will be more clear.
I need to get an equation which describes a curve with certain points.
...
1
vote
1answer
75 views
determinant of matrix of transformation from Cartesian to orthogonal curvilinear
Let $(x_1, x_2)$ and $(y_1, y_1)$ be two orthogonal coordinate system with unit vectos $(\hat i_1, \hat i_2)$ and $(\hat e_1, \hat e_2)$ respectively defined by the
$x_1 = x_1(y_1,y_2)$ and $x_2 = ...
2
votes
1answer
28 views
gradient in polar coordinate by changing gradient in Cartesian coordinate
I'm tried to do following and I can't see what went wrong.
$$\begin{bmatrix}
\hat r\\
\hat \theta
\end{bmatrix} = \begin{bmatrix}
\cos \theta & \sin \theta \\
-\sin \theta & \cos \theta
...
1
vote
1answer
128 views
Gradient in curvilinear coordinates
The gradient is usually written as the product of the unit vectors
times the derivative with respect to that coordinate.
In Einstein summation convention:
$\hat e_i \partial_i$
I've seen it written ...
2
votes
2answers
113 views
On a two dimensional grid is there a formula I can use to spiral coordinates in an outward pattern?
I don't know exactly how to describe it, but in a programmatic way I want to spiral outward from coordinates 0,0 to infinity (for practical purposes, though really I only need to go to about ...
0
votes
1answer
547 views
how to change polar coordinate into cartesian coordinate using transformation matrix
I would like to change $(3,4,12)$ in $xyz$ coordinate to spherical coordinate using the following relation
It is from the this link. I do not understand the significance of this matrix (if not for ...
1
vote
0answers
956 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 $
$$ \begin{bmatrix}
A_x\\
A_y\\
A_z
\end{bmatrix}
= \begin{bmatrix}
\sin ...
0
votes
2answers
266 views
convert values from one coordinate system (x,y) to another coordinate system (x', y')
Following is a graph that contains both coordinate systems (x,y) and (x',y'). x, y, x', and y' are all axes
...
0
votes
1answer
2k views
Transformation of unit vectors from cartesian coordinate to cylindrical coordinate
Let $ (\hat i, \hat j, \hat k) $ be unit vectors in Cartesian coordinate and $ (\hat e_\rho, \hat e_\theta, \hat e_z)$ be on spherical coordinate.
Using the relation, $$ \hat e_\rho = ...
0
votes
0answers
130 views
Converting global coordinates into set of local matrices for ik skeleton creation
I have the 3d global positions of a set of joints as they move over time and the ik skeleton structure which relates them. I am currently writing some code to convert this information in .bvh file. I ...
11
votes
1answer
134 views
Was there some prior idea that inspired both Fermat & Descartes to invent coordinates?
It seems incredible to me that both Descartes & Fermat could have both simultaneously discovered such a novel & significant idea, without there being some single prior idea that they both ...
2
votes
2answers
182 views
Triangle related coordinate geometry question
Given triangle $\triangle ABC$ , with $AB=AC$ and 2 times(length of
inradius) which is equal to the length of exradius of excirle opposite
vertex $A$. Setup the coordinate system in the plane ...
0
votes
2answers
50 views
Is there a simple way of arriving at this solution?
Suppose we are given the matrix $$\begin{pmatrix}x'\\y'\end{pmatrix}=\begin{pmatrix}\cos(\omega t)& -\sin(\omega t)\\\sin(\omega t)& \cos(\omega ...
5
votes
2answers
101 views
Why does it always take n numbers to characterize a point in n-dimensional space (or does it)?
I don't know if this is obvious and a dumb question or not, but, here we go. To characterize a point in 2-d space we can use standard $x,y$ coordinates or we can use polar coordinates. There are ...
2
votes
1answer
73 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, ...
1
vote
2answers
305 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 ...
2
votes
1answer
251 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
195 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
132 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.
...
0
votes
0answers
108 views
Plotting any conic (Tips and tricks)
Recently In physics our teacher has been giving us plenty of Plotting the graph/relation questions and generally physics graphs are conics or 2 variable functions
In High School Mathematics ...
4
votes
3answers
2k 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
109 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
59 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
138 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
95 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 ...
1
vote
2answers
3k 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
120 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 ...
