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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3answers
33 views

Cylindrical - Spherical coordinates

We are given a point in cylindrical coordinates $(r, \theta , z)$ and we want to write it into spherical coordinates $(\rho , \theta , \phi)$. To do that do we have to write them first into ...
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1answer
24 views

Cylindrical coordinates - Surfaces

I found the following: Cylindrical coordinates $(\rho , \theta , z)$. This system consists of the following coordinate surfaces: Cylinders with common $z-$axis: $\rho=\sqrt{x^2+y^2}=\text{ ...
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0answers
39 views

Show that the point satisfies the conditions

A round membrane in space, is over the space $x^2+y^2 \leq a^2$. The maximum coordinate $z$ of a point of the membrane is $b$. We suppose that $(x, y, z)$ is a point of the inclined membrane. ...
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0answers
65 views

Volume between a paraboloid and a parabolic cylinder

Find the volume of the region bounded by the paraboloid x=y^2 + z^2 and the parabolic cylinder x=2-y^2. I set up the integral as the integral of theta from 0 to 2pi, integral of (2/(sin^2theta + ...
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1answer
28 views

Multiplication order of rotation matrices

I have three 3D coordinate frames: O, A and B, as shown below. I want to know the rotation matrix RAB between A and B, that is the rotation that is required, with respect to the frame A, to move ...
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1answer
77 views

Transformations between two coordinate systems on a rigid body

I have two coordinate frames, A and B, which are rigidly attached to each other on a body. This body then translates and rotates, such that A starts at A1, and moves to A2, and B starts at B1, and ...
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2answers
48 views

Rotation matrix between right- and left-handed systems, with an additional rotation

I have two coordinate frames, A and B. I want to create the rotation matrix RAB which takes you from A to B. A is a right-handed system, and B is a left-handed system. Furthermore, after moving from a ...
6
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3answers
88 views

Why is $\partial_z\partial_{\bar z}=\frac14\left(\partial_r^2+\frac1r\partial_r+\frac1{r^2}\partial_{\theta}^2\right)$?

I have to show the identity I wrote in the title: it should be $\partial_z\partial_{\bar z}=\frac14\left(\partial_r^2+\frac1r\partial_r+\frac1{r^2}\partial_{\theta}^2\right)$ but some computation ...
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0answers
39 views

Integrals For AMC 10B #25?

Could an answer be found to this AMC 10B #25, using integration? A rectangular box measures abc, where a, b, and c are integers and 1<=a<=b<=c. The volume and the surface area of the box are ...
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0answers
26 views

Multiplication order for coordinate frame transformations

Suppose I have three coordinate frames: $A$, $B$ and $C$. If $T_{AB}$ is the transformation from $A$ to $B$, then which of the following is correct? $T_{AC} = T_{AB} \cdot T_{BC}$ $T_{AC} = T_{BC} ...
15
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1answer
685 views

Abscissa, Ordinate and ?? for z-axis?

Like x-axis is abscissa, y-axis is ordinate what is z-axis called? It is one of basic doubts from my childhood.
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0answers
25 views

Moving die on cartesian plane so as to minimize sum of facing face

I have a problem that I have been working on for which I cannot find a solution. Problem: Assume you are on a cartesian plane, and you want to move a die to a specific point. You can move the die ...
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0answers
33 views

Tangent undefined for polar curves ($r^2=a^2sin(s\theta)$)?

I am considering the function $r^2=a^2\sin(2\theta)$ and am trying to find tangents perpendicular to the initial line, so $\frac{dx}{d\theta}=0.$ However, when I take the derivative by implicit ...
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0answers
61 views

Tangents perpendicular to the initial line for cardioid? Polar coordinates…

For the polar curve $r=a(1+cos\theta)$, I am trying to find the equations of the tangents perpendicular to the initial line by setting $\frac{dx}{d\theta}$ equal to zero. I am able to factorise a sine ...
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1answer
36 views

How can I prove non-geometrically that there is a bijective correspondence between polar and cartesian representations of coordinates?

We have a function $f: \mathbb{R}^2 \rightarrow \mathbb{R}^2$ as $f(x,y) = (\sqrt{x^2 + y^2}$, $\tan^{-1}\left(\frac{y}{x}\right))$ which takes a Cartesian pair $(x,y)$ to its polar form, and a ...
0
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1answer
24 views

Minimum points to choose from a set such that midpoint is also in the set

Consider the set $S =\{ (x, y)$ : $x$ and $y $ are integers $\}$. The midpoint of a pair of points $ P_1$ = ($ x_1 $, $y_1 $) and $P_2 $= ($x_2$ , $y_2$ ) is $ ( \frac{x_1 + x_2}{2}, ...
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0answers
18 views

Confused by Parameterizations and Coordinate Conversions

So I have a few questions regarding parameterizations and coordinate conversion. Ever since dealing with parametric equations last semester I have felt like I have never truly understood ...
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0answers
98 views

Parametric integration negative area?

I know there is a question very similar to mine already here Why does using an integral to calculate an area sometimes return a negative value when using a parametric equation? , but I am still a bit ...
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0answers
21 views

Polar coordinates for vector difference in $\mathbb{R}^2$

I have a function $F(\boldsymbol X)=\tilde F(x,y)$ of $x$ and $y$ in the plane, and I can transform it in a function of $r$ and $\theta$, say $f=f(r,\theta)$, through the change of coordinate $$x=r ...
0
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1answer
62 views

Using Barycentric coordinates to check whether a point lies within a Degenerate triangle

http://www.blackpawn.com/texts/pointinpoly/ I used this site to learn how to determine whether a point lies within a triangle. However, the site does not say whether or not this method can handle ...
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0answers
45 views

Coordinate Systems on the Complex Plane: Rectangular, Polar, Exponential, … Imaginary?

In the complex plane there is a nice relationship between rectangular, polar, and exponential coordinates: $$(x+iy) = r(\cos\theta + i~\sin\theta) = re^{i\theta} $$ $$where~~x ,y ,\theta, r \in ...
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0answers
24 views

Cylindrical coordinates: Paradox?

Let's say the vector field $\vec A_1 = \begin{pmatrix} r\\ 0 \\ z\end{pmatrix}$ in cylindrical coordinates is given and I want to calculate $\vec A_1 \cdot \vec e_r$, where $\vec e_r = \begin{pmatrix} ...
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0answers
20 views

Transforming a vector field in cylindrical coordinates - simple

I want to transform $\vec F = \alpha \vec r$ in cylindrical coordinates, i.e. $x=\rho \cos(\phi), y=\rho \sin(\phi), z=z$ Now since $\vec r = \begin{pmatrix} x \\ y \\ z\end{pmatrix}$ I receive $ ...
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0answers
23 views

How to formulate a coordinate transformation

Thank you in advance for taking the time to consider this. I'm trying to figure out how to formulate a coordinate transformation problem (at least that is what I think it is). Background: I have an ...
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0answers
20 views

Transform to cylindrical coordinate system

I tried so many approaches , at least give me a hint on how to find The unit vectors $$ \vec{V} = y\vec{i} + x\vec{j} + \frac{x^2}{\sqrt[2]{x^2+y^2})} \vec{k}\ $$
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0answers
22 views

Syncronize positions of 2 rectangles with different origin point while rotation

Suppose we have 2 rectangles in Cartesian coordinate system with (0,0) at the top left corner of the screen. Both of rectangles (a and ...
0
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0answers
173 views

Can someone help me convert definitions of hip movement in Cartesian coordinates into spherical coordinates?

I am a biomechanist. I am having a problem converting an idea in Cartesian coordinates $(x,y,z)$ to spherical coordinates $(r,\theta,\phi)$. I wondered if someone could help me. I can physically ...
0
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0answers
18 views

Polar-Cartesian Plot Interconversion

The Question How can we interconvert any general graph of polar or cartesian function so they give the same plot in the other coordinate system. Note: I do not mean to ask about interconverting a ...
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1answer
20 views

What symmetry statement can be made about the points $(a, b)$ and $(b, a)$?

The question is: if $a$ and $b$ are any two numbers, what symmetry statement can be made about the points $(a, b)$ and $(b, a)$? I'm not sure whether this is a symmetry statements and whether it is ...
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4answers
49 views

Find a point on the line through $A=(2,3)$ and $B=(-5,-4)$ that is twice as far from $A$ as from $B$

Find a point on the line through $A=(2,3)$ and $B=(-5,-4)$ that is twice as far from $A$ as from $B$. Please indicate the actual position of the point.
1
vote
1answer
66 views

Equilateral triangular grid generation algorithm

In a research that I'm doing I need to generate an equilateral triangular grid and use this grid to mesh a region of space represented as a polygon to solve a PDE on this mesh. The problem is I need ...
1
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1answer
164 views

Calculating the angular velocity from x, y coordinate data

I have some video footage where I'm tracking insects over several hundred to thousand frames, resulting in a list of x, y coordinates for where the insect has been. I've found it pretty ...
5
votes
3answers
153 views

If ABCD is a square with A (0,0), C (2,2). If M is the mid point of AB and P is a variable point of CB, find the smallest value of DP+PM.

I assumed the coordinates of P = (h,2) to get the value of DP+PM= $\sqrt { (h-2)^2 +4}+\sqrt{h^2+1}$. Then I differentiated the equation wrt to h to get: $h(\sqrt{h^2+1}) -2\sqrt{h^2+1}+ ...
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0answers
5 views

How do i draw a circular polygon with angles and distances

My input data has 360 entries each corresponding to a angle, something like this 0° -2 1° -2.2 2° -2.1 3° -2.3 ... Each entry shows the distance from the center ...
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0answers
24 views

A function defined on a cylindrical surface, shift in x direction, and expansion in cylindrical coordinate system

A function is defined on a cylindrical surface ($r=r_0$), $\psi_1(r,\phi,z)=f(z)cos(m\phi)\delta(r-r_0)$, where m is a integer, can be 1,2,3..;$r,\phi,z$ are coordinate system variable. If $\psi$ ...
0
votes
1answer
22 views

Method in calculating distance from a point ta a line in 3D rectangle coordinate system

I have a problem while trying to calculating the distance form point $B(0,3,4)$ to the y-axis in xyz coordinate system. Here is how I calculate it: There is point $Y(0,t,0)$ belonging to the y-axis ...
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0answers
19 views

Finding coordinate axis vectors to yield a specific transformation

For a project I am working on, I will be given a point $\textbf{a}$ in a global 3-D coordinate system, as well as a point $\textbf{a}^\prime$ in a local coordinate system. (The global coordinate ...
0
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1answer
28 views

Which Points are not Contained in the Line

The Circle $$x^2+y^2-4x=0$$ is cut by a line $AB$ at two points. If $A$,$B$ and two other points $C(1,0)$ and $D(0,1)$ are Concyclic, Then which of the Following points are not contained by the line. ...
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0answers
17 views

Transform Confocal Ellipsodal to Spherical Coordinates

I heard that someone published a paper showing that the confocal ellipsoidal coordinate system can transform into the spherical coordinates under special limit evaluations, however I was unable to ...
0
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2answers
17 views

Question regarding vectors within a circle in an $x$- and $y$-plane.

In an $x$ and $y$ coordinate plane, with respect to the points $A, B$, and $C$ on a circle of radius $1$, find the minimum value of $\vec {AB} \cdot \vec {AC}$ So far, taking $O$ as the origin I've ...
0
votes
1answer
26 views

Writing same equation in different forms

I am working with a unit circle with imaginary integration. I know from experience that this can be written as $f(\theta)=\cos t+ i \sin t$ or $e^{i \theta } $ My question would be if i have a circle ...
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1answer
23 views

Proving that $2$-D parabolic coordinates are orthogonal

How can we prove that the parabolic coordinate system in two dimensions is orthogonal? I tried using the dot product, but don't know where to start or what basis vectors can be used in two dimensions. ...
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0answers
22 views

Show the equation for the length of a path on the surface of a sphere.

Here is my problem. What I am confused about is going from cartesian to spherical coordinates. I do know that L= integral from point $1$ to point $2$ of $(\sqrt{(dx^2+dy^2)})$. (in cartesian ...
0
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0answers
24 views

Coordinates in file isn't in the range -180 to 180 respective -90 to 90?

Hello! I'm creating an android version of a PC program (I've contacted the complany who owns the PC program, so it's legal). The program is in the core a GPS, but is used to navigate pre-defined ...
0
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1answer
40 views

coordinate transformation and tensor

A 2 dimensional Euclidean space is represented by two different coordinate systems: the Cartesian system $(x_1,x_2)$ and an alternative system $(\xi^1,\xi^2)$ where ...
0
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1answer
21 views

Integral in Spherical and Rectangular Coordinates

If I'm evaluating $\int^b_a r dz$, where $r$ is a variable in spherical coordinates and $z$ is a variable in rectangular coordinates, do I need to transform $dz$ in spherical coordinates? If so, how ...
0
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1answer
187 views

Z coordinates of 3rd point (vertex) of a right triangle given all data in 3D

this is my first post.. I hope this good I have 1 triangle in space (3D)... and I know all data except the coordinates of 3er point(vertex)... for example this: then: ...
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0answers
12 views

how to visualize this statement: Matrix M falls in a Ball-set.

So the question is simple: Assume you are told that a matrix M has the following property: $\|M\|_2<1$, i.e. it falls in unitary ball. When we say it is inside a ball set, if you imagine a ...
4
votes
2answers
395 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 ...
0
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4answers
94 views

Equation of circle touching a parabola

Suppose we have a parabola $y^2=4x$ . Now, how to write equation of circle touching parabola at $(4,4)$ and passing thru focus? I know that for this parabola focus will lie at $(1,0)$ so we may ...