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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Change of Basis Matrix: Cartesian to Spherical Laplacian

I was looking at how a change of basis matrix, $[P_{\beta\leftarrow\alpha}]$, is made. While this is a bit more advanced that than what was taught at the course, I wonder what would be the change of ...
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Extrinsic and intrinsic Euler angles to rotation matrix and back

currently I'm working on the visualization of coordinate systems in space to understand rotation matrices better. Until now I thought everything would be ok, but there is a thing that does not get ...
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Equation for coordinates [on hold]

Hi my class just started a new unit and the teacher told us to find the equation for each set of coordinates. So if the coordinates are (-2,4),(-2,3),(-2,8),(-2,-5),(-2,-7), how do we find it?
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Transforming 2d coordinate system while keeping points placement

I don't know if my question is too simple. Hopefully I can make it clear. I want to find a matrix that I could multiply point with in one coordinate system into another. The first coordinate system ...
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Finding bounds of integration

Let $S$ be the region in the first quadrant of the $xy$-plane bounded by the $x$-axis and the parabolas $$x=1-\dfrac{1}{4}y^2,$$ $$x=\dfrac{1}{4}y^2-1$$ and $$x=4-\dfrac{1}{16}y^2.$$ Use the ...
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Change of Coordinates matrix.

If Q is the change of coordinates matrix From some basis B to B', then Q inverse is the change of coordinates matrix from B' to B? Is this true? I think/ know it is the, but don't know how to prove ...
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Build an orthogonal coordinate transformation?

I am supposed to build an orthogonal coordinate transformation $Q:G\to \Omega$ whose inverse is not orthogonal $Q^{-1}:\Omega\to G$. I am allowed to make the coordinate transformation as simple as ...
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28 views

find which two points an arbitrary point is nearest to

I would like to solve for a point $P$ regarding its proximity to the line segment it resides within. I can make a guarantee that the point will be placed along a line. In the included example, we ...
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How to find the value of standard coordinate frame in a new coordinate frame?

I have a custom coordinate frame which has T as a point and A, B, C are three orthogonally normalized vectors whose coordinates are T = [Xt Yt Zt], A = [Xa Ya Za], B = [Xb, Yb, Zb] and C = ...
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Realistic Bounce (Using Trig?)

background: I am making a graphics program where the major purpose of it is to have a ball (traveling on an arbitrary slope) to bounce realistically off of a line (which is also at a arbitrary slope). ...
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How can I find the domain of this diffeomorphism (coordinate transformation)?

I have been struggling with this coordinate transformation in $R^2$. $Q:\begin{bmatrix}\rho\\\phi\end{bmatrix}\to \begin{bmatrix}\cosh(\rho)cos(\phi)\\sinh(\rho)sin(\phi)\end{bmatrix}$ I am ...
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Problem in calculating angles of a tringle with co-ordinate geometry

There are three equations. $$(a+b)x+(a-b)y-2ab = 0 \tag1$$ $$(a-b)x+(a+b)y-2ab = 0 \tag2$$ $$x+y = 0 \tag3$$ The question is, So that the triangle formed by these equations is an isosceles ...
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Find the tangents to circle

Let $ \Gamma : x^{2} + y^{2} - 6x - 4y + 8 = 0 $ be a circle. Find the equations of the tangents to $ \Gamma $ which pass through $ D(8, 7) $.
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Question about the following coordinate transformation.

$Q:\begin{bmatrix}\rho\\\phi\end{bmatrix} $$\to$ $\begin{bmatrix}cosh(\rho)cos(\phi)\\ sinh(\rho)sin(\phi)\end{bmatrix}$ The task is to pick a domain as big as possible so that Q is a ...
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transform orthonormal coordinate system to another

I have one orthonormal coordinate system ABC that it's origin is the point p0. I would like to transform it to another orthonormal coordinate system A'B'C', that it's origin is p1. I know how to ...
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Check if point is within quadratic area.

I have two dimensional Cartesian system and I need to check if certain point is within the geometry formed by four other points. I have few thousands different geometries all with different points to ...
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Converting fractional coordinates to cartesian coordinates

I have a set of fractional coordinates with the following vectors: 2.950 -1.475 0.0000 0.000 2.5547 0.0000 0.000 0.0000 77.5379 with the ...
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Computing local coordinates

Let $p=[x_0,y_0,1]\in \mathbb P_2(k)$ (projective space). Determine a projective transformation $\phi\in GL(3,k)$ such that $\phi(p)=[0,0,1]$ and name the coordinates explicit. Its easy to see that ...
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commutation relation of angular momentum operator in non cartesian coordinates

The angular momentum operator $J$ in quantum mechanics with the commutation relation \begin{equation*} [J_l,J_m]=i\hbar\epsilon_{lmn}J_n \end{equation*} has the structure of a Lie-algebra. It is ...
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under what conditions can orthogonal vector fields make curvilinear coordinate system?

I am considering n-dimensional Euclidean space $\mathbb{R}^n$. For any $x\in\mathbb{R}^n$, $v_1(x), \cdots, v_n(x)$ are orthogonal vectors. As functions of $x$, $v_i$'s are differentiable and non-zero ...
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Education tool for learning 3D angles

I hope it is not an off-topic. I have started working on 3D frame transformation and transforming a vector such as acceleration or angular velocity from one coordination to earth coordination. My ...
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How to get the coordinates of the point of a line segment

I have the coordinates of the 2 end points a and b thanks to which I can draw a line. How can I get the coordinates of all the points of the segment of line starting from point a to point b ?
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Torus coordinates and triple integration

Torus coordinates are given by $$x=(R+r \cos\theta)\cos\phi,\space y=(R+r \cos\theta)\sin\phi,\space z=r\sin\theta,$$ with $R>0$. A given torus $T_b$ is defined by $$T_b=\{(r,\theta,\phi):0\leq ...
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Calculate point's coordinates relative to rotation in 3D-space

I have a point "A" in 3D-space, let's say in coordinates (2, 3, -1). Then there's a point "B" which position is A + (-1, 2, -1), so now it's ...
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Using axis coordination to represent rotation matrix instead of angles

Euler angles give us clear matrix for conversion of a vector from car reference $Fr^C$ to earth reference $Fr^E$. If $\vec V$ is a vector in different frames it is represented differently: $$\vec ...
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Transform vector from xy plane to “another vector's plane”

I've not had linear algebra yet, so bear with me if I write something weird. Given vector A and B as shown above, how do I transform vector B so that one of its components is parallel to A, and the ...
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Transforming coordinates according to Point of View.

Imagine I have two cameras (A and B) in the same axis and looking at the same white wall with a black dot. Both cameras see the black dot. I'd like to know how to proceed in order to derive the black ...
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41 views

Coordinate systems in physics problem (damped pendulum)

A simple pendulum of lenght $\ell$ is vibrating freely (with small oscillations). The pendulum is set into forced vibration by moving its point of suspension horizontally with a Simple Harmonic ...
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Using trigonometry to predict future position

Intro I'm currently creating an AI for a robot whose aim is to shoot another robot. All I want to do is to be able to calculate at what angle to shoot my bullet, so that it hits my enemy, with the ...
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2answers
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How to calculate angles and areas (circles)- AS Maths

Hi here's the question: A(-1,-4) and B(6,-5) are points on the circumference of a circle, centre D(3,-1). The tangents at A and B intersect at C. How would I find the angle ACB and the area of ACBD? ...
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Using azimuthal and polar angles in ECEF coordinate system

I have a physical cone, which its vertex located in some point (x,y,z) in ECEF coordinates, and I want to check if another point is inside this cone. In order to do it, I have to take into ...
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Benefit from local coordinates

I am reading Elliptic Curves by Anthony Knapp. Its the first time that I am dealing with local coordinates. In page 21 he introduces them as follows: Let $[x_0,y_0,w_0]\in \mathbb P_2(k)$ where $k$ ...
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1answer
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Clamp Distance Between Two Vectors

I was wondering if there is a formula to clamp distance between two Vectors. Let me elaborate. I have two Vectors, say, $V_1(x_1,y_1)$ and $V_2(x_2,y_2)$. I can find the distance '$d$' between them ...
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convert coordinates from non-orthogonal axes to cartesian in 3-dimensions

I'm having issues converting from a non-orthogonal coordinate space (abc) to a cartesian space (xyz). I think I may have just thought myself into a corner, and I can't get out. The systems have a ...
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Find coordinates of the rotation center

My software is going to control a Laser. I know the Laser's current Position defined as $P_1$ with coordinates $(x,y)$ and the place where it will be after a clockwise rotation around a point $C$, ...
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1answer
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Calculate x and y coordinates of n'th cell in table

If we have table with $c$ number of columns and $r$ number of rows, and we iterate through the table from left to right and then to the next row (below), how do we calculate to which row and to which ...
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Transform of the Cartesian plane that maps hyperbolic arcs $xy = C$ to line segments

I have the finite set of curves: $$y = \frac{C}{x}, \qquad C = 2, 3, \ldots, C_{\max},$$ with $C$ and $x$ positive integers, $2 \le x \le C$ ($x$ varies on a finite domain). Is it possible to apply ...
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Calculate mean and std.dev from a lot of coordinates

How do i calculate the mean coordinate and the standard deviation of a cloud of (x,y) coordinates. I know how to calculate the mean, but i am struggling with calculating the std. deviation.
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Given 4 coordinates from the perimiter of a square, can the square be constructed?

I have a square, tilted at an unknown angle. I am given 4 coordinates of the square. They lie on the perimeter, one per side. With these 4, and nothing else, am I able to determine the vertices of ...
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Conditions for point lying inside triangle formed by three complex numbers.

The question states $z_1,z_2,z_3$ are three non-collinear complex numbers such that $$z=\frac{lz_1+mz_2+nz_3}{l+m+n}$$ lies inside the triangle formed by $z_1,z_2,z_3$. If $l,m,n$ are the ...
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How can I calculate Distance of line?

I have a picture. I want to measure of $P_{1}$ to $P_{4}$ distance. Also I know $P_{1}$ to $P_{2}$ to real distance. and $P_{2}$ to $P_{3}$ real distance $P_{1}-P_{2}$ real distance = $100$ mm ( ...
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1answer
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Calculating the x, y coordinate a set distance between two points

I'm trying to calculate the x and y coordinates that are a set distance between the coordinates of two pixels in an image. For example, if I travel from my original location (x1=4, y1=3) to a new ...
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How to obtain a rectangle's side's positions if its origin isn't in its middle?

Basically I have an algorithm which generates rooms and corridors randomly and each time a room is made, a new corridor is placed on $1/4$ of the room's sides and its origin point is set to that ...
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Area of triangle formed by angle bisector, altitude and median

Question:- Given a triangle ABC with side length a, b and c. Calculate the area of a triangle in terms of a, b and c formed by angle bisector from vertex A, altitude from vertex B and median from ...
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How to derive $r, \theta, \phi$ for the sperical coordinate gradient?

I'm trying to figure out how to get the gradient in spherical coordinates. I'm as far as the author writes in this answer: http://physics.stackexchange.com/a/78514 and I understand how and why to get ...
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coordinate geometry : intersection of a curve with a line

I'm having difficulties with the question below. It is from a Cambridge past paper. The equation of a curve is $xy=12$ and the equation of a line $l$ is $2x+y=k$, where $k$ is a constant. In the ...
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Finding coordinates of the third point of a triangle from given?

In ABC triangle we know the coordinates of A and B vertices. We also know lengths of 2 edges shown in the picture and the third edge is calculatable. What is the most efficient functon to find x3 and ...
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Short question about spherical coordinates

If I have a vector orthogonal to the $x$-$y$ plane of an $xyz$ axis system, I mean, a vector with just $z$ component: How can I express it in spherical coordinates?
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Combining two different 2D coordinate points in order to find a 3rd dimension

I'm working in a project where I'm working with two cameras that give me the coordinates of a determined object. The coordinate systems of the two cameras are separated by a known distance (let's ...
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How to get a Right Triangle's points' coordination in the space?

I have a Right Triangle with equal legs of 1 unit long rotated on 3 individual angles in the space like in the picture below: As could be seen in the picture, the input I have are the angles 'a' ...