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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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 ...
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1answer
30 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 ...
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1answer
34 views

Sum of vectors in coordinate system [on hold]

How to find the sum of vectors by having only their (x,y) coordonates and the forces? For exaple I have: Vector A point 1 (7,-5); point 2 (17,-2); Force:10 Vector B point 1 (7,-5); point 2 ...
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1answer
15 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 ...
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1answer
25 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
10 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 ...
2
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1answer
24 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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4answers
44 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 ...
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0answers
14 views

Computing the angular momentum in spherical coordinates [migrated]

How to compute the angular momentum of a particle in spherical coordinates? It's given by: $$x_1=r\cdot\cos(\phi)\cdot\sin(\theta)$$ $$x_2=r\cdot\sin(\phi)\cdot\sin(\theta)$$ ...
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0answers
15 views

Converting points in a right hand z vertical coordinate system to left hand y vertical [migrated]

I have a series of points in space from Fanuc (robot manufacturer). The points are in a right hand system with positive z up. I need to convert this system to Direct X, which is left handed and has ...
2
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1answer
47 views

If $x=\pi a y^{1/2}$ then why is $\frac{\partial^n}{\partial x^n}=-2\left(\frac{y^{3/2}}{\pi a}\right)^n \frac{\partial^n}{\partial y^n}$?

While I was reading this question, I was surprised that the transformation of a 'simple' differential operator $\displaystyle \frac{\partial^n}{\partial x^n}$ by substituting $x=\pi a y^{\frac{1}{2}} ...
6
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0answers
115 views

Physical components of a third-order tensor

Aris' book Vectors, Tensors, and the Basic Equations of Fluid Mechanics describes how to convert between covariant, contravariant, and physical components of vectors and tensors. For example, in ...
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3answers
77 views

What Vector Operation Performs $(a,b)*(c,d)=(ac-bd,ad+bc)$?

When you multiply two complex numbers, you get \begin{equation} (a+bi)\times(c+di)=(ac-bd)+(ad+bc)i \end{equation} As betterexplained.com points out, this multiplication of two complex numbers can be ...
1
vote
1answer
19 views

Point coordinates at a fixed distance from a vector

I would like to solve the following generic problem by using vector notation that I will use it to improve my algorithm. I have a vector P1P2 that points P1 and P2 are known. Furthermore, an ...
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1answer
20 views

Cartesian to spherical coordinate system

Hey I want to convert Cartesian to spherical coordinate system. I referred many site and for calculating elevation angle $\theta$ from positive z axis they all used formula $\arctan \frac { ...
0
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0answers
24 views

Locus of the Orthocentre of a triangle.

Vertices of a variable triangle are $(3,4),(5\cosθ,5\sinθ)$ and $(5\sinθ,−5\cosθ)$ , where $θ∈R$. Locus of its orthocentre is. A. $x^2+y^2+6x+8y−25=0$ B. $x^2+y^2−6x−8y+25=0$ C. ...
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2answers
36 views

Finding two vertices of a rectangle given two vertices and angle?

I have a rectangle where I know the coordinates of the opposite diagonal corners. I also know the angle that the rectangle is rotated. I would like to solve to find the coordinates of the other two ...
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2answers
34 views

How to determine the distance to one point from another in a 3D coordinate system?

I wonder how I can calculate the distance between two coordinates in a $3D$ coordinate-system. Like this. I've read about the distance formula: $$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$$ (How) Can ...
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2answers
40 views

Coordinate geometry reflection of point

I have point in $1st$ octant($ x, y, z$ all positive). Now I take the mirror image of that point about $xy$ plane. I guess that new point will be simple $ (x, y ,-z)$. Verify if I am right. Further ...
13
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1answer
682 views

Conditions for two straight lines to intersect: is this exam question wrong?

I am pretty sure this question (from a university admission test exam) is wrong. Two lines: $a_1x+b_1y+c_1=0$, $a_2x+b_2y+c_2=0$, intersect only if (a) $a_1a_2-b_1b_2=0\;\;\;$ (b) ...
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2answers
28 views

Show that both the given lines are parellel (3-D)

Guys I am trying to solve the problem below which I found in a book: Show that the lines $\frac{x-1}{2}=\frac{2-y}{1}=\frac{5-z}{1}$ and $\frac{4-x}{4}=\frac{3+y}{2}=\frac{5+z}{2}$ are parallel. ...
2
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0answers
84 views

Problem regarding the speed of two points $A$ and $B$ moving with constant speed in the plane [duplicate]

Consider a Point A that moves linearly on the positive x-axis with the speed 1 m/s and another Point B at a distance L from A with position (L,0). With each forward motion of point A the Point B moves ...
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3answers
48 views

How to determine the equation and length of this curve consistently formed by the intersection of Circles

Consider a Point $A$ that moves linearly on the positive $x$-axis with the velocity $1$ m/s and another Point $B$ at a distance $L$ from $A$ with position $(L,0)$. With each forward motion of point ...
3
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2answers
66 views

Is there a structure similar to a graph but which includes a sense of direction, like north, west, east, south?

I understand that graphs do not have any notion of "facing", that is, a sense of relative or cardinal directions. Using a conventional graph, it's not possible to say "go left at vertex A," as far as ...
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0answers
41 views

Compute the quaternion of a bone knowing the position of two joints

I met a problem in my project to compute the orientation of a bone. Suppose I have a bone with two joint on each end. The length of the bone is $L$. Assume the 3D position of two joints, notated as ...
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1answer
22 views

Determining third vertex of the right angled isosceles triangle

If A(9,-9), B(1,-3) are the vertices of a right angled isosceles triangle, then the third vertex is?? Here in this question i got stuck to the point that which side is taken as the given coordinates. ...
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1answer
22 views

Given two points, I need to find all of the 'sections' of the graph that the line segment travels through.

What do I mean by "sections"? Imagine a piece of graph paper. Each square bounded by integer horizontal and vertical grid lines is a "section", and is named after its lower left coordinate — (1,1), ...
3
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3answers
95 views

3D coordinates of circle center given three point on the circle.

Given the three coordinates $(x_1, y_1, z_1)$, $(x_2, y_2, z_2)$, $(x_3, y_3, z_3)$ defining a circle in 3D space, how to find the coordinates of the center of the circle $(x_0, y_0, z_0)$?
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1answer
32 views

How to find the velocity and accelaration in a 3d space with 6 degrees of freedom?

I have the following rigid body: I assume that the body is a symmetric cylinder.x,y,z are the axes of the reference frame resulting from a transformation involving three orthogonal rotations ...
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1answer
28 views

Construct a procedure which determines the location of the shadow of a rectangluar box.

I drew a 3d rectangular box on a coordinate plan consisting of x, y, and z. A procedure is to be created that will determine the location of the shadow of the box on one of the coordinate planes. I ...
0
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1answer
23 views

Determining transformation matrix from six points

Given that I have the locations of three points: p1 = [1.0,1.0,1.0] p2 = [1.0,2.0,1.0] p3 = [1.0,1.0,2.0] ...and I know their transformed counterparts: ...
2
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0answers
42 views

Intesection point of feet of altitudes

If triangle has vertexes at $(x_1,y_1),(x_2,y_2),(x_3,y_3)$, is the intersection points of feet of altitudes $$x_h = \frac{x_1x_2(y_2-y_1) + x_2x_3(y_3-y_2) + x_3x_1(y_1-y_3) + y_1^2(y_3-y_2) + ...
0
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1answer
24 views

Solving for $x$ in terms of $y$ using coordinates

A line passes through $(4,1),(1,y),$ and $(x,2)$. What is the value of $x$ in terms of $y$? What equation do I have to use for this problem? $m=\frac{y_2-y_1}{x_2-x_1}$ , $y=mx+b$ , $y-b=m(x-a)$ I ...
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0answers
4 views

Underlying connections between parametric surfaces and co-ordinate transforms

I've recently been learning about parametric surfaces and surface integrals involving various co-ordinates systems. I was wondering, is there a fundamental connection between parametrization and ...
5
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2answers
106 views

Number of solutions of a simple equation

Problem How to count the number of distinct integer solutions $(x_1,x_2,\dots,x_n)$ of the equations like : $$|x_1| + |x_2| + \cdots + |x_n| = d $$ the count gives the number of coordinate points ...
0
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1answer
21 views

Trying to figure out coordinates of isoscleles triangle

I'm programming some application, which heavily depends of geometry. Let's say, in 2D coordinates system I have i.e. : Bxy = (5,-2) Cxy = (2,-5) ABlength = 5.5 ...
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1answer
29 views

How to find circumference origin position?

I need to find origin of circumference which is defined by two points and vertex angle of isosceles triangle: I've got radius of triangle by ...
0
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1answer
38 views

Equation Of A Straight Line Passing Through A Point and Having an Intercept

The question is as follows: "Find the equation of the straight line passing through (-2,-7) and having intercept of length 3 units between straight lines 4x + 3y = 12 and 4x + 3y = 3." I really ...
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3answers
36 views

Coordinate Geometry of triangle question

Can someone please explain how I can get coordinates for B using the slopes that are shown in the question? I'm not sure how I came to my solution where I tried to use y=mx+b. For e.g. to solve for ...
1
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2answers
23 views

Orthonormal basis in a cylindrical coordinate system

So I am supposed to show if these vectors make an orthonormal basis in a cylindrical coordinate system. $\vec e_p=\bigl(\begin{smallmatrix} cos(\theta )\\ sin(\theta )\\0 \end{smallmatrix}\bigr); ...
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0answers
14 views

Minimum and maximum points

The question is : Find the shortest distance from the point (2,1,-1) to the plane : x+y-z=1 . So can we solve this problem by using the rules of stationary points ( minimum points ) , if not , How ...
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1answer
29 views

defining a closed curve in cartesian coordinates

I am trying to implement a track in cartesian coordinates, such that X and Y coordinates are accepted and those are linearly interpolated. The problem is, I want to include circular shapes on ...
0
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1answer
22 views

How do I get the start and endpoint of a line using the middle point and the angle?

I have a line that goes from P1 to P2 in a 2D space. I have the location of the middle point of that line, and the angle of inclination of the line. The thing is that I don't know the length of the ...
5
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0answers
76 views

Elastic wave equation in curvilinear coordinates: how do you perform a coordinate change?

The essence of this question is that I don't know how to convert an equation from Cartesian coordinates into curvilinear coordinates, and would like to know how, preferably using the language of ...
6
votes
1answer
104 views

Transforming a PDE given basis vectors

I have a non-orthogonal coordinate system defined by $\mathbf x=\mathbf x(r,\beta,z)$, and so I can find the basis vectors as $$ \mathbf g_r=\frac{\partial \mathbf x}{\partial r},\quad\mathbf ...
2
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1answer
21 views

Calculate Coordinates

I have the following two circles (n1, n2). I know the coordinates of them. They are connected with a line. I also know the angle "alpha" and the diameter of the circles. Now I try to calculate the ...
0
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3answers
87 views

Volume of the solid bounded by the sphere $x^2 + y^2 + z^2 = 9$ and paraboloid $8z = x^2 + y^2$

Find the volume of the solid bounded above by the sphere $x^2 + y^2 + z^2 = 9$ and below by the paraboloid $8z = x^2 + y^2$ I'm having some trouble finding the correct limits of integration in ...
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2answers
76 views

Finding closest point perpendicular to B

Given: A = 8,4 B = 4,8 C = 4,4 D = ?,? From point C (4,4) (red dot) how would I find the coordinate that would be perpendicular to AB and CD being parallel to ...
0
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1answer
40 views

Having 2 coordinates putting the third coordinate on the closest 90 degree point

I've got a follow-up question for the previously asked and answered question here What I am trying to do now is that when I have a third coordinate I want it to be converted to the closest point on ...
0
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1answer
42 views

Having 2 coordinates calculating the 90 degree angle formula of the next point

I have 2 coordinates, what would be the 90 degree formula to the next point I am drawing? Say ...