# Tagged Questions

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### How to calculate Global co-ordinates from local co-ordinates and vice versa

I am trying to find the method to calculate/convert local co-ordinates into global co-ordinates and vice versa. I can easily find these co-ordinates by using CAD but I would like to know the ...
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### What is (fundamentally) a coordinate system ?

Consider the following construction of vectors and points. Let's start with a vector space, or more specifically a coordinate space $F^N$ over a field $F$ and of $N$ dimensions. The elements of this ...
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### Rigorous definition and relations between point/vector/affine space/vector space/basis/frame/coordinate system

I am trying to understand the exact relation between all these things: point vector affine space vector space basis frame coordinate system Can you explain me rigorously (in the mathematical ...
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### Question on Co-ordinate Geometry

Four points $A(6,3)$, $B(-3,5)$, $C(4,-2)$, $D(x,3x)$ are given in such way that: $$\frac{\text{Area of triangle (ABC)}}{\text{Area of triangle (DBC)}} = \frac{1}{2}$$ I have to find $x$ in the ...
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### A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$…

A rectangle $OACB$ with two axes as two sides,the origin $O$ as a vertex is drawn in which the length $OA$ is four times the width $OB$.A circle is drawn passing through the points BC and touching ...
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### Rolling of a circle along the positive $x$-axis without slipping and finding the locus of a point lying on the circumference of the circle.

Consider the circle of radius $1$ with its centre at the point $(0,1)$. From this initial position, the circle is rolled along the positive $x$-axis without slipping. Find the locus of the point $P$ ...
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### coordinate geometry - find point in right-angled triangle

I'm making a map. I've come across a geometry problem, and I'm not so knowledgeable about maths! Let me illustrate with pictures. I am trying to plot flightpaths with a curved line, using a ...
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### Great circle and how to “imagine” it in this case?

I am currently working on a riddle. I have to search and locate a person, but I do not know, where he is. I only have some informations, concerning the probability where he might be. A satellite ...
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### To prove that the centre of 2 circles and the two points at which the 2 circles cut and the origin lie on a circle.

Let the circles $$x^2+y^2-2cy-a^2=0~~~~and~~~~x^2+y^2-2bx+a^2=0$$ with centres at $A$ and $B$ intersect at $P$ and $Q$. Show that the points $A,B,P,Q$ and $O=(0,0)$ lie on a circle. My work: I ...
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### Why does a figure look the same in every coordinate system?

After reading Maximilian M. Answer here: Gauss' Theorem - Can't understand a parameterization I'm trying to figure out why does a figure look the same in every coordinate system I choose. For ...
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### Rectangle In a Triangle or Circle

I guess this is simple enough fellas, but I'm falling short. What is the ideal way to calculate the best fit square in a equilateral triangle, and for that matter a circle too. Any suggestions?
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### Number of classes of K-sets

I am having a plane in N dimension. Th distance between 2 points (a1,a2,...,aN) and (b1,b2,...,bN) is max{|a1-b1|, |a2-b2|, ..., |aN-bN|}. I need to to know how many K-sets exist(here K-set refers to ...
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### Converting from spherical coordinates to cartesian around arbitrary vector $N$

So if I'm given an arbitrary unit vector $N$ and another vector $V$ defined in spherical coordinates $\theta$ (polar angle between $N$ and $V$) and $\phi$ (azimuthal angle) and $r = 1$. How do I ...
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### Geometric accuracy analysis of 2d rectangular models

I have reconstructed set of rectangular objects lie on a 2D plane (for ex. ABCD). All these objects are in a one coordinate system. On the other hand, I have reference models for all of them ...
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### Check Points are line, triangle, circle or rectangle

How to determine geometric properties of four distinct points in a plane (x1,y1), (x2,y2), (x3,y3), (x4,y4) represented in the 2-D Cartesian coordinate system, whether these four points are on a ...
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### What's the slope of the mirrored line?

If I have line $M$ with slope $m$, and line $A$ with slope $a$, and I wish to mirror $A$ over $M$ to form some new line $B$, what is the slope of $b$?
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### Re-Calculate Rectangle Width/Height After Translating One Coordinate

I'm trying to put resizing handles on the four corners of a rectangle, which can be dragged to resize the rectangle. What I'm having trouble with is calculating the new width, new height, and new ...
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### Simple way to parameterize two perpendicular vectors

Given are two vectors in $\mathbb{R}^3$, $\bar{u}$ and $\bar{v}$, such that they are perpendicular ($\bar{u}\cdot\bar{v}=0$) and of equal length ($|\bar{u}|=|\bar{v}|$). Is there a "nice" way to ...
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### Project point onto line in Latitude/Longitude

Given line AB made from two Latitude/Longitude co-ordinates, and point C, how can I calculate the position of D, which is C projected onto D. Diagram:
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### Fixed points through a general circle.

The circle $C: x^2 + y^2 + kx + (1+k)y - (k+1)=0$ passes through two fixed points for every real number $k$. Find $(i)$ co-ordinates of these two points and $(ii)$ the minimum value of the radius.
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### how to calculate the volume of irregular shape by the Cartesian coordinates of its corners?

I've 4 points in a plane "A" and another 4 in another plane "B". is there a way to automatically calculate the volume contained into this irregular box? The automation is important as this set of 8 ...
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### How do I find the middle(1/2), 1/3, 1/4, etc, of a line?

Similar to this question: How to calculate the middle of a line? where it's explained how to find the middle of a line (x,y), so that's half the line 1/2, but I also need to find one third of the ...
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### Find the Bounding Rectangle of Rotated Rectangle

I have rectangle with co-ordinates(x1,y1) and (x2,y2) and I have to rotate the rectangle an amount of Īø about it centre using Rotation Matrix ...
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### Indexing Goldberg (0,n) polyhedron faces

I would to know how to uniquely identify a face of a Goldberg (0,n) polyhedron: http://en.wikipedia.org/wiki/Goldberg_polyhedron#Icosahedral_G.280.2Cn.29_polyhedra It's possible to uniquely assign ...
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### Rotate 3D coordinate system such that z-axis is parallel to a given vector

Assume I have a Cartesian $xyz$ coordinate system with a point $p=(p_x,p_y,p_z)$. In addition a vector $n=(n_x,n_y,n_z)$ is given. How do I rotate the coordinate system to obtain a new $uvw$ system ...
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### Geometry: angle relative to x-axis for a tangent of a circle (see picture)

Excuse my poor description in the title, I think a picture is needed to explain my question: Theta is the angle to the x-axis. So my question is: given the radius of the circle, theta, and beta, ...
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### Getting latitude/longitude from a 2d co-ord system [duplicate]

Given a latitude/longitude and a distance and bearing in relation to that point, how can I find the latitude/longitude of the new position? Distances can range from 0-100km so curvature of the earth ...
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### Approximate sector between two lines?

I need to approximate a red figure. I know coordinates of three points (little transparent circles). I also know a count of segments I need to divide this figure. The angle may be from 0 to Pi and ...
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### Perpendicular at a defined distance from point on line intersects another line in coordinates?

It approximatelly look likes the following picture The figure may be rotated at any angle. I know the coordinates of points A, B, C, D and the length of BF. ABD and CBD are equal (AD = CD and AB = ...
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### Linejoin for fat lines?

I draw a figure with 2 fat lines. I need to draw a join between these lines correctly. Long red lines are in a middle of each fat line. What I know: coordinates of white points. the angle between ...
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### 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 given ...
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### Perpendicular unit vectors

I have a known unit vector $p (a,b,c)$. First I want a unit vector $q$ which is perpendicular to $p$ and passing through a known point $V(X_0,Y_0,Z_0)$. Then a another unit vector $r$ which ...
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### How to set dihedral values to null?

I have a protein with many residues, but I would like to set the phi and psi angles of residue 15 to value of null. I have a file containing all residues and Cartesian coordinates, and I have another ...
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### 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 ...
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### Given 2 points/coordinates, how do I express in $ax + by + c = 0$ form?

Given 2 points eg. $(x_1, y_1), (x_2, y_2)$ how do I express in $ax + by + c$ form? I am supposed to find the intersection of 2 lines. I have 2 points for 1 line, and the other line will be ...
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### Parameterizing a spherical cap in cylindrical coordinates

In calculating the mean curvature for a surface of the form $(f(z)\cos(\theta), f(z)\sin(\theta), z)$ I need to use some checks to ensure I haven't made any mistakes along the way. The one I would ...
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### coordinate of shorter line

If I have a line segment with endpoints AB,CD. The length of the line is 5 units. If I make the line shorter (eg. 3 units), and one of the endpoints is still AB, how do I figure out what the new CD ...
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### Geometry finding area problem

A regular 2N -sided polygon of perimeter L has its vertices lying on a circle. Find the radius of the circle and the area of the polygon.
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### Calculate the X,Y values of an ellipse

I guess am confused somewhere. I have the length(l) and breadth(b) of an ellipse enclosing rectangle. I know the center point and the angle(x) that the line makes with the center. I want to know the ...
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### How to calculate the coordinates of orthocentre.!!

How to calculate the coordinates of orthocentre.!! I was surfing through the net and got this formula.. $$x-\rm coordinate= \frac{x_1\tan A+x_2\tan B+x_3\tan C}{\tan A+\tan B+\tan C}$$ ...
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### Calculate Camera Pitch & Yaw To Face Point

How do you calculate pitch & yaw for a camera so that it faces a certain 3D point? Variables Camera X, Y, Z Point X, Y, Z Current Half Solution Currently I know how to calculate the pitch, ...
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### Change of coordinates in 3D

It's been a while since my last geometry class and I need some help in solving a very simple problem I have. I need to implement a zoom function in 3D in a piece of software I am writing. My system ...
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### graph of moving object

let us consider following three picture grouped as in one picture suppose that we have following problem: during the $1$ hour,biker was moving around station $A$ and during this $1$,he did not ...