# Questions tagged [geometric-transformation]

A geometric transformation is any bijection of a set having some geometric structure to itself or another such set. (from Wikipedia)

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### Rotate a body to align z axis in a particular direction

I have the orientation of a body in world frame, $_wP_b$. Let us say, a bottle with the z axis representing the height, lying on its sides on the table. Now, I have a direction vector $\textbf{v}$, ...
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### How to transform global coordinates to local coordinates?

For example, I have 4 points with the following global coordinates $(4,2),(5,3),(6,4),(8,5)$. Graph How to transform these global coordinates into local, such that the first point is $(0,0)$ in the ...
1 vote
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### Transform point in the Poincaré disc to point in tile

I have a set of image files that I want to use to use to texture a set of tiles with (one image per tile), in order to render a textured version of the Poincaré disc with a specific tiling by using ...
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1 vote
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### How to figure out the transformation matrix for rotation and then sheer?

I was watching this video. (Actually, I watched it 3 times because I couldn't understand it.) And right then, he showed that the trasformation matrix for rotation and then sheer is I understood how ...
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### On the proof about the dimension of the conformal group of a manifold

I have been reading the book "Transformation Groups in Differential Geometry" by S. Kobayashi. More concretely, I am trying to understand the proof of the Theorem 6.1 of Chapter IV. Theorem ...
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### Point within the interior of a given angle

The point $M$ is within the interior of given angle $\alpha$. Find the distance between $M$ and the vertex of the angle ($OM=?$) if $a$ and $b$ are the distances from $M$ to the sides of the angle. ...
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### Midpoint of a line segment passing through two points.

Let $C_1$ be a circle defined with $X(-2,7)$ and $Y(2,-5)$ as the endpoints of the diameter of the circle. Let $C_2$ be a circle defined with $Y(2,-5)$ and $Z(4,-11)$ as the endpoints of the diameter ...
1 vote
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### The image of a line through an inversion

I am going to start by saying that geometry is not my strong suit, but I am taking a course on analytic geometry where I learnt about inversions and there is this question that bugs me. The following ...
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### Conformal map $\mathbb{C} \setminus (\{ z \mid \mathrm{Im}(z) \leq 0\} \cup\{z = x+ iy \mid y \geq \sqrt{x^2 + 1}, x \leq 0\})$ onto unit disk

For figure $\mathbb{C} \setminus (\{ z \mid\mathrm{Im}(z) \leq 0\} \cup\{z = x+ iy \mid y \geq \sqrt{x^2 + 1}, x \leq 0\})$ find a conformal mapping to closed unit disk. What I have done so far: I ...
1 vote
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### How to remap points on 2d plane to another plane with regression kind of approach?

The title can not be clear enough as I really don't know how to call this problem. Let me describe it briefly. I have some points in coordinate system as (x,y). All points have to move to a new ...
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### A geometry question...

In the given figure, $ABCD$ is a square of side $3$cm. If $BEMN$ is another square of side $5$cm & $BCE$ is a triangle right angled at $C$. Then the length of $CN$ will be:- I plotted this on ...
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### To prove $EA = FB$ or that $CQ'$ is radical axis

Given disjoint circles $c_1 = \odot(P,PA), c_2 = \odot(O,OB)$ such that $B$ and $A$ are in the same half-plane wrt $OP$ and that $PA \parallel OB \perp OP$. Line $CDQ$ is the perpendicular bisector ...
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### Problem with right angle triangle, circumscribed circle, tangent and the half of its height

(An interesting problem inspired by this one but still different. And, no, I'm not looking for your help to solve a detail here in order to provide a full solution elsewhere. I'll stop here). A right-...
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### Prove that IK, AC, BD are concurrent.

Given a circle (O, R) with diameter AB. Point M on (O), A, B are not coincident. Two lines through O and perpendicular to AM, BM intersects the tangent of (O) through M at C, D, respectively. OC ...
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### A Transformation of a cross-shaped grid filled with 1s (Proof of impossibility?)

Consider a cross-shaped grid of size 7 as it shows on the figure (compared to one of size 3). Each cell contains a 1. Le'ts define a transformation $\pi$ of the grid as follows: take any 3 sized sub-...
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### How to reconstruct a quadrilateral ABCD only using compass and straight edge?

Reconstruct a quadrilateral ABCD given length of its sides and the length of the midline between the first and third sides (namely all the segments drawn in the given figure) using compass and ...
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### Prove that $BXOY$ is cyclic with spiral similarity over a midpoint

Let $O$ be the circumcenter of triangle $ABC$. Line $CO$ intersects the altitude from $A$ at point $K$. Let $P,M$ be the midpoints of $AK$, $AC$ respectively. If $PO$ intersects $BC$ at $Y$, and the ...