<p>I must convert a isosceles trapezoid to a rectangle in 2-D with a shearing transformation (or with 2 shearing transformations).  The isosceles trapezoid is centered in the origin of axes.
It is right write:</p>

<pre><code> x' = x + αy
 y'=y
</code></pre>

<p>with α>0  per y>0 ,  and α&lt;0  per y&lt;0 (then 2 transformations)?
And if it's right how can I calculate the parameter α?
Otherwise if it is all wrong as I do?     </p>

CC BY-SA 3.0
2016-09-30T11:17:14.117Z
Are you shearing the left and right halves of the [trapezoid](https://en.wikipedia.org/wiki/Isosceles_trapezoid) independently? Could you explain the underlying problem you are trying to solve?
trichoplax is on Codidact now
CC BY-SA 3.0
2016-09-30T12:11:01.070Z
@trichoplax    yes independently, but I am not convinced of the correctness of the exposed solution.      The underlyng problem is transform the view frustum , a truncated pyramid, in a parallepiped  (in 3-D) but isn't important for now.
Nick
CC BY-SA 3.0
2016-09-30T12:36:22.783Z
I'd recommend describing the background of what you're trying to do because it can affect which solution is most useful. For example, if your objective is to draw a parallelepiped, a simple answer may be "start with a cube instead of a truncated pyramid". If your objective is to convert a 3D texture then the use of a shear may be essential to the end result you require. In other cases there may be an easier approach. Without knowing the reasons behind it, it's hard to know what simplifying assumptions can be made.
trichoplax is on Codidact now
CC BY-SA 3.0
2016-09-30T13:30:39.337Z
thing And this is one transformation when you have perspective divide but not possible with one 3x3 matrix without one.
joojaa
<transformations><computational-geometry><geometry><mathematics><affine-transformations>
Transform a centered isosceles trapezoid in a rectangle in 2-D
Nick
# Transform a centered isosceles trapezoid in a rectangle in 2-D

(Asked by: username_0 on 2016-09-30)

I must convert a isosceles trapezoid to a rectangle in 2-D with a shearing transformation (or with 2 shearing transformations). The isosceles trapezoid is centered in the origin of axes.
It is right write:

```
 x' = x + αy
 y'=y

```

with α>0 per y>0 , and α<0 per y<0 (then 2 transformations)?
And if it's right how can I calculate the parameter α?
Otherwise if it is all wrong as I do?

**Tags:** transformations, computational-geometry, geometry, mathematics, affine-transformations

> **Comments:**
> **username_1**: Are you shearing the left and right halves of the [trapezoid](https://en.wikipedia.org/wiki/Isosceles_trapezoid) independently? Could you explain the underlying problem you are trying to solve?  
> **username_0**: @username_1    yes independently, but I am not convinced of the correctness of the exposed solution.      The underlyng problem is transform the view frustum , a truncated pyramid, in a parallepiped  (in 3-D) but isn't important for now.  
> **username_1**: I'd recommend describing the background of what you're trying to do because it can affect which solution is most useful. For example, if your objective is to draw a parallelepiped, a simple answer may be "start with a cube instead of a truncated pyramid". If your objective is to convert a 3D texture then the use of a shear may be essential to the end result you require. In other cases there may be an easier approach. Without knowing the reasons behind it, it's hard to know what simplifying assumptions can be made.  
> **username_2**: thing And this is one transformation when you have perspective divide but not possible with one 3x3 matrix without one.  

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## 0 answers

