POV-Ray : Newsgroups : povray.advanced-users : Skewness (long) : Skewness (long) Server Time23 Jun 2024 06:39:27 EDT (-0400)
 Skewness (long)
 From: Francois LE COAT Date: 4 Oct 2018 16:30:10 Message: <5bb67852@news.povray.org>
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Hi,

When the raytracing POV-Ray program projects a 3D movement in a 2D
image sequence, it uses what is called "projective transformation" that
produces the images. This projective transform is well known in the
literature, and is called "homography". It takes the aspect of :

(up*w)   (m00, m01, m02) (u)
(vp*w) = (m10, m11, m12) (v)
( w  )   (m20, m21, m22) (1)

where (u,v) is the coordinates in the first image, and (up,vp) its
movement's transform correspondent in the second image, in homogeneous
notations. This projective transformation takes 9 parameters (mij),
but you can consider that it takes only 8 parameters, if those are
normalized (one of the parameters (mij) is forced to 1.0 value).

If you consider those 8 unique parameters, because it allows to
project a 3D movement, in 2D images, are linked to the 6 degrees
of freedom in 3D space, via the 3 Euler angles in rotations, and
3 translations. Those (mij) parameters are linked to :

(Tx, Ty, Tz) the 3 translations in pixels of images, and
(Rx, Ry, Rz) the (yaw, pitch, roll) Euler angles in degrees.

When someone like me, uses POV-Ray scripting capabilities, I have
the following directives in the language that represent the movement :

translate <Tx, Ty, Tz> and
rotate <Rx, Ry, Rz>

in the 3D space. But these directives only takes account of 6 parameters
of the projective transform, and I miss 2 more parameters in "skewness".

<http://stackoverflow.com/questions/13206220/3d-skew-transformation-matri
x-along-one-coordinate-axis>

This is well represented in the above document. When I consider a
movement in 3D space, projected in a 2D sequence of images, I must
consider two other parameters (Sx,Sy) in (x,y) coordinates of image,
that are linked to (x,y) skewness. My question is, how are those skew
angles present in the POV-Ray scripting language ? There should be a

skew <Sx, Sy>

directive that would render the skewness type of movement of the camera.
I can't figure out myself, how these 2 skew movements are represented
in the POV-Ray scripting language directives. It must be linked to
the way how the perspective is generated in the camera properties.

Can somebody tell me how to generate those parameter movements with
POV-Ray language ? I'm confused, and probably not very clear, but maybe