Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
Geometric Transformations with POV-Ray -
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    Elementary
    Transformations
    - "translate<  ... >"
    - "rotate<  ... >"
    - "scale<  ... >"
    - mirror symmetry

    Other
    Transformations
    - "matrix<  ... >"
    - Shearing
    - transforms.inc

    - "transform{ ...}"
       and "inverse"

    Vectors and
    Transformations

    Insert Menu Add-on
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Shearing with matrix

shearing

Simple transformations like moving (translate), streching (scale) or truning (rotate) normally should not be descriped by matrices, because this way is more difficult to imagine. Shearing is another simple transformation we can only descripe by matrix in POV-Ray.

Sample: Shearing of y axis in direction x with factor 0.5 (30°):


  matrix< 1 , 0, 0,
         0.5, 1, 0,
          0 , 0, 1,
          0 , 0, 0 >



Shearing matrices and the Visualisation of the according effect:

matrix < 1,0.5,  0,
         0,  1,  0,
         0,  0,  1,
         0,  0,  0 > 
 
matrix < 1,  0,0.5,
         0,  1,  0,
         0,  0,  1,
         0,  0,  0 > 
matrix < 1,  0,  0,
       0.5,  1,  0,
         0,  0,  1,
         0,  0,  0 > 
 
matrix < 1,  0,  0,
         0,  1,0.5,
         0,  0,  1,
         0,  0,  0 > 
matrix < 1,  0,  0,
         0,  1,  0,
       0.5,  0,  1,
         0,  0,  0 > 
 
matrix < 1,  0,  0,
         0,  1,  0,
         0,0.5,  1,
         0,  0,  0 > 
The transformations shown here are also available as text templates in the section "Shearing & transform" in my "Insert Menu Add-on"

translate | rotate | scale | matrix | shearing | transforms.inc | transform | vector transformations
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© Friedrich A. Lohmüller, 2006
www.f-lohmueller.de