Descriptions and Examples for the POV-Ray Raytracer by Friedrich A. Lohmüller
Geometric Transformations with POV-Ray -
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    - "matrix<  ... >"
    - Shearing
    - transforms.inc

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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