IND 0735 dimetric anamorphosis
This is a setting to represent a ten-fold symmetric figure as a dimetric view of a 3D mesh.
Required camera pitch angle is α = asin(tan(π/10)) ≈ 18.961° for this dimetric view instead of ≈ 35.264° for standard isometric view, so the additional rectangle on top labeled "Camera plane" has been rotated by the appropriate angles (yaw 45° + pitch α) and helps you rotate the view as required by clicking on it (or in classic mode using the "View in front of" command).
In this setting the shapes that will be duplicated must be on the YZ plane (a slightly different setting could work with the XZ plane instead)
- The basic shape q1 is here it is a square with a cut at a corner so that it will form a decagonal hole in the final mesh. The proportion between the decagon radius and the square side is a factor s3 that I have set by defaut to 1/3 to match approximately the pattern I was trying to reproduce https://tilingsearch.mit.edu/HTML/data206/SM28.html but it can be increased to a particular value (that turns out to be equal to another factor s2 already used elsewhere) so that it matches this other variant of the pattern https://tilingsearch.mit.edu/HTML/data206/SM6.html where the central ring of pentagons is made of regular pentagons.
- This original shape q1 is first duplicated four times with different orthogonal rotations to get the other yellow items q2 to q5
- Then those five intermediates yellow shapes are reused to create the five final blue shapes q6 to q10 with different additional scales and rotations:
- the two lower shapes q6 q7 are simply scaled along Z axis by factor s1 using a matrix m0
- the two upper shape q8 q9 are scaled along respectively X and Y axes by factor s2 and sheared using vertically the factor s1. For the two shapes the transformations are done once using respectively matrices m1 and m2, each matrix being a combination of a non-uniform scale matrice and a shear matrice
- the central uppermost shape q10 is transformed using both the m1 and m2 matrices that where previously applied to the adjacent shapes.
- Then the shapes q6 to q10 are duplicated with point symmetry to create the shapes q6' to q10'