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Monthly Archives: November 2013
tired of rhombs ?
Just only rhombs may become tiring. You want to have a quasiperiodic tiling of ten-fold rotational symmetry with other tiles ? Well, we can easily find a different decoration of a tiling such as the one shown in “Dualization method … Continue reading
Posted in Quasiperiodic design, Tilings
Tagged Geometry, ornament, Penrose tiling, programming, quasiperiodic Tiling, rose window
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smooth images with the pdf-renderer
The images of the tilings look good on the computer screen but not so if printed out. We do not want to see pixels on paper. We could remedy this using roughly 16 times as much pixels, because the computer … Continue reading
Posted in Extra, programming, Quasiperiodic design, Tilings
Tagged Geometry, pdf, processing, programming, smoothing images
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tiling with rhombs of 12-fold rotational symmetry
If we use n=3 in “Dualization method for ten-fold rotational symmetry – the code” we get the well-known periodic tiling with rhombs of 60 degree acute angle and hexagonal symmetry. It is useful for isometric projections, see the geometricon.wordpress.com blog … Continue reading
Breaking the rotational symmetry in the dualization method
We now proceed as we did earlier for the projection method in “breaking the ten-fold rotational symmetry“. The sets of parallel lines are moved alternatingly back and forth from the origin. Thus s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)+plusMinus for even i and s_i=0.5+xTrans*cos(i*PI/n)+yTrans*sin(i*PI/n)-plusMinus for odd … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged quasiperiodic Tiling, Rotational symmetry
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Dualization method for ten-fold rotational symmetry – the code
// this is for the main tab // generates 2n-fold rotational symmetry // can be broken to get n-fold rotational symmetry float unitLength; float xRange,yRange; // visible coordinates from -(xy)Range to +(xy)Range float sqrt2=sqrt(2.),sqrt05=sqrt(0.5),rt3=sqrt(3.); float small,lineLenghtSquare; Grid grid,gridTwo; void setup(){ … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged Ammann–Beenker tiling, Penrose tiling, processing, programming
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Dualization method for ten-fold rotational symmetry
We now use the dualization method with grids made of several sets of parallel lines. It is important to take the same grids as earlier for the projection method, see “projection method for ten-fold rotational symmetry” and “Projection method for … Continue reading
Problem in “combination of grids – the code”
I tried to follow Eric (see his comments on “dualization method for the Stampfli tiling“). But the program crashed sometimes because it generated grid lines with endpoints that are both the same and length equal to zero. There seems to … Continue reading
dualization method for the Stampfli tiling – the code
// ********* use processing 2 **************** you can download from processing.org //———————————————————————————— // this is the main code to generate the Stampfli tiling // it shows you how to use the dualization method, // you can generate other tilings with … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged Geometry, processing, programming, quasiperiodic Tiling, Stampfli tiling
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Dualization method for the Stampfli tiling
I am now showing step by step how to get the Stampfli tiling with the dualization method. In the next post you will find the code, which you could change to make other quasiperiodic tilings. First, we combine two hexagon … Continue reading
Posted in programming, Quasiperiodic design, Tilings
Tagged Geometry, programming, quasiperiodic Tiling, Stampfli tiling
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combination of grids – the code
//lines between a1 and b1, a2 and b2 // intersection: interpolation parameter t=0…1 on line 1 // t<0 or t>1 means there is no intersection. float intersectionAt(Vector a1,Vector b1,Vector a2,Vector b2){ if ((max(a1.x,b1.x)<min(a2.x,b2.x))||min(a1.x,b1.x)>max(a2.x,b2.x)) return -1; // check intersection of … Continue reading
Geometry in color 