A sort of artwork
Drag'n'drop the image of your choice on the canvas to generate a hilbert or gosper curve version.
Optionnaly create a virtual environment, then install the jsonToSVG.py dependencies with pip install -r requirements.txt.
Choose a curve type, drag-and-drop an image, choose some thresholds, and it will generate a curve. You can then export it with "exportJSON" and then use jsonToSVG.py to create an SVG drawing.
Only Gosper curve can be colored. There is one threshold per iteration / level. The global threshold sets all other thresholds to the same value, it's just a shortcut.
The lightness parameter enable to reduce the amount of black when in color mode. It does not have any effect in black and white mode.
You can choose the scale and position of the image, and hide / show the image which will be drawn.
Use python jsonToSVG.py -i path/to/drawing.json to create the corresponding drawing.svg. You can add a small margin around the drawing with the --margin option (in percentage of the max side of the drawing bounding box).
A Space Filling Curve (Hilbert curve or a Gosper curve) is computed from a grayscale image, refined where the image is darker than thredhold.
The image is recusively divided in tiles.
- Generate image mipmaps: pre-calculated, optimized sequences of images, each of which is a progressively lower resolution representation of the same image
- Subdivide the image with the lowest resolution in tiles and for each tile:
- if the tile is darker than threshold:
- resubdivide in tiles and continue recursively until the tile is light enough
- otherwise draw the corresponding curve at proper scale
- if the tile is darker than threshold:
The implementation is much more specific than the Gosper curve one, thus less elegant and more complicated.
For the Hilbert curve, the "tiles" correspond to four quadrant, which means the image is recusively divided in four quadrants, numbered from 0 to 3.
The goal is to compute the traversing order of the quadrants (for example [0, 1, 2, 3], [3, 0, 1, 2], etc.).
The tricky part is to rotate the curve in the proper way when it must be refined.
The first and last quadrant must be rotated in opposite direction, the traversing order of the quadrants must be inverted, and depending on the previous refinements the rotations must happen in one way or another.
The final algorithm keeps track of the rotation which sums up at each iteration, and whether or not rotation inversion must happen.
At each iteration, the rotation and inversion is computed in the following way:
- for quadrant 0:
- rotation += inversion ? -1 : 1
- inversion = !inversion
- inverse the traversing order of the quadrants
- for quadrant 1:
- rotation += inversion ? 1 : -1
- inversion = !inversion
- inverse the traversing order of the quadrants
- for quadrant 2 and 3:
- do not change anything