Continuing my geometry minimalism series. This time, packing squares in triangles. Black fountain pen on 300g/m paper.

Continuing my geometry minimalism series. This time, packing squares in triangles. Black fountain pen on 300g/m paper.

packing squares in triangles

Continuation of <a href="/plots/180">plot#180</a>.
Third iteration on packing iso triangles in a square. two fountain pens on 300g/m paper.

Third iteration on packing iso triangles in a square. two fountain pens on 300g/m paper.

triangle packing

Continuation of <a href="/plots/179">plot#179</a>.
Second iteration on packing rotated squares in a square. Black fountain pens on a 300g/m paper. It&#39;s interesting how the paper makes the ink having different shade of greys.
This time, the rotations are less random and aligned on 10 possible angles. (but these are squares so not it repeats)
There is also two concentric squares drawn each time.
<h2 id="technical-notes">Technical notes</h2>
This is also a continuation of the code of <a href="/plots/179">plot#179</a>.
I did an improvement of the search algorithm using a dichotomic search:
search
<pre><code class="language-rust">fn poly_square_scaling_search(
 boundaries: (f64, f64, f64, f64),
 polys: &amp;Vec&lt;Polygon&lt;f64&gt;&gt;,
 x: f64,
 y: f64,
 angle: f64,
 min_scale: f64,
 max_scale: f64,
) -&gt; Option&lt;f64&gt; {
 let overlaps = |size| {
 let poly = rotated_square_as_polygon(x, y, size, angle);
 let bounds = poly.bounding_rect().unwrap();
 let topleft: Point&lt;f64&gt; = bounds.min().into();
 let bottomright: Point&lt;f64&gt; = topleft + point!(
 x: bounds.width(),
 y: bounds.height()
 );
 out_of_boundaries(topleft.x_y(), boundaries)
 || out_of_boundaries(bottomright.x_y(), boundaries)
 || poly_collides_in_polys(polys, &amp;poly)
 };

 let mut from = min_scale;
 let mut to = max_scale;
 loop {
 if overlaps(from) {
 return None;
 }
 if to - from &lt; 0.1 {
 return Some(from);
 }
 let middle = (to + from) / 2.0;
 if overlaps(middle) {
 to = middle;
 }
 else {
 from = middle;
 }
 }
}
</code></pre>

Second iteration on packing rotated squares in a square. Black fountain pens on 300g/m paper.