Monday, February 13, 2023

Using the area works well for a circle, but, what about a donut? The hole in the middle reduces the total area. This also happens with stars and other shapes. Holes and concave segments should probably be ignored. A method to do this exists, and it’s typically called a convex hull. It’s like stretching a rubber band around the entire object. That’s probably a pretty good formula to work out visual weight that matches human perception. Here’s some more shapes, using the convex hull area to set the scale.

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For triangles, the center of the bounding box often does not feel like the center of the triangle, and aligning by this method looks incorrect.

Triangles have many different types of centers, including centroid, incenter, circumcenter, and orthocenter. For equilateral triangles, those all coincide, so it doesn’t matter which is used. Aligning the triangle centroid to the center of the circle now looks right — the distance from the triangle points to the edge of the circle are consistent and it appears perfectly centered.