# Circles and Triangles

### Circles and Triangles: A Consideration of Graphical Nuance

How many ways can you think of to convert a circle to a triangle?
In this Circles to Triangles project, I demonstrate 14 methods that I could think of.
The point of this demonstration is to sensitize you to details of computational craft.

1. (code) by sampling a circle into many vertices, and then locally averaging each point with its neighbors, except for the three special corner vertices
2. (code) by progressively deleting all points except for the triangle’s corners
3. (code) by approximating a circle with three Bezier cubic splines and modulating the spline control points
4. (code) by approximating a circle with three circular arcs whose radii lengthen to infinity
5. (code) by linearly interpolating points on the circle towards points on the triangle, along radii of the circle
6. (code) by progressively moving points evenly sampled along the circle, towards points on the triangle, resampled at equal intervals, by small random amounts
7. (code) by treating it as a rounded triangle, whose (rounded) corners have a dynamic radius
8. (code) by treating it as a multisided polygon whose number of sides gradually decreases to three
9. (code) by gradually flattening the circle on three sides
10. (code) by gradually shrinking the circle’s radius, revealing triangular corners within
11. (code) by treating points along the perimeter as a series of springy particles
12. (code) by considering it as a set of alternating straight lines and arcs in which the arcs shrink while the lines grow
13. (code) by treating the form as a series of 6 circular arcs, alternatingly with small and large radii
14. (code) by progressively subdividing it into a 3-gon, 6-gon, 12-gon, 24-gon, etc., with smooth interpolations.

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