{"id":4459,"date":"2020-09-02T12:20:47","date_gmt":"2020-09-02T16:20:47","guid":{"rendered":"https:\/\/courses.ideate.cmu.edu\/60-212\/f2020\/?page_id=4459"},"modified":"2020-09-02T12:20:47","modified_gmt":"2020-09-02T16:20:47","slug":"circles-and-triangles","status":"publish","type":"page","link":"https:\/\/courses.ideate.cmu.edu\/60-212\/f2020\/daily-notes\/september\/09-02-loops\/circles-and-triangles\/","title":{"rendered":"Circles and Triangles"},"content":{"rendered":"

Circles and Triangles: A Consideration of Graphical Nuance<\/h3>\n

How many ways can you think of to convert a circle to a triangle?<\/em>
\nIn this\u00a0Circles to Triangles<\/a>\u00a0project, I demonstrate 14 methods that I could think of.<\/em>
\nThe point of this demonstration is to sensitize you to details of computational craft.<\/em><\/p>\n

\"\"<\/a><\/p>\n

 <\/p>\n

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

    If you find this interesting you might also enjoy:<\/em><\/p>\n