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What should be the tessellation of an arbitrary polygon?
The polygon may be convex (but bonus points if you come up with an algorithm that works for concave shapes) The amount of tessellation (preferably the number of vertices added by the algorithm) should be parametrized Triangles should be nearly uniform in size and shape (i.e. corners will tend towards 60 degrees)
Which is the best definition of a polygon triangulation?
Polygon Triangulation. † A polygonal curve is a finite chain of line segments. † Line segments called edges, their endpoints called vertices. † A simple polygon is a closed polygonal curve without self-intersection. Simple Polygon Non-Simple Polygons. † By Jordan Theorem, a polygon divides the plane into interior, exterior, and boundary.
What’s the best way to tessellate a convex polygon?
This can be done for concave/convex polygons using a simple ear-clipping method (assuming we don’t need to support holes). Rotate edges between triangles where the area divided by the perimeter is smaller once the edge is rotated into the new state.
What do you call a well centered triangulation?
A well-centered triangulation is one in which all the circumcenters of triangles lie inside the respective triangle. Since you want something slightly different, you could simply try to change the error metric involved. You could find a measure of “non-congruence” among the triangles and minimize that error.
Can You tessellate a pentagon with three hexagons?
there is a regular tessellation using three hexagons around each vertex. We have already seen that the regular pentagon does not tessellate. A regular polygon with more than six sides has a corner angle larger than 120° (which is 360°/3) and smaller than 180° (which is 360°/2) so it cannot evenly divide 360°.
Which is the sum of angles of a polygon tessellation?
The resulting parallelogram tessellates: The picture works because all three corners (A, B, and C) of the triangle come together to make a 180° angle – a straight line. This property of triangles will be the foundation of our study of polygon tessellations, so we state it here: The sum of angles of any triangle is 180°.