#DRAW A TESSELLATION CODE#
#DRAW A TESSELLATION MAC#

The finest examples of tessellation patterns in architecture and art can be found in Islam. Not only was the geometry of tessellation patterns fascinating to the tessellating artists, but intellectuals too began to show a deep interest in the mathematical structure of these tessellating patterns found from the Middle Ages and through the 19th century.

Many of these designs have regional characteristics, which make them unique to the people and culture they originated from. Modern archeologists have uncovered many beautiful examples of tessellation art created by the Sumerian civilization, where it then spread to many other ancient civilizations such as the Romans, Chinese, Greek, Egyptians, Arabs, Moors, and Persians. The use of tessellation patterns in temples and homes can be traced back to sometime in 4,000 BC in Sumeria. Tessellation pattern of a street pavement in Zakopane, Poland Dmharvey, Public domain, via Wikimedia Commons This hints at the historical use of tessellation ideas that stretch far back into our history when small tiles made of glass, stone, or clay were used to create patterns on public and domestic surfaces. The word derives from the Latin word tessellātus (square small stones) and the Greek word tessera (four). The use of tessellation ideas and concepts throughout our history has resulted in the creation of beautifully decorated architecture, such as temples and mosques, as well as magnificent works of art.Īn understanding of ancient languages in history can help one better understand the tessellation definition. Also known as tiling, this process results in a mosaic pattern that can be used in a highly creative manner, despite its largely confining mathematical structure. What is Tessellation? Tessellation art is created through the process of covering a surface with a number of geometric shapes that fit together almost like a jig-saw puzzle, never overlapping and leaving no spaces between them.

3.2 Are People Still Creating Tessellation Art Today?.

Escher’s Work Considered to Be Tessellation Art?

1.1 A Brief History of Tessellation Patterns.

#DRAW A TESSELLATION CODE#

Please refer to the source code monotone.c if you want to know more verbose monotone algorithm implementation.Īnd the tessellator interfaces usage from gbox/gl/render.

#DRAW A TESSELLATION MAC#

The drawing result with opengl(60 fps on my mac pro): Get the monotone regions with the left face marked “inside”.Process some degenerate cases for the mesh faces which were generated when we fixed some cases.We need fix it if the intersection with numerical errors violate the mesh topology or active edge list ordering.Sweep all events from the event queue using the Bentley-Ottman line-sweep algorithm and calculate the intersection and winding number.

Build an active edge region list and sort it (uses the partial insertion sort).Build a vertex event queue and sort it (uses the priority queue with min-heap).Simplify the mesh and process some degenerate cases.There are seven stages to the tessellation algorithm: Merge the triangulated regions into the convex regions.Tessellate the mesh into the monotone regions if the polygon is concave.Build a mesh (DCEL, be similar to quad-edge) from polygon.(you can see libtess2/alg_outline.md if want to known more details of algorithm.) We have not counted the vertices for each region, so it will be faster than libtess2.We optimizate the algorithm of merging into the convex polygon from the triangulated mesh.We change the algorithm of comparing the active edge and make it more stable for numerical errors.We processed more cases of the intersection with some numerical errors,.We need not project the vertices because our graphic engine is 2d,.

We change the coordinate system and the sweep direction (sweep line by horizontal here).

The differents between our algorithm and libtess2’s algorithm: The algorithm is based on libtess2 here and we optimizated some implementation and fixed some bugs. Gbox c tessellate polygon algorithm drawing monotone triangulation

Draw a tessellation