DRAFT:
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Escher Ball Tiler: Creating Spherical Three-Dimensional Tilings

M.C. Escher created a myriad of amazing planar tilings, yet only
designed a few three-dimensional tilings such as the wooden fish ball
and dodecahedral flower.  It is mentally challenging to design
three-dimensional tiles and equally difficult to transform the design
into a physical model.  We have developed a program that allows the
user to easily create and manufacture an "Escher ball" - a set of
tiles with bas-relief that can be assembled into a ball.


In particular, the user chooses from a set of predefined symmetry
groups and then manipulates a simple tile. As points are moved the
system maintains the three-dimensional symmetry by moving
corresponding points on the outline of the tile.  Once a design is
completed the system automatically creates a solid model by extruding
the tile toward the center of the sphere.

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FINAL:
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Escher Tilings of the Sphere

M.C. Escher created a myriad of amazing planar tilings yet only a few
three-dimensional tilings such as his wooden fish ball and his
dodecahedral flower.  We have developed a program to design and
manufacture an "Escher ball" - a set of tiles with bas-relief that can
be assembled into a spherical ball.  The user chooses from a set of
predefined symmetry groups and then deforms the boundaries of the
basic domain tile; all corresponding points based on the chosen
symmetry class move concurrently. The interior of the tile can be
embellished with a bas relief.  Finally the tile is radially extruded
and output as a solid model suitable for solid free-form fabrication.
