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| The
Main Idea |
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Details
are important. One of the challenges a designer faces when creating
rich, expressive, and interesting models is the specification
of large amounts of appropriate surface detail. Automatic methods
for generating detail are known as shape amplification techniques.
We believe such techniques will become increasingly important
as the field of complex modeling grows. This paper shows how
some simple concepts of geometric and topological transformations
may be used to automatically build detail that resonates with
an underlying surface, in order to create complex models from
simpler structures. |
| Results |
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The simplest substitutions are two-dimensional.
The left two images each started with the same equilateral triangle.
To create the far-left image I replaced the triangle with a
series of four rules, each of which extracted the current triangles
and replaced each one with a new set. This resulting pattern
won a prize at the Siggraph '92 t-shirt competition. In the
middle design I applied a rule which changed a logical marker
on the triangles as well as their geometry. Then following rules
changed only some of the triangles, affecting their shapes and
colors. The third example is the result of applying two rules
to a more interesting starting shape. |
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We can take designs in 2D, and with
appropriate boundary conditions, move them into 3D. These three
examples are all derived from a single fourth-generation icosahedron.
I applied just two rules to the icosahedron in each case. |
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This final example shows how one
can transform not just polygons, but entire polyhedra. This
is an example of a Rubik's Snake, a plastic toy that
was popular a few years ago. The toy consists of 24 right-triangular
prisms that are linked up so that the two square faces of each
prism each touch the square face of the next prism. Each piece
is free to rotate about this link. I modeled the snake as a
set of prisms, and then twisted it into one of my favorite shapes,
which I call the "tri-loop". Then I replaced each
triangular polyhedron with a set of four half- and quarter-toruses.
I produced this model by alternating the phase of the toruses
between two different orientations. This transformed a blocky
set of rectangles and triangles into a flowing and curved structure. |
| Details |
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The technique of Geometric Substitutions
is a geometric modeling method. The basic idea is to start with
a simple shape, and then layer more complex geometry onto and
into it. The trick is to design a method whereby the new geometry
is harmonious with the underlying shape, interesting to view,
and controllable and predictable by the designer.
To carry out this method, you need only design a starting
shape and a set of transformation rules that take a piece
of geometry and replace it with a new piece. The geometry
need not be orientation-sensitive, though that's a possibility
if you want it. The technique is closely related to Alvy Ray
Smith's ideas of graphtals, which are an evolution
of shape grammars.
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| More
Info |
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You can see many more examples and
read more discussion of these techniques in my paper, "A
Tutorial on Geometric Replacements". Here's the complete
citation:
Glassner, Andrew S., "A Tutorial on Geometric Replacements",
IEEE Computer Graphics & Applications, volume 12, Number
1, January 1992, pp. 22-36.
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