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P 1
P 2
Q 1
Q 2
Q 4
Q 3
P 4
P 3
Figure 1.5. Example of the viewable region quadrilateral boundary points.
region with an applied offset that is either half or double the size of R λ . Without
performing a smooth transition between the two differently sized viewable regions,
there would be visible discontinuities or other visual anomalies when rendering.
We describe a method that offers a smooth transition between differently sized
viewable regions. By rendering a viewable region as a set of quadrilaterals, we are
able to morph the quadrilaterals in such as way to make the boundary between
the larger and smaller viewable regions indistinguishable. This method eliminates
seams, T-junctions, and visible boundaries between neighboring viewable regions
of different sizes. A similar method was described by Filip Strugar [Strugar 10],
although we have extended it to handle various boundary cases to ensure no
cracks form anywhere within the mesh.
Each viewable region is rendered by splitting the viewable region into four
quadrilaterals, denoted by Q 1 , Q 2 , Q 3 ,and Q 4 (see Figure 1.5). The boundary
points for each quadrilateral, comprised from the collection of static boundary
points ( P 1 ,P 2 ,P 3 ,P 4 ) and the morphing boundary points ( P L ,P T ,P R ,P B ,P C ),
are defined as follows:
Q 1 =
P 1 ,P T ,P C ,P L }
Q 2 =
P T ,P 2 ,P R ,P C }
Q 3 =
P C ,P R ,P 3 ,P B }
Q 4 =
P L ,P C ,P B ,P 4 }
Collectively, these nonoverlapping quadrilaterals will cover the same surface
area as the viewable region they are created from. The boundary points of each
quadrilateral are calculated to align with the boundary points of the neighbor-
ing viewable region quadrilaterals. The morphing quadrilateral boundary points
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