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Texture is described using an orientation distribution function (ODF), describing the distribution of crystal orientations over a three-dimensional orientation space.
In thicker media, the fibers can have a three-dimensional orientation with a characteristic uni-axial angle measured relative to the Z-axis, where the Z-axis is perpendicular to the X Y plane.
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When geologists and seismologists try to examine the orientation of faults in map view to either assess the relationship between a given earthquake and nearby fault, or to investigate the nature of the aftershocks are generated, they use a diagram to illustrate the three-dimensional orientation of a fault in the two-dimensions of a map.
I've written a set of fast routines for exact floating-point addition and multiplication, which I've used to create fast correct geometric predicates, namely the two- and three-dimensional orientation and incircle tests.
We show that the secondary structures of junctions encode readily computable topological constraints that accurately predict the three-dimensional orientation of helices across all two-way junctions.
We first obtain two-dimensional cathodoluminescence maps of a three-dimensional nanostructure at various orientations.
Add in a three-dimensional object with three different axes of orientation, which the robot has to push across a table, and the size of the search space swells to 16 dimensions, which is too large to search efficiently.
Since by this point we have a three-dimensional model of the surface, we know its location and orientation relative to our spotlight, so we can easily remove this dependence.
Can you draw a three-dimensional cube?
It's tough to represent a three-dimensional world in a two-dimensional map.
It's trying to put out a three-dimensional thing over a two-dimensional transmitter.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com