Nascent Papers: Difference between revisions
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== Çağatay == | == Çağatay == | ||
====Coloring 3d line fields using Boy’s real projective plane immersion==== | |||
''Abstract'': | ''Abstract'': | ||
It’s often useful to visualize a line field, a function that sends each | It’s often useful to visualize a line field, a function that sends each | ||
point P of the plane or of space to a line through P; such fields | point P of the plane or of space to a line through P; such fields | ||
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of the projective plane in 3D, as a model for coloring line fields, | of the projective plane in 3D, as a model for coloring line fields, | ||
and show results from its application in visualizing orientation in | and show results from its application in visualizing orientation in | ||
diffusion tensor fields. This coloring method is smooth and | diffusion tensor fields. This coloring method is smooth and one to | ||
one except on a set of measure zero (the double curve of Boy’s | one except on a set of measure zero (the double curve of Boy’s | ||
surface). | surface). | ||
---- | ---- | ||
Revision as of 02:11, 27 January 2009
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Çağatay
Coloring 3d line fields using Boy’s real projective plane immersion
Abstract:
It’s often useful to visualize a line field, a function that sends each point P of the plane or of space to a line through P; such fields arise in the study of tensor fields, where the principal eigendirection at each point determines a line (but not a vector, since if v is an eigenvector, so is −v). To visualize such a field, we often assign a color to each line; thus we consider the coloring of line fields as a mapping from the real projective plane (RP2) to color space. Ideally, such a coloring scheme should be smooth and one-to-one, so that the color uniquely identifies the line; unfortunately, there is not such mapping. We introduce Boy’s surface, an immersion of the projective plane in 3D, as a model for coloring line fields, and show results from its application in visualizing orientation in diffusion tensor fields. This coloring method is smooth and one to one except on a set of measure zero (the double curve of Boy’s surface).