Automatic Construction of Polyhedral Surfaces From Voxel Representations
Automatic Construction of Polyhedral Surfaces From Voxel Representations
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In our eReader you can find the full English version of the book. Read Automatic Construction of Polyhedral Surfaces From Voxel Representations Online - link to read the book on full screen. Our eReader also allows you to upload and read Pdf, Txt, ePub and fb2 books. In the Mini eReder on the page below you can quickly view all pages of the book - Read Book Automatic Construction of Polyhedral Surfaces From Voxel Representations
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We call this a "birth" event. At this level the section consists of a single point, which immediately opens into a loop as we ascend. A series of loops is produced until a second critical pxjint of the doughnut is reached. At this point, the loop becomes a "figure eight", and splits into two disjoint loops. We call this event "splitting. " Then, at the third critical point, the loops fuse back into a "figure eight". We call this a "merge" event. The figure eight immediately becomes a simple loo...p. Finally, the single loops shrink down to a point and disappear at the fourth and final criti- cal point (a "death" event).
For the embedding of the torus implied by this sectioning, there are four isolated critical points. It can be proven that any differentiable 2-manifold can be embedded in Euclidan 3-space in such a way that its critical points are finite in number, and no more than one occurs on a given level. Also, it can be shown that the only topological changes which can occur are the "birth", "death", "splitting" and "merging" events illus- trated for the torus ^ Each topological change is accompanied by an Euler transition, that is, a change in the Euler number of a contour.
What to read after Automatic Construction of Polyhedral Surfaces From Voxel Representations?
You can find similar books in the "Read Also" column, or choose other free books by Alan Shaw to read onlineMoreLess
To quickly assess the difficulty of the text, read a short excerpt:
We call this a "birth" event. At this level the section consists of a single point, which immediately opens into a loop as we ascend. A series of loops is produced until a second critical pxjint of the doughnut is reached. At this point, the loop becomes a "figure eight", and splits into two disjoint loops. We call this event "splitting. " Then, at the third critical point, the loops fuse back into a "figure eight". We call this a "merge" event. The figure eight immediately becomes a simple loo...p. Finally, the single loops shrink down to a point and disappear at the fourth and final criti- cal point (a "death" event).
For the embedding of the torus implied by this sectioning, there are four isolated critical points. It can be proven that any differentiable 2-manifold can be embedded in Euclidan 3-space in such a way that its critical points are finite in number, and no more than one occurs on a given level. Also, it can be shown that the only topological changes which can occur are the "birth", "death", "splitting" and "merging" events illus- trated for the torus ^ Each topological change is accompanied by an Euler transition, that is, a change in the Euler number of a contour.
What to read after Automatic Construction of Polyhedral Surfaces From Voxel Representations?
You can find similar books in the "Read Also" column, or choose other free books by Alan Shaw to read onlineMoreLess
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