For the point cloud representation, how is the granularity of given points decided ? Because, it might be difficult to visualize or make new surfaces, if we end up sampling very less number of points.
pkukreja
In that case, it would lead to aliasing
keenan
@rasterize That's actually a tough question! It depends very much on how much you can say about your point sampling. If you have a really "nice" sampling, things get easier; if you have a totally random and unpredictable sampling, it's pretty hard. A "nice" sampling might mean something like: the biggest distance between any point and its closest neighbor is no more than some fixed constant $\alpha$, AND the smallest distance between any point and its closest neighbor is no less than some fixed constant $\beta$. This way you know that samples are evenly spread out, and can more easily downsample/upsample according to the current screen resolution (e.g., how big is the size of a projected pixel relative to $alpha$ and $beta$?).
You can make this sampling even nicer by asking for a so-called "blue noise" property, which says, roughly speaking, that if you do a Fourier transform of the points (for now pushing under the rug exactly what this means...) you have very close to a uniform distribution of power in the frequency domain. This is the kind of point sampling that is also nice for, say, stippling images.
For the point cloud representation, how is the granularity of given points decided ? Because, it might be difficult to visualize or make new surfaces, if we end up sampling very less number of points.
In that case, it would lead to aliasing
@rasterize That's actually a tough question! It depends very much on how much you can say about your point sampling. If you have a really "nice" sampling, things get easier; if you have a totally random and unpredictable sampling, it's pretty hard. A "nice" sampling might mean something like: the biggest distance between any point and its closest neighbor is no more than some fixed constant $\alpha$, AND the smallest distance between any point and its closest neighbor is no less than some fixed constant $\beta$. This way you know that samples are evenly spread out, and can more easily downsample/upsample according to the current screen resolution (e.g., how big is the size of a projected pixel relative to $alpha$ and $beta$?).
You can make this sampling even nicer by asking for a so-called "blue noise" property, which says, roughly speaking, that if you do a Fourier transform of the points (for now pushing under the rug exactly what this means...) you have very close to a uniform distribution of power in the frequency domain. This is the kind of point sampling that is also nice for, say, stippling images.