Didn't we previously learn that we can get smoother surfaces by taking lower frequencies values of the model. Is this the same process ??

jzhanson

It was my understanding that in subsampling we begin with a coarse model of relatively few faces/vertices and subdivide each face/edge/vertex and then average or interpolate their values to form a smooth surface, while here we are taking a fine model of many elements, dividing it arbitrarily, and then averaging parts of it, resulting in a coarser model. In subsampling we are adding elements, whereas here we are combining elements.

keenan

@BellaJ The method you mention, compression using Fourier modes, is different from the one here. Fourier-based compression is rarely used in geometry processing for a variety of reasons (e.g., expensive to compute Fourier modes, singularities in reconstructed surface, compressed data doesn't work directly within the rest of the geometry processing pipeline) but is still an important concept used in many algorithms beyond just compression. The method illustrated here (one of many) produces an explicit polygon mesh that is simpler than the given one.

keenan

@jzhanson Yes, though do be careful about the terminology:

subdivision is the process you describe: splitting up a mesh to obtain a higher-resolution mesh

subsampling broadly refers to the opposite process: approximating the original signal by a smaller set of samples

merc

How exactly do they divide the fine model into generic planes?

Didn't we previously learn that we can get smoother surfaces by taking lower frequencies values of the model. Is this the same process ??

It was my understanding that in subsampling we begin with a coarse model of relatively few faces/vertices and subdivide each face/edge/vertex and then average or interpolate their values to form a smooth surface, while here we are taking a fine model of many elements, dividing it arbitrarily, and then averaging parts of it, resulting in a coarser model. In subsampling we are adding elements, whereas here we are combining elements.

@BellaJ The method you mention, compression using Fourier modes, is different from the one here. Fourier-based

compressionis rarely used in geometry processing for a variety of reasons (e.g., expensive to compute Fourier modes, singularities in reconstructed surface, compressed data doesn't work directly within the rest of the geometry processing pipeline) but is still an important concept used in many algorithms beyond just compression. The method illustrated here (one of many) produces an explicit polygon mesh that is simpler than the given one.@jzhanson Yes, though do be careful about the terminology:

subdivisionis the process you describe: splitting up a mesh to obtain a higher-resolution meshsubsamplingbroadly refers to the opposite process: approximating the original signal by asmallerset of samplesHow exactly do they divide the fine model into generic planes?

@merc You can read all about it in the original paper.