https://www.vistrails.org//api.php?action=feedcontributions&feedformat=atom&user=Jmeier 2026-06-03T15:39:06Z User contributions MediaWiki 1.36.2 https://www.vistrails.org//index.php?title=GeometryProcessing/Spring2009/Schedule/Spectral_Processing3&diff=1801 2009-02-05T17:00:41Z

<p>Jmeier: New page: *John Meier I feel like I'm getting a better grasp of the concepts spectral processing is based on and what can be accomplished using it. This is the high-level understanding I have so far...</p> <hr /> <div>*John Meier<br /> I feel like I'm getting a better grasp of the concepts spectral processing is based on and what can be accomplished using it. This is the high-level understanding I have so far (comments/corrections welcome):<br /> :Method<br /> ::Build a (roughly) symmetric matrix encoding a useful pairwise relationship between vertices in the mesh (e.g., Discrete approx. of the Laplacian or Laplace-Beltrami operators). Since the resulting matrix is similar to a symmetric matrix, it has real eigenvalues that we can compute. Since the eigenvectors form an n-dimensional orthogonal basis, we can project each mesh vertex into the resulting space and operate on the mesh &quot;signal&quot;.<br /> :Applications<br /> ::Smoothing - Taubin proposed a method for effectively low-pass filtering the mesh in the lower dimensions of the eigenspace that does not even require explicit computation of the eigen information.<br /> ::Segmentation - Liu et. al. propose a method for performing mesh segmentation by examining the projection of the mesh in lower-dimension subspaces of the eigen space of two Laplacian operators.<br /> <br /> I'm still a little unclear on what the distinction is between eigenvectors and eigenfunctions (interpolations of the respective eigenvectors?), and how the latter are used to produce the mesh colorings we saw at the end of lecture last week.</div>

Jmeier https://www.vistrails.org//index.php?title=GeometryProcessing/Spring2009/Schedule/Spectral_Processing1&diff=1779 2009-01-28T18:36:08Z

<p>Jmeier: </p> <hr /> <div>*John Meier<br /> It's definitely going to take some read-throughs to get my head around this topic. Would it be possible to have the lecture slides from 1/27 posted?<br /> <br /> * Brad Loos<br /> <br /> I got it, but it seems to be almost the exact same paper as the Eurographics 2000 Star Report. Is there supposed to be something we get out of the second paper that wasn't in the first?</div>

Jmeier https://www.vistrails.org//index.php?title=GeometryProcessing/Spring2009/Schedule/Spectral_Processing1&diff=1775 2009-01-27T16:59:59Z

<p>Jmeier: New page: *John Meier I can't seem to access the link for the second paper in the required reading (G. Taubin. A signal processing approach to fair surface design, 1995). Has anyone else run into th...</p> <hr /> <div>*John Meier<br /> I can't seem to access the link for the second paper in the required reading (G. Taubin. A signal processing approach to fair surface design, 1995). Has anyone else run into this?</div>

Jmeier https://www.vistrails.org//index.php?title=GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction2&diff=1774 2009-01-27T16:54:43Z

<p>Jmeier: New page: *John Meier I was impressed with the quality of the results of the advancing front algorithm we discussed in lecture on Thursday, but it seems like its inability to handle sharp features (...</p> <hr /> <div>*John Meier<br /> I was impressed with the quality of the results of the advancing front algorithm we discussed in lecture on Thursday, but it seems like its inability to handle sharp features (like the dual-contouring method) is a disadvantage. Is there any reasonable way to overcome this limitation? Would reconstructing piecewise parts of a target isosurface (each with the required continuity) and then combining them be feasible?</div>

Jmeier https://www.vistrails.org//index.php?title=GeometryProcessing/Spring2009/Schedule/Surface_Generation_Extraction1&diff=1762 2009-01-21T19:11:56Z

<p>Jmeier: New page: *John Meier I liked the structure of Tuesday's lecture: 1) the build-up to the topic of marching cubes from marching tets, and 2) examination of the aspects of marching cubes that have bee...</p> <hr /> <div>*John Meier<br /> I liked the structure of Tuesday's lecture: 1) the build-up to the topic of marching cubes from marching tets, and 2) examination of the aspects of marching cubes that have been &quot;solved&quot;, like how to prevent ambiguous surface extraction by automatically generating the intersection lookup table, and optimizing runtime with structures likes octrees or span spaces. The biggest mental hurdle for me among the lecture topics was the reason for building an octree of an implicit surface from the bottom up as a preprocessing step, which Carlos cleared up well (once the structure is built, it can be queried for any constant). The analogy to sorting an array before searching for elements was intuitive and appreciated. I have a remaining question due to my lack of experience: What steps would take place when using marching cubes to extract a surface from an implicit representation? (i.e., when would the ability to quickly query an octree for multiple values be useful?).</div>

Jmeier https://www.vistrails.org//index.php?title=GeometryProcessing/Spring2009/Schedule/Surface_Representations&diff=1755 2009-01-17T22:59:21Z

<p>Jmeier: John Meier, discussion of surface representations lecture</p> <hr /> <div>*John Meier<br /> I thought Thursday's lecture and the assigned reading provided a good definition of the meaning of &quot;surface representation&quot; in the context of the course. Since my studies to this point have dealt mostly with practicing rendering techniques, I haven't had much cause to think about the effectiveness of the representation of the geometric data (especially for purposes of modification/smoothing/compression/storage). So I feel like the surface representation material is helping me get my thinking oriented in the right direction for this course, or considering the actual structure and properties of the geometric data rather than just how to visualize it. I have run across many of the topics from the lecture in varying degrees of detail (parametric/implicit representations, splines, octrees/BSPs, compression as distance from predicted value, etc.) and it was good to get a brief review of their definitions, but I will definitely need to pull out some textbooks from earlier courses if we're going to be coding them from scratch ourselves (i.e., spline surfaces or mesh compression schemes). I'm interested in the half-edge mesh data structure and seeing how it can be used (I assume from the further reading that we might be using the OpenMesh library?), and while I have an intuitive grasp of the Edgebreaker compression algorithm, I'm still a bit unsure on the details of its operation.</div>

Jmeier