I guess you are referring to this... http://graphics.pixar.com/library/HarmonicCoordinates/paper.pdf
The scan conversion bit with the laplacian solver seems like a lot of work. There is the idea of mean value coordinate systems which may allow for a smooth interpolant across the arbitrary convex polygons without the laplacian solve (I am suggesting you can combine this with some of the principles of the above paper): http://morphoxx.googlecode.com/svn/trunk/Biblio/Mean%20Value%20Coordinates%20for%20Arbitrary%20Planar%20Polygons.pdf Not sure if there is quality issues with it that I don't know about. You probably don't want to be doing novel research on a tight deadline. On Thu, Dec 12, 2013 at 8:55 AM, Alok Gandhi <[email protected]>wrote: > Thanks Ben. That is some good info. I was thinking more along > implementing the Harmonic Coordinates approach. I think Pixar had some > papers on it. > > Sent from my iPhone > > On Dec 11, 2013, at 10:50 PM, Ben Houston <[email protected]> wrote: > > My knowledge is out of date, but off the top of my head.... > > Cage deformers are often written using a cubic interpolant rather than > affine ones. If you use a grid cage you can use Bezier Volumes, which are > just a generalization of https://en.wikipedia.org/wiki/B%C3%A9zier_surface. > If you are using a regular grid, you can just take 3D coordinates relative > to each grid. If you use a tetrahedral mesh, you can use generalization of > the Cubic Triangle for deformation: > https://en.wikipedia.org/wiki/B%C3%A9zier_triangle and then you need to > use barycentric coordinates to get a relative spatial relationship. > > So I think yes, barycentric coordinates within a space filling > discretization of space, either a grid or a tetrahedralization with a cubic > interpolate as you start to deform them. > > I implemented the grid-based deformation with cubic volumes and got this > result: > > http://www.exocortex.org/ben_software/hd-ffd.zip > > I have also implemented the tetrahedral-based discretization with > Christopher Batty to deform a high resolution object to follow the path of > a low resolution object to really good success. The only issue is that > tetrahedral meshes suck to create and maintain efficiently. It is the > bunny getting crushed in the gears at the end of this video -- the actual > simulation bunny was super low res, but we uprezed it for rendering: > http://vimeo.com/874168 > > Best regards, > -ben > > > > On Wed, Dec 11, 2013 at 5:09 PM, Alok Gandhi <[email protected]>wrote: > >> Hi All, >> >> Very soon, I am starting on my own generic custom cage deformer. A mix of >> C++/Cython/Python. >> >> I am thinking of implementing fast calculations on barycentric >> coordinates with affine transformations. I have some good papers (in my >> treasure trove but haven't checked it yet). >> >> Anyone suggest a different approach other than barycentring coordinates. >> >> The reason I will be writing this is for (proof of concept / prototype >> for now) is to be able to get point cache data from a low res geometry and >> then use this outside of an DCC to convert to high res deformations. >> >> This ways existing animation pipelines which have to rely on switching to >> higher resolutions before caching out do not have to do so. Simply export >> out point caches (alembic, pc2, mdd, bgeo, icecache etc.) and then apply >> this to a high res point data outside of any DCC as post process, even on >> farms from command line for example. >> >> -- >> > > > > -- > Best regards, > Ben Houston > Voice: 613-762-4113 Skype: ben.exocortex Twitter: @exocortexcom > http://Clara.io - Professional-Grade WebGL-based 3D Content Creation > > -- Best regards, Ben Houston Voice: 613-762-4113 Skype: ben.exocortex Twitter: @exocortexcom http://Clara.io - Professional-Grade WebGL-based 3D Content Creation
