Turns out mean value coordinates on closed polygon meshes to do deformation was already done:
http://www.cs.rice.edu/~jwarren/papers/meanvalue.pdf -ben On Thu, Dec 12, 2013 at 9:45 AM, Ben Houston <[email protected]> wrote: > 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 My knowledge is out of date, but off the top of my head....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 > -- Best regards, Ben Houston Voice: 613-762-4113 Skype: ben.exocortex Twitter: @exocortexcom http://Clara.io - Professional-Grade WebGL-based 3D Content Creation
