Rapid Deformation of Isocontours by Interactive Editing of Implicit Functions

@inproceedings{Frank05GM,
 abstract = { In this article we present a method to deform iso-contour shapes - like geological horizons - rapidly in an
interactive way. We define an implicit function j on the nodes of a simplicial complex. An isovalue contour
is a shape where j takes the constant value w so j −w = 0 is true. Let us consider an isovalue surface Sw
of j(x,y, z) that is defined on the nodes of a tetrahedral mesh in the 3D Euclidean space. Editing the implicit
function j(x,y, z) automatically leads to a deformation of Sw.
In our approach we use the Discrete Smooth Interpolation (DSI) method to interpolate j(x,y, z) on a
three dimensional Euclidean domain. Changing the location of one or more property control points and a
successive re-interpolation of j(x,y, z) results in a modified implicit function j∗(x,y, z) and consequently
to a deformed isovalue surface S∗
w. To achieve immediate model update the re-interpolation has to be
performed as fast as possible. Therefore we use a matrix version of DSI and only update the altered coefficients.
Further the new solution j∗(x,y, z) for this interpolation problem lies very close to the initial solution
j0(x,y, z), so a numerical method like Conjugate Gradient converges very fast. Restrictions of the model
editing on local regions additionally speed up our algorithm. By this we can deform isovalue surfaces like
geological horizons in real-time with immediate graphical user feedback. Topological constraints like the
non-intersection of horizons is granted automatically by this method. },
 author = { Frank, Tobias AND Mallet, Jean-Laurent },
 booktitle = { Proc. 25th Gocad Meeting, Nancy },
 title = { Rapid Deformation of Isocontours by Interactive Editing of Implicit Functions },
 year = { 2005 }
}