Real-time tetrahedral volume editing accounting for discontinuities

Geological systems can be represented as unstructured tetrahedral grids where faults are topological discontinuities in the volume and each fault block is a connected component. These grids are built from interpretations of seismic and borehole data. Obtaining additional data or new interpretations can point out errors in the tetrahedralised volume. When the location of a fault is slightly off, a new tetrahedralised volume has to be created from scratch. Directly editing the volume would be more effective and comfortable. A free-form deformation technique was developed to implement this interaction. The deformation is confined to a zone around the fault to be edited. Volume deformation is achieved by dragging control points; the geometry of the volume in the vicinity of the discontinuity is updated in realtime. A constraint maintains model consistency throughout editing by preventing tetrahedrons from flipping over. A smoothness constraint distributes the displacement in the whole active region.

[1]  Ari Rappoport,et al.  Simple constrained deformations for geometric modeling and interactive design , 1994, TOGS.

[2]  J. Mallet.  Space–Time Mathematical Framework for Sedimentary Geology , 2004 .

[3]  Thomas W. Sederberg,et al.  Free-form deformation of solid geometric models , 1986, SIGGRAPH.

[4]  Ming C. Lin,et al.  Fast volume-preserving free-form deformation using multi-level optimization , 2000, Comput. Aided Des..

[5]  Ming C. Lin,et al.  Fast volume-preserving free form deformation using multi-level optimization , 1999, SMA '99.

[6]  Alyn P. Rockwood,et al.  A generalized de Casteljau approach to 3D free-form deformation , 1994, SIGGRAPH.

[7]  Rémi Moyen.  Paramétrisation 3D de l'espace en géologie sédimentaire : le modèle GeoChron , 2005 .

[8]  J. Mallet,et al.  Building and Editing a Sealed Geological Model , 2004 .

[9]  Alan H. Barr,et al.  Global and local deformations of solid primitives , 1984, SIGGRAPH.

[10]  Eugene Fiume,et al.  Wires: a geometric deformation technique , 1998, SIGGRAPH.

[11]  Sarah F. Frisken.  3D Chainmail: A Fast Algorithm for Deforming Volumetric Objects , 1997, SI3D.

[12]  Sabine Coquillart,et al.  Extended free-form deformation: a sculpturing tool for 3D geometric modeling , 1990, SIGGRAPH.

[13]  Suzanne M. Shontz,et al.  A Mesh Warping Algorithm Based on Weighted Laplacian Smoothing , 2003, IMR.

[14]  Hong Qin,et al.  Free-form deformations via sketching and manipulating scalar fields , 2003, SM '03.