Modeling and Visualizing Volumetric and Surface-on-Surface Data

An introduction and overview of methods for modeling and visualizing trivariate data is presented. One variable is identified as being dependent on three other, independent variables. Data of this type arises often in practical problems of science and engineering The modeling portion is concerned with finding a mathematical relationship which represents the data. Visualization is concerned with using Computer generated images to convey information so that the user can learn about the relationship. The discussion on modeling methods will concentrate on the two application areas of surface-on-surface and Volumetric data. Volumetric data Covers the case where the independent data values represent points in a three dimensional domain. The surface-on-surface case is where the independent data is restricted to lie on some surface such as the earth or the surface of an airplane wing. Mathematical models with volume or surface domains are developed, discussed and compared. Graphing and visualizing trivariate relationships is quite challenging. Extending methods which have proven to be successful in other situations is a starting point. Several resulting modifications and extensions for both the case of surface-on-surface and Volumetric data are presented, discussed and compared. This includes some interactive techniques, isosurface algorithms, volume rendering and hypersurface projection graphs. Some new interrogation methods are also presented.

[1]  Bernd Hamann,et al.  The asymptotic decider: resolving the ambiguity in marching cubes , 1991, Proceeding Visualization '91.

[2]  Gregory M. Nielson,et al.  Visualizing functions over a sphere , 1990, IEEE Computer Graphics and Applications.

[3]  Bernd Hamann,et al.  Visualizing and modeling scattered multivariate data , 1991, IEEE Computer Graphics and Applications.

[4]  Larry L. Schumaker,et al.  Topics in Multivariate Approximation , 1987 .

[5]  Gregory M. Nielson,et al.  Interpolation over a sphere based upon a minimum norm network , 1987, Comput. Aided Geom. Des..

[6]  Daniel Thalmann,et al.  New trends in animation and visualization , 1991 .

[7]  Bui Tuong Phong.  Illumination for computer generated pictures , 1975, Commun. ACM.

[8]  C. Lawson.  Software for C1 Surface Interpolation , 1977 .

[9]  Gregory M. Nielson.  Visualization in scientific and engineering computation , 1991, Computer.

[10]  G. Nielson.  A method for interpolating scattered data based upon a minimum norm network , 1983 .

[11]  Gregory M. Nielson,et al.  Towards animating ray-traced volume visualization , 1990, Comput. Animat. Virtual Worlds.

[12]  G. Nielson.  The side-vertex method for interpolation in triangles☆ , 1979 .

[13]  R. E. Carlson,et al.  The parameter R2 in multiquadric interpolation , 1991 .

[14]  Gregory M. Nielson,et al.  Coordinate Free scattered Data interpolation , 1987, Topics in Multivariate Approximation.

[15]  Gregory M. Nielson,et al.  Direct manipulation techniques for 3D objects using 2D locator devices , 1987, I3D '86.

[16]  Hans Hagen,et al.  Interpolation of scattered data on closed surfaces , 1990, Comput. Aided Geom. Des..

[17]  William E. Lorensen,et al.  Marching cubes: A high resolution 3D surface construction algorithm , 1987, SIGGRAPH.

[18]  Marc Levoy,et al.  Display of surfaces from volume data , 1988, IEEE Computer Graphics and Applications.

[19]  Martin J. Dürst,et al.  Re , 1988 .

[20]  G. Nielson.  Minimum Norm Interpolation in Triangles , 1980 .

[21]  Gregory M. Nielson,et al.  Scattered Data Interpolation and Applications: A Tutorial and Survey , 1991 .

[22]  W. Lorensen,et al.  Two algorithms for the three-dimensional reconstruction of tomograms. , 1988, Medical physics.

[23]  Gregory M. Nielson.  On the topic of interactive scientific visualization , 1991 .

[24]  Helmut Pottmann,et al.  Interpolation on surfaces using minimum norm networks , 1992, Comput. Aided Geom. Des..