110361 Topics in Modeling: Visualization
Lars Linsen
Associate Professor
Computational Science and Computer Science
School of Engineering and Science
Class Project 2:
Isosurface Extraction from Volumetric Scalar Field
A. Marching Cubes
Given:
A volumetric scalar field defined over a uniform rectilinear grid.
Goal:
Visualize the volume data using the marching cubes isosurface extraction including the 2D
asymptotic decider.
Detailed description:
The isosurface is supposed to be extracted with respect to any valid isovalue. The marching
cubes algorithm should be applied to compute the isosurface components within each cell of
the given grid. All topological cases within the cell need to be considered. The output will be
a collection of triangles describing a polygonal mesh. The mesh should be rendered in an
interactive 3D environment that allows for rotation and translation of the object as well as
zooming. For all cells that have ambiguous faces, the ambiguity needs to be resolved using
the 2D asymptotic decider.
Features:
 The isovalue should be interactively selectable and modifiable.
 The isosurface should be rendered using flat rendering and wire frames.
 More than one real data set is supposed to be used.
Optional features:
 The 3D asymptotic decider could be used to decide “tunnel” ambiguities.
 The isosurface may be rendered using smooth shading. In order to apply smooth
shading, the normal at each vertex of the mesh needs to be defined. Normals can be
estimated as the average of the surrounding face normals.
Data sets:
Data sets can be downloaded at http://www.volvis.org.
B. Dual Contouring on Adaptive Rectilinear Grids
Given:
A volumetric scalar field defined over an adaptively refined rectilinear grid with no
restrictions on the adaptivity.
Goal:
Develop a dual contouring approach that consistently deals with all possible configurations.
Detailed description:
Starting from the standard dual contouring approach, solve the problems that may occur when
using arbitrary adaptive configurations. In particular, come up with a consistent solution for
all cases like the following one (shown in 2D):
Features:
 The method should be implemented.
 For the regular case: The exact positions of the isosurface points within the cells do
not need to be computed. Placing them in the cells’ centers suffices.
 For the regular case: One point per cell suffices.
 The isosurface should be rendered using flat rendering.
 At least one real data set is supposed to be used.
Data sets:
Data sets can be downloaded at http://www.volvis.org. Some values need to be thrown away
in order to get an adaptive configuration
C. Splitting Cubes into Tetrahedra via Asymptotic Decider
Given:
A volumetric scalar field defined over a uniform rectilinear grid.
Goal:
Develop a case table for splitting the cells (cubes) of the grid into tetrahedral cells, which is
consistent with the asymptotic decider.
Detailed description:
Each cell of a uniform rectilinear grid should be subdivided into a set of tetrahedra such that
the resulting isosurface when applying the marching cubes algorithm with the asymptotic
decider to the original cells would be the same as the resulting isosurface when applying the
marching tetrahedra algorithm to the subdivided cells. All topological cases need to be
considered. A case table should be developed that includes all topological cases.
Features:
 The splitting method should be implemented.
 Synthetic examples should demonstrate that the method works.
 The marching tetrahedra algorithm should be applied to these cases.
 The isosurface should be rendered using flat rendering.
Data sets:
Data sets can be downloaded at http://www.volvis.org.
D. Marching Cubes with Normals
Given:
A volumetric scalar field defined over an anisotropic rectilinear or curvilinear grid.
Goal:
Use gradient / normal information to reduce staircasing effect.
Detailed description:
When extraction an isosurface with marching cubes from an anisotropic rectilinear grid (i.e.
cells are cuboids, no cubes), there may appear staircasing artifacts.
To reduce these artifacts, one may consider gradient (normal) information. Computing the
gradients at the marching cubes isosurface points, these should point in the same direction as
the surface normal coming out of the triangulation. If not, the position of the isosurface point
should be adjusted along the edge to minimize the deviation of surface normal and scalar field
gradient.
Features:
 The marching cubes algorithm does not need to be implemented. You will be provided
with a solution.
 The solution needs to be applied to anisotropic rectilinear grids.
 The solution needs to be applied to curvilinear grids.
 Real data sets are supposed to be used.
Data sets:
Rectilinear data sets can be downloaded at http://www.volvis.org. For curvilinear data contact
the lecturer.
E. Segmentatation of High-resolution Cryosections
Given:
A 2D scalar field defined over a uniform rectilinear grid.
Goal:
Segment the distinct regions of the cryosection data and show the segments using contours.
Detailed description:
Considering the following example of a cryosection through a monkey brain:
There are clearly distinguishable regions based on the density of the neurons. Obviously, a
simple thresholding does not suffice to segment these regions. Come up with a method that
segments the visible regions. The method should work for all such slices. The segmentation
should be shown using a contour.
Features:
 More than one slice is supposed to be used to document the work.
Data sets:
Data sets can be downloaded at
http://brainmaps.org/index.php?p=speciesdata&species=chlorocebus-aethiops.
Pick one of the five proposed project!
Handed out: Wednesday, November 8, 2006.
Due:
Friday, December 8, 2006.