This section briefly describes a general set of 3D scalar and
vector surface rendering techniques. The first four descriptions
deal with scalar field techniques and the other two with vector
field techniques.
Scalar glyphs
Scalar glyphs is a technique which puts a sphere or a diamond on
every data point. The scale of the sphere or diamond is
determined by the data value. The scalar glyphs may be colored
according to the same scalar field or according to another scalar
field. In this way correlations can be found. As no
interpolations are needed for this technique it consumes few CPU
seconds.
Isosurfaces
This technique produces surfaces in the domain of the scalar
quantity on which the scalar quantity has the same value, the
so-called isosurface value. The surfaces can be colored
according to the isosurface value or they can be colored
according to another scalar field using the texture technique.
The latter case allows for the search for correlation between
different scalar quantities.
There are different methods to generate the surfaces from a
discrete set of data points. All methods use interpolation to
construct a continuous function. The correctness of the generated
surfaces depends on how well the constructed continuous function
matches the underlying continuous function representing the
discrete data set. The method which is implemented in the
software packages described in chapter 3, is the Marching Cube
Algorithm.
Cutting planes
This technique makes it possible to view scalar data on a
cross-section of the data volume with a cutting plane. One
defines a regular, Cartesian grid on the plane and the data
values on this grid are found by interpolation of the original
data. A convenient colormap is used to make the data visible.
Orthogonal slicers
It often occurs that one wants to focus on the influence of only
two independent variables (i.e. coordinates). Thus, the other
independent variables are kept constant. This is what the
orthogonal slicer method does. For example, if the data is
defined in spherical coordinates and one wants to focus on the
angular dependences for a specific radius, the orthogonal slicer
method constructs the corresponding sphere. No interpolation is
used since the original grid with the corresponding data is
inherited. A convenient colormap is used to make the data
visible.
Vector glyphs
This technique uses needle or arrow glyphs to represent vectors
at each data point. The direction of the glyph corresponds to the
direction of the vector and its magnitude corresponds to the
magnitude of the vector. The glyphs can be colored according to a
scalar field.
Streamlines, streaklines, and particle advection
This is a set of methods for outlining the topology, i.e. the
field lines, of a vector field. Generally, one takes a set of
starting points, finds the vectors at these points by
interpolation, if necessary, and integrates the points along the
direction of the vector. At the new positions the vector values
are found by interpolation and one integrates again. This process
stops if a predetermined number of integration steps has been
reached or if the points end up outside the data volume. The
calculated points are connected by lines.
The difference between streamlines and streaklines is that the
streamlines technique considers the vector field to be static
whereas the streaklines technique considers the vector field to
be time dependent. Hence, the streakline technique interpolates
not only in the spatial direction, but also in the time
direction. The particle advection method places little spheres at
the starting points representing massless particles. The
particles are also integrated along the field lines. After every
integration step each particle is drawn together with a line or
ribbon tail indicating the direction in which the particle is
moving.
Textures
This is a technique to color arbitrary surfaces, e.g. those
generated by the isosurface techniques, according to a 3D scalar
field. An interpolation scheme is used to determine the values of
the scalar field on the surface. A colormap is used to assign the
color.
