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
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.
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.
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.
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.
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.
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.