By Charles D. Hansen, Chris R. Johnson
This booklet is reasonably whole. It has broad aspect in terms of explaining the contents of the publication
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Extra info for Visualization Handbook
These regions are defined as F (x, y, z) < 0, F (x, y, z) ¼ 0, and F (x, y, z) > 0, respectively. Scalar generation. Implicit functions convert a position in space into a scalar value. That is, given an implicit function, we can sample it at a point (xi , yi , zi ) to generate a scalar value ci . An example of an implicit function is the equation for a sphere of radius R F (x, y, z) ¼ x2 þ y2 þ z2 À R2 (1:14) This simple relationship defines the three regions F (x, y, z) ¼ 0 (on the surface of the sphere), F (x, y, z) < 0 (inside the sphere), and F (x, y, z) > 0 (outside the sphere).
Color mapping and isocontour generation are the predominant methods used in scientific visualization. Scalar visualization techniques are easily adapted to a variety of situations through creation of a relationship that transforms data at a point into a scalar value. Other examples of scalar mapping include an index value into a list of data, computing vector magnitude or matrix determinant, evaluating surface curvature, or determining distance between points. Scalar generation, when coupled with color mapping or contouring, is a simple yet effective technique for visualizing many types of data.
10. In practice the simplest approach is to create a case table consisting of all 256 possible combinations and to design them in such a way as to prevent holes. , interior edges are used by exactly two triangles; boundary edges are used by exactly one triangle). We can extend the general approach of marching squares and marching cubes to other topological types such as triangles, tetrahedra, pyramids, and wedges. 7 Using marching triangles or marching tetrahedra to resolve ambiguous cases on rectangular lattice (only the face of the cube is shown).