1. Computer Graphics: Programming, Problem Solving, and Visual Communication Steve Cunningham California State University Stanislaus and Grinnell College PowerPoint Instructor’s Resource

2. Graphical Problem Solving in Science Making images that communicate about real problems in the sciences

3. Why Do We Make Images? We need a subject for our images and a reason for making them in order to get the most from our work The field of scientific visualization gives us an important set of subjects and an important audience This chapter looks at making images for science

4. Problem-Solving with Graphics The problem-solving cycle: getting insight from images

5. This Chapter’s Process We will look at several techniques for representing and understanding scientific processes We will consider the images we get from using these processes for modeling We hope you will compare the images with your understanding of the science to see how they do or do not help you understand better

6. Data and Visual Communication As we work with data, we need to know what kind of data we have so we can make appropriate images –Interval data –Ordinal data –Nominal data Each has its own vocabulary for displays

7. Diffusion Processes What happens at one point depends on what is happening at neighboring points Examples: heat in a bar (left) and disease spread (right)

8. Function Surfaces Process is to create a domain grid in 2D space and compute a function value f(x,y) for each point in the grid The points (x,y,f(x,y)) in 3D space, with the arrangement from the domain, form a set of triangles or quads that can be graphed Lighting, shading, or texture mapping can be used to clarify the surface

9. Function Surfaces (2) A simple surface based on a trigonometric function The surface can be animated to show dynamics

10. Function Surfaces (3) A surface based on a physical principle: Coulomb’s law This figure shows coordinate axes and both a lighted surface and a 2D pseudocolor display

11. Function Surfaces (4) Wave interactions: linear wave trains (left) and circular waves (right)

12. Parametric Curves and Surfaces Parametric curves - one parameter Parametric surfaces - two parameters In 3D space, there are three functions: f X (s,t), f Y (s,t), f Z (s,t) As before, you build a grid in parameter space and evaluate the functions at each grid point to determine vertices in 3D space

13. Parametric Curves Two simple examples

14. Parametric Surfaces Boy’s surfaceKlein bottle

15. Parametric Surfaces (2) The (4,3) torus

16. Limit Processes There are limit processes such as the that defining the blancmange surface These processes can be carried out as far as you like and the results then shown

17. Scalar Fields If you have data values across a region, you can use the same kind of function graphing processes to create a surface. If you also have other data on the region, you can then map that data onto the surface In our examples, the data is photographic but other operations can work

18. Scalar Fields (2) This example uses a digital elevation map for height values and aerial photos for surface data:

19. Scalar Fields (3) The main problem is registering the height values with the image values, but the result is excellent and useful

20. Simulated Landscapes A scalar field can be simulated by creating an artificial landscape and using the elevations to generate synthetic effects

21. Random Walks Random walks are simulations of processes such as molecular motion It is straightforward to generate a 3D random walk The properties of the walk can then be used with simulations of various processes

22. Random Walks (2) Simulation of diffusion through semipermeable membrane Notice the readout from the simulation

23. Molecular Display There is abundant information on the geometry of molecules from several sources This includes the location and type of each atom in the molecule and all the molecular bonds The information is in standard-format files so it’s easy to read

24. Molecular Display (2) With the geometry of the molecule known, it’s simple to draw it -- but you must still think about the presentation

25. Simulating Scientific Instruments An excellent application of graphic is the presentation of how instruments work An example of the gas chromatograph shows this well

26. Monte Carlo Simulations Model a complex process or situation using random values

27. 4D Graphing 2D functions of a 2D variable 1D function of a 3D variable All are 4D problems and require us to think of ways to show the operations

28. 4D Graphing (2) Real function of a 3D variable: real function defined in a volume Can be shown by isosurfaces or slices

29. 4D Graphing (3) 2D functions of a 2D variable 2D value associated with each point in a 2D space Break down the function into direction and magnitude and use separate encoding

30. Higher Dimensions Displaying a function with 3D values defined in 3D space This is a six-dimensional problem

31. Data-Driven Graphics Innovative approaches can make even simple line graphs into revealing and interesting displays