Chapter 10: Graphics

1. Chapter 10:Graphics MATLAB for Scientist and Engineers Using Symbolic Toolbox

2. You are going to • Review the basics of plotting simple 2-D/3-D graphs and animations • Create graphs with different attributes • Generate advanced animated graphs with timing control • Handle cameras for static and animated 3-D graphs

3. Introduction • Graphics – Tool for exploring math objects • MuPAD: Easy 2-D, 3-D and animated graphs • Interactive graph attributes editor • Plot library does it all

4. 2-D Simple Function Graphs • Simple function graph with range

5. 2-D Multiple Function Graphs • Multiple plots wo/wt legend

6. 2-D Graphs – Matrix Eigenvalues • Max. Eigenvalues of a Matrix

7. 2-D Piecewise Graphs • Piecewise functions

8. 2-D Function Graphs with Y Range • Y range control

9. 2-D Simple Animations • Additional animation parameter

10. 2-D Multiple Function Animations • Additional animation parameter Default No. of Frames = 50

11. Attributes of 2D Graphs • Mesh Control 121 2

12. Attributes Control Details • Grid, Ticks and Header

13. Specifying Viewing Box • Y Range of Viewing Box

14. Specifying Viewing Box (cont.) • Semi-automatic control of Y Range

15. 3-D Function Graphs

16. 3-D Function Graphs (cont.) • Generated 3-D Graphs

17. Submesh for Smoother Surface • Submesh Without Submesh With Submesh

18. 3-D Animations Animation Parameter Default No. of Frames = 50 Flying Carpet

19. Advanced 2-D Graphs • Several objects with different attributes in a single graph Plot primitives

20. Anatomy of Complex 2D Graph • Function and its tangential line at a point plot::Point2d plot::Line2d plot::Function2d

21. Advanced 2-D Animation • Line and point are animated.

22. Moving Tangential Line • Function and its tangential line at a moving point

23. Example: Interpolated Curve • Original curve and its sampled points • Interpolated points using cubic spline • Both curves and sampled points

24. Compare the Curves • Original curve, sampled points and interpolated curve

25. Example: Cycloids • A cycloid is the curve that you get when following a point fixed to a wheel rolling along a straight line. We visualize this construction by an animation in which we use the xcoordinate of the hub as the animation parameter. Thewheel is realized as a circle. There are 3 points fixed to the wheel: a green point on the rim, a blue point inside the wheel and a red point outside the wheel: source code can be found in 'ch10_graphics_demo.mn'

26. Example: ODE Vector Field • We wish to visualize the solution of the ordinary differential equation (ODE) y′(x) = −y(x)3 + cos(x)with the initial condition y(0) = 0. Thesolution shall be drawn together with the vector field ⃗v(x, y) = (1,−y3 + cos(x))associated with this ODE (along the solution curve, the vectors of this field are tangents of the curve). source code can be found in 'ch10_graphics_demo.mn'

27. Example: Surface by Rotated Curve • Create an interpolated curve from a series of data points. • Rotate the curve to get the corresponding surface. source code can be found in 'ch10_graphics_demo.mn'

28. RGB Colors Opacity

29. Simple Animation

30. Animation: Arc

31. Animation Parameters • Animation parameters are for each objects.

32. Animation Parameter - Global • Animation parameter serves as a global var.

33. Time Synchronization

34. Integration and Area source code can be found in 'ch10_graphics_demo.mn'

35. Transformations • Translate, rotate and scale a group of graph objects.

36. Animated Rotation

37. Using Camera

38. Animated Camera • Camera trajectory • Lorenz attractor source code can be found in 'ch10_graphics_demo.mn'

39. Key Takeaways • Now, you are able to • plot 2-D and 3-D graphs using different objects and attributes, • generate 2-D and 3-D animations with different objects and attributes, • and to control colors and cameras for your graphs.

40. Notes