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

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 2

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 3

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

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

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

2-D Piecewise Graphs Piecewise functions 7

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

2-D Simple Animations Additional animation parameter 9

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

Attributes of 2D Graphs Mesh Control

Attributes Control Details Grid, Ticks and Header 12

Specifying Viewing Box Y Range of Viewing Box 13

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

3-D Function Graphs 15

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

Submesh for Smoother Surface Submesh 17 Without Submesh With Submesh

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

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

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

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

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

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

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

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 x coordinate of the hub as the animation parameter. The wheel 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: 25 source code can be found in 'ch10_graphics_demo.mn'

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. The solution 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). 26 source code can be found in 'ch10_graphics_demo.mn'

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

RGB Colors 28 Opacity

Simple Animation 29

Animation: Arc 30

Animation Parameters Animation parameters are for each objects. 31

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

Time Synchronization 33

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

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

Animated Rotation 36

Using Camera 37

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

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. 39

Notes 40