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Explore advanced techniques for creating 2-D/3-D graphs and animations using MATLAB's Symbolic Toolbox. Learn to manipulate attributes, handle timing control, and craft dynamic visualizations. Discover how to design static and animated 3-D graphs with precision. Dive into MuPAD for easy 2-D, 3-D, and animated graphs, plot libraries, and interactive editors. Enhance your skills in creating simple function graphs, matrix eigenvalues, piecewise functions, animations, and advanced graph attributes. Experiment with submeshes, flying carpets, plot primitives, and intricate 2-D plot constructions. Engage in in-depth studies on interpolated curves, cycloids, ODE vector fields, rotated surfaces, RGB colors, animations, and transformations. Develop expertise in translating, rotating, and scaling graph objects with animated camera views. By mastering these tools and techniques, you'll gain control over graph representation, visualization, and customization in MATLAB.
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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
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
2-D Simple Function Graphs • Simple function graph with range
2-D Multiple Function Graphs • Multiple plots wo/wt legend
2-D Graphs – Matrix Eigenvalues • Max. Eigenvalues of a Matrix
2-D Piecewise Graphs • Piecewise functions
2-D Function Graphs with Y Range • Y range control
2-D Simple Animations • Additional animation parameter
2-D Multiple Function Animations • Additional animation parameter Default No. of Frames = 50
Attributes of 2D Graphs • Mesh Control 121 2
Attributes Control Details • Grid, Ticks and Header
Specifying Viewing Box • Y Range of Viewing Box
Specifying Viewing Box (cont.) • Semi-automatic control of Y Range
3-D Function Graphs (cont.) • Generated 3-D Graphs
Submesh for Smoother Surface • Submesh Without Submesh With Submesh
3-D Animations Animation Parameter Default No. of Frames = 50 Flying Carpet
Advanced 2-D Graphs • Several objects with different attributes in a single graph Plot primitives
Anatomy of Complex 2D Graph • Function and its tangential line at a point plot::Point2d plot::Line2d plot::Function2d
Advanced 2-D Animation • Line and point are animated.
Moving Tangential Line • Function and its tangential line at a moving point
Example: Interpolated Curve • Original curve and its sampled points • Interpolated points using cubic spline • Both curves and sampled points
Compare the Curves • Original curve, sampled points and interpolated curve
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'
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'
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'
RGB Colors Opacity
Animation Parameters • Animation parameters are for each objects.
Animation Parameter - Global • Animation parameter serves as a global var.
Integration and Area source code can be found in 'ch10_graphics_demo.mn'
Transformations • Translate, rotate and scale a group of graph objects.
Animated Camera • Camera trajectory • Lorenz attractor 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.