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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 - PowerPoint PPT Presentation
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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
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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
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2-D Simple Function Graphs Simple function graph with range
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2-D Multiple Function Graphs Multiple plots wo/wt legend
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2-D Graphs – Matrix Eigenvalues Max. Eigenvalues of a Matrix
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2-D Piecewise Graphs Piecewise functions
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2-D Function Graphs with Y Range Y range control
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2-D Simple Animations Additional animation parameter
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2-D Multiple Function Animations Additional animation parameter
Default No. of Frames = 50
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Attributes of 2D Graphs Mesh Control
121 2
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Attributes Control Details Grid, Ticks and Header
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Specifying Viewing Box Y Range of Viewing Box
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Specifying Viewing Box (cont.) Semi-automatic control of Y Range
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3-D Function Graphs
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3-D Function Graphs (cont.) Generated 3-D Graphs
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Submesh for Smoother Surface Submesh
Without Submesh With Submesh
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3-D Animations
Default No. of Frames = 50
Animation Parameter
Flying Carpet
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Advanced 2-D Graphs Several objects with different attributes in a
single graph
Plot primitives
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Anatomy of Complex 2D Graph Function and its tangential line at a point
plot::Point2dplot::Line2d
plot::Function2d
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Advanced 2-D Animation Line and point are animated.
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Moving Tangential Line Function and its tangential line at a moving
point
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Example: Interpolated Curve Original curve and its sampled points
Interpolated points using cubic spline
Both curves and sampled points
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Compare the Curves Original curve, sampled points and interpo-
lated curve
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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:
source code can be found in 'ch10_graphics_demo.mn'
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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 so-lution shall be drawn together with the vector field v⃗ (x, y) = (1,−y3 + cos(x)) associated with this ODE (along the solution curve, the vec-tors of this field are tangents of the curve).
source code can be found in 'ch10_graphics_demo.mn'
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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'
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RGB Colors
Opacity
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Simple Animation
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Animation: Arc
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Animation Parameters Animation parameters are for each objects.
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Animation Parameter - Global Animation parameter serves as a global var.
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Time Synchronization
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Integration and Area
source code can be found in 'ch10_graphics_demo.mn'
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Transformations Translate, rotate and scale a group of graph
objects.
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Animated Rotation
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Using Camera
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Animated Camera Camera trajectory
Lorenz attractor
source code can be found in 'ch10_graphics_demo.mn'
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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.
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Notes