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

Chapter 10:

Graphics

MATLAB for Scientist and Engineers

Using Symbolic Toolbox

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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

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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