My Mathematica Experience Symbolic computational software Starting - - PowerPoint PPT Presentation

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My Mathematica Experience Symbolic computational software Starting - - PowerPoint PPT Presentation

Jan 12, 2024 866 likes •1.27k views

My Mathematica Experience Symbolic computational software Starting in 2008 Friendly syntax Extensive documentation Visualization capabilites My Mathematica Experience Symbolic computational software Starting in 2008

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SLIDE 1
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SLIDE 2

My Mathematica Experience

  • Symbolic computational software
  • Starting in 2008
  • Friendly syntax
  • Extensive documentation
  • Visualization capabilites
slide-3
SLIDE 3

My Mathematica Experience

  • Symbolic computational software
  • Starting in 2008
  • Friendly syntax
  • Extensive documentation
  • Visualization capabilites
slide-4
SLIDE 4

My Mathematica Experience

  • Symbolic computational software
  • Starting in 2008
  • Friendly syntax
  • Extensive documentation
  • Visualization capabilites
  • Research Exploration
  • Experimental Math
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SLIDE 5

My Mathematica Experience

  • Symbolic computational software
  • Starting in 2008
  • Friendly syntax
  • Extensive documentation
  • Visualization capabilites
  • Research Exploration
  • Experimental Math
  • In my Teaching
  • Math Models, MV Calc, Math w/Mathematica
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SLIDE 6

Teaching Methods

  • Give students the tools to succeed
  • How to use the Documentation Center
  • Stand-alone tutorials
  • One-on-one help
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SLIDE 7

Teaching Methods

  • Give students the tools to succeed
  • How to use the Documentation Center
  • Stand-alone tutorials
  • One-on-one help
  • Project-based learning
  • Let them explore individually
  • Clear instructions and rubric
  • 3D printing since Spring ‘15
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SLIDE 8

Mathematics in 3D Printing

Design in Mathematica requires specifying coordinates

  • 3D Coordinate System
  • Transformations
  • Rotation, Translation, Scaling
  • Parametric Curves / Vector Functions
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SLIDE 9

Mathematics in 3D Printing

Design in Mathematica requires specifying coordinates

  • 3D Coordinate System
  • Transformations
  • Rotation, Translation, Scaling
  • Parametric Curves / Vector Functions
  • Trigonometry
  • Angles between lines, sine, arctan,
  • Geometric Objects
  • Equations of Torus, Ellipsoid, …
  • Polyhedra
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SLIDE 10

Example: Geometry Basics

How does it work?

  • Coordinates for Primitives:

Sphere[{0, 0, 0}, .28] Cuboid[{-.05, -.05, .26}, {.05, .05, .35}] Cone[{{0, 0, 0}, {0, 0, -1}}, .3] mathartshop.com/jewelry/2.html

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SLIDE 11

Example: Geometry Basics

How does it work?

  • Coordinates for Primitives:

Sphere[{0, 0, 0}, .28] Cuboid[{-.05, -.05, .26}, {.05, .05, .35}] Cone[{{0, 0, 0}, {0, 0, -1}}, .3]

What doesn’t work?

  • Certain primatives not exportable!
  • e.g. Tetrahedron, Pyramid

mathartshop.com/jewelry/2.html

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SLIDE 12

Example: Geometry Basics

How does it work?

  • Coordinates for Primitives:

Sphere[{0, 0, 0}, .28] Cuboid[{-.05, -.05, .26}, {.05, .05, .35}] Cone[{{0, 0, 0}, {0, 0, -1}}, .3]

What doesn’t work?

  • Certain primatives not exportable!
  • e.g. Tetrahedron, Pyramid
  • Resolution in STL file is poor
  • Sphere, Cone
  • Use ParametricPlot3D

mathartshop.com/jewelry/2.html

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SLIDE 13

Example: Curves and Surfaces

How does it work?

  • BSplineCurve, Interpolation
  • ParametricPlot3D
  • 𝑔: ℝ → ℝ3 plots a curve
  • 𝑔: ℝ2 → ℝ3 plots a surface

ParametricPlot3D[ … ,PlotStyle → Tube[.1]]

blog.mathzorro.com/2017/03/

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SLIDE 14

Example: Curves and Surfaces

How does it work?

  • BSplineCurve, Interpolation
  • ParametricPlot3D
  • 𝑔: ℝ → ℝ3 plots a curve
  • 𝑔: ℝ2 → ℝ3 plots a surface

ParametricPlot3D[ … ,PlotStyle → Tube[.1]]

  • Secret option: Extrusion

blog.mathzorro.com/2017/03/

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SLIDE 15

Example: Curves and Surfaces

How does it work?

  • BSplineCurve, Interpolation
  • ParametricPlot3D
  • 𝑔: ℝ → ℝ3 plots a curve
  • 𝑔: ℝ2 → ℝ3 plots a surface

ParametricPlot3D[ … ,PlotStyle → Tube[.1]]

  • Secret option: Extrusion
  • Plot3D[ x^2 + y^2, … ,Extrusion → 1]
  • ContourPlot3D[ … ,Extrusion → 0.1]

blog.mathzorro.com/2017/03/

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SLIDE 16

Example: Curves and Surfaces

How does it work?

  • BSplineCurve, Interpolation
  • ParametricPlot3D
  • 𝑔: ℝ → ℝ3 plots a curve
  • 𝑔: ℝ2 → ℝ3 plots a surface

ParametricPlot3D[ … ,PlotStyle → Tube[.1]]

  • Secret option: Extrusion

What doesn’t work?

  • Can’t export Tube[curve] .
  • Must add Tube in PlotStyle

blog.mathzorro.com/2017/03/

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SLIDE 17

Example: Curves and Surfaces

How does it work?

  • BSplineCurve, Interpolation
  • ParametricPlot3D
  • 𝑔: ℝ → ℝ3 plots a curve
  • 𝑔: ℝ2 → ℝ3 plots a surface

ParametricPlot3D[ … ,PlotStyle → Tube[.1]]

  • Secret option: Extrusion

What doesn’t work?

  • Can’t export Tube[curve] .
  • Must add Tube in PlotStyle
  • Caps of tubes are missing
  • Insert them independently

and mind their resolution blog.mathzorro.com/2017/03/

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SLIDE 18

Example: Polyhedra

How does it work?

  • PolyhedronData
  • Imports curated polyhedra
  • Extract for modifications
  • Vertices, Incidences…

blog.mathzorro.com/2017/04/

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SLIDE 19

Example: Polyhedra

How does it work?

  • PolyhedronData
  • Imports curated polyhedra
  • Extract for modifications
  • Vertices, Incidences…
  • GraphicsComplex
  • Create your own polyhedron!

blog.mathzorro.com/2017/04/

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SLIDE 20

Example: Polyhedra

How does it work?

  • PolyhedronData
  • Imports curated polyhedra
  • Extract for modifications
  • Vertices, Incidences…
  • GraphicsComplex
  • Create your own polyhedron!

What doesn’t work?

  • Time intensive to specify EVERYTHING

Is it manifold? blog.mathzorro.com/2017/04/

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SLIDE 21

Example: MeshRegion Objects

How does it work?

  • DiscretizeRegion / DiscretizeGraphics
  • Triangulates 2D and 3D objects

blog.mathzorro.com/2017/05/

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SLIDE 22

Example: MeshRegion Objects

How does it work?

  • DiscretizeRegion / DiscretizeGraphics
  • Triangulates 2D and 3D objects
  • ImageMesh
  • Image → MeshRegion

blog.mathzorro.com/2017/05/

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SLIDE 23

Example: MeshRegion Objects

How does it work?

  • DiscretizeRegion / DiscretizeGraphics
  • Triangulates 2D and 3D objects
  • ImageMesh
  • Image → MeshRegion
  • Mesh Operations
  • RegionProduct, RegionUnion,

RegionIntersection blog.mathzorro.com/2017/05/

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SLIDE 24

Example: MeshRegion Objects

How does it work?

  • DiscretizeRegion / DiscretizeGraphics
  • Triangulates 2D and 3D objects
  • ImageMesh
  • Image → MeshRegion
  • Mesh Operations
  • RegionProduct, RegionUnion,

RegionIntersection

  • Extraction for Modifications
  • MeshCoordinates, MeshPrimitives

blog.mathzorro.com/2017/05/

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SLIDE 25

Example: MeshRegion Objects

How does it work?

  • DiscretizeRegion / DiscretizeGraphics
  • Triangulates 2D and 3D objects
  • ImageMesh
  • Image → MeshRegion
  • Mesh Operations
  • RegionProduct, RegionUnion,

RegionIntersection

  • Extraction for Modifications
  • MeshCoordinates, MeshPrimitives

What doesn’t work?

  • Can’t intersect 3D MeshRegions!

blog.mathzorro.com/2017/05/

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SLIDE 26

Example: RegionPlot3D

How does it work?

  • Specify Boolean operations

𝑦2 + 𝑧2 + 𝑨2 ≤ 1 && 𝑦2 + 𝑧2 + (𝑨 − 1)2 ≤ 1 mathartshop.com/home/3.html

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SLIDE 27

Example: RegionPlot3D

How does it work?

  • Specify Boolean operations

𝑦2 + 𝑧2 + 𝑨2 ≤ 1 && 𝑦2 + 𝑧2 + (𝑨 − 1)2 ≤ 1

  • Thicken a 2D surface

PlotStyle -> {Directive[Thickness[.1]]} mathartshop.com/home/3.html

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SLIDE 28

Example: RegionPlot3D

How does it work?

  • Specify Boolean operations

𝑦2 + 𝑧2 + 𝑨2 ≤ 1 && 𝑦2 + 𝑧2 + (𝑨 − 1)2 ≤ 1

  • Thicken a 2D surface

PlotStyle -> {Directive[Thickness[.1]]}

What doesn’t work?

  • Poor edges / smoothing
  • Improve via PlotPoints

mathartshop.com/home/3.html

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SLIDE 29

Mathematica’s Power

  • Programmable & Algorithmic approach to all
  • Notebook interface: No point and click!
  • Table and Map to apply systematically
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SLIDE 30

Mathematica’s Power

  • Programmable & Algorithmic approach to all
  • Notebook interface: No point and click!
  • Table and Map to apply systematically
  • Easy to add randomness. RandomReal[]
  • Easy to add color. Hue[]
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SLIDE 31

Mathematica’s Power

  • Programmable & Algorithmic approach to all
  • Notebook interface: No point and click!
  • Table and Map to apply systematically
  • Easy to add randomness. RandomReal[]
  • Easy to add color. Hue[]
  • Exports to multiple file formats
  • Export[“filename.stl”,model]
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SLIDE 32

Mathematica’s Power

  • Programmable & Algorithmic approach to all
  • Notebook interface: No point and click!
  • Table and Map to apply systematically
  • Easy to add randomness. RandomReal[]
  • Easy to add color. Hue[]
  • Exports to multiple file formats
  • Export[“filename.stl”,model]
  • Visualization Capabilities
  • Scheduled Updates
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SLIDE 33

Drawbacks

  • 3D printing rather new to Mathematica.
  • It doesn’t “just work”.
  • Certain commands not exportable at all
  • Never know when it will export or crash
  • Difficult to understand error messages
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SLIDE 34

Drawbacks

  • 3D printing rather new to Mathematica.
  • It doesn’t “just work”.
  • Certain commands not exportable at all
  • Never know when it will export or crash
  • Difficult to understand error messages
  • Requires license ($$$)
  • Colleagues use Sage
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SLIDE 35

Resources

  • Documentation Center
  • Mathematica StackExchange
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SLIDE 36

Resources

  • Documentation Center
  • Mathematica StackExchange
  • Henry Segerman’s

3D Printing for Mathematical Visualisation

  • My class tutorials:
  • 213.mathzorro.com
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SLIDE 37

Resources

  • Documentation Center
  • Mathematica StackExchange
  • Henry Segerman’s

3D Printing for Mathematical Visualisation

  • My class tutorials:
  • 213.mathzorro.com
  • My blog: (3D design with Mathematica series)
  • blog.mathzorro.com
  • blog.wolfram.com
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SLIDE 38

THANK YOU!

Queens College Students and Colleagues qc.edu du/~ /~chan hanusa usa

> Research earch > Talk lks

mathartsh rtshop.c

  • p.com
  • m

Shapeways & Lauren Slowik