Educational Materials

Introduction to Mathematica for High School Math (for Students and Teachers) #14

Ruth Dover

Author

Ruth Dover

Title

Introduction to Mathematica for High School Math (for Students and Teachers) #14

Description

Introduction to Mathematica for High School Math

Tutorial 14: Graphics Primitives

R. Dover, IMSA

As stated many notebooks ago, Mathematica's® ability to show graphics is truly impressive. We have seen some of this with built-in commands such as

Plot

and

Plot3D

. In addition, the Wolfram Language™ includes a collection of "graphics primitives." One of these, a rectangle, was used in an earlier example. Very simply, these are geometric objects that may be placed and colored as desired.

Simple 2D Examples

We will begin simply:

In[]:=

pr1=Graphics[Circle[{0,0},1]]

What you may have guessed from the syntax is that

{0,0}

represents the center and the radius is 1, but these are hardly obvious from the graphic. We can see this in the following:

pr1=Graphics[Circle[{0,0},1],AxesTrue]

For a rectangle with sides parallel to the axes, two vertices are sufficient:

pr2=Graphics[Rectangle[{1,1},{4,2}],AxesTrue]

Line

may be a simple line segment or a sequence of connected segments:

pr3=Graphics[Line[{{-2,-1},{-1,1},{2,0},{0,-1}}],AxesTrue]

We can show these together using the

Show

command, if we had any reason to do this:

Show[pr1,pr2,pr3]

Other 2D graphics primitives include a

Disk

(a filled circle), a

Point

, a

Polygon

and

Text

. Open the Documentation Center and search each of these to find out a little more. Play a little.

More Options

The options make this much more fun. Note that several methods of control are possible for some items (with the semicolon at the end, the object is created in Mathematica's memory but the output is withheld):

bluepoly={Blue,Polygon[{{-3,1},{-1,2},{3,0}}]};

redline={Hue[0],Thick,Line[{{-3,-1},{2,1}}]};

mytext=Text["Here's my artwork!",{0,-1}];

Show[Graphics[{bluepoly,redline,mytext}]]

Note that the red line is on top of the blue poly since the red line was listed later in the Show command. Alternatively, you can include the command

Graphics

in each piece, but not include it in the Show command at the end. The method shown in the previous example requires a little less typing.

Here is a more advanced picture with more options:

nubluepoly={Blue,EdgeForm[Thick],Polygon[{{-3,1},{-1,2},{3,0}}]};

nuredline={Hue[0],Dashing[.1],Thickness[.03],Line[{{-3,-1},{2,1}}]};

numytext=Text[Style["Here's my artwork!",Large,Bold,Italic,Pink],{0,-1}];

Note that you can also combine the graphics with regular plots of graphs. This must be listed separately in Show, rather than being put inside of graphics:

nugraph=Plot[

,{x,-3,3},PlotStyle{Thick,Purple},AxesFalse,PlotRange{-2,4}];

Show[nugraph,Graphics[{nubluepoly,nuredline,numytext}]]

3D Examples

In 3D, Point, Line, Polygon and Text are available again. In addition, there are

Cuboid

Sphere

and

Cylinder

We will use a couple of new things here, edited very slightly from the Documentation Center:

rcoord:=RandomReal[1.,{3}]

pts=Table[Point[rcoord],{12}]

Graphics3D[{PointSize[Large],pts}]

Graphics3D[Table[Sphere[10rcoord],{10}]]

Now, another little issue. Note the

rcoord

was defined with

so that the command will be recalculated each time it is used. Reevaluate the preceding commands to see this.

Exercise

Create a smiley face! Clearly, this may be very simple or very elaborate. Your choice, but practice is always good!

Cite this as: Ruth Dover, "Introduction to Mathematica for High School Math (for Students and Teachers) #14" from the Notebook Archive (2021), https://notebookarchive.org/2021-09-6h2k5e2