Introduction to Winplot Richland College Spring 2012 John Ganci [email protected]

Introduction to Winplot

Richland College Spring 2012John Ganci

[email protected]

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Presentation Outline

• What is Winplot?• Obtaining and installing Winplot• Learning about Winplot• Drawing 2-dimensional graphs• Drawing 3-dimensional graphs• Copying Winplot graphs into other

applications• Sources of documentation• Summary• Appendix

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What is Winplot?

• A Windows application that draws graphs– 2-dimensional curves– 3-dimensional curves and surfaces

• A lot more than a graphing calculator• A tool to illustrate mathematical concepts

– Slopes of lines, areas, volumes, vectors, to name a few– Animation allows one to show values as they change

• Best of all, it’s free!– The author is a faculty member at Phillips Exeter

Academy

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Obtaining and Installing Winplot

• http://math.exeter.edu/rparris/winplot.html• Download the self-extracting zip file

wp32z.exe• Run the program

– The default installation directory is c:\peanut– Recommend that you change it to something else– Resulting unzipped file is winplot.exe

• The next few slides show parts of this process

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Obtaining Winplot

Downloadlink

Lots of good info!

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Installing Winplot

• Run the self-extracting zip file wp32z.exe

Recommend that you

change this

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Learning About Winplot• Search the web for “winplot tutorial”

These two arevery good

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Learning About Winplot• Supplemental materials on Winplot home page

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Learning About Winplot• Al Lehnen’s home page; good stuff!!; scroll down

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Learning About Winplot

Tutorial and

examples

Tutorial

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Learning About Winplot

Tutorial, examples, links, and a Power Point Introduction to Winplot

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Using Winplot

• Enough about learning!• It’s time to fire up Winplot and take it out for a

spin• 2-dimensional graphs

– Draw some simple ones– Show the various ways to draw graphs– Show how to show and see additional data about

them• Adding labels• Viewing table of values

• 3-dimensional graphs• Copying Winplot data to other applications• Okay, start Winplot

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Winplot Initial Screen• Close tip box• Resize the Winplot screen the first time you invoke it

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Winplot Initial Screen• Everything is accessed via the Window menu item• Next slide shows the two menu items

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Winplot Initial Screen• Note Window values; we’ll start with 2-dim• Recommend checking Use defaults

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2-dimensional Initial Screen• Before we graph anything we’ll add grid lines; click View

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Adding Grid Lines …• Click Grid

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… Adding Grid Lines• Dialog box appears• Axes is checked, as is both, so the x- and y-axes are shown• Ticks, arrows, and labels are checked• In the grid sub-box

– Check rectangular … then check dotted

– Then Apply, Close

• We’ll look at polar a little later

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2-dimensional Plotting• Now we want to plot something (an equation); click

Equa

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2-dimensional Plotting• Note values; we’ll do 1-4; click Explicit …

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2-dimensional Plotting• Dialog box appears• Set the f(x)= value to 2*x+1• Leave the low and high x values at -5 and 5• Click color to select a color for the graph

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2-dimensional Plotting• Click on one of the colored squares (blue); then

click Close

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2-dimensional Plotting• Back to the equation dialog box• Change pen width for thicker line• Click ok

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2-dimensional Plotting• A graph is displayed along with an inventory box• If you want to change the color or line thickness,

click Edit• Click View

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2-dimensional Plotting• We’ve already looked at Grid; note values; click

View …

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2-dimensional Plotting• Here’s how you can set the displayed bounds of the

graph• Click “set corners” to set the x and y bounds• Click “set center” to set the center point and width

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2-dimensional Plotting• Next we will draw a graph several different ways• First we delete the current graph so that we begin

“fresh”• The first graph will again use Explicit• We enter sqrt(16-x^2) for the function• We take the default range, [-5,5], for x (wrong, but

ok)• We choose a color and click ok

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2-dimensional Plotting• A graph is displayed along with an inventory box• We want the other half of the semicircle; click dupl(icate)

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2-dimensional Plotting• Another explicit equation dialog box• Enter minus sign to the left of sqrt(16-x^2); click ok

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2-dimensional Plotting• Now have entire circle; note the two items in the

inventory

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2-dimensional Plotting: Parametric

• Graph using parametric equations; click Equa, then Parametric

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• The equation dialog box for parametric is displayed• This time two functions must be entered; x=f(t), y=g(t)• Enter 3cos(t) for f(t) and 3sin(t) for g(t)• Note that t ranges from 0 to 1• Change high t to 2pi• As before, click color; click a color; click close; click ok

f(t)=3cos(t)g(t)=3sin(t)

2pi

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• Note the new graph and the new inventory entry

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2-dimensional Plotting: Implicit

• Next is implicit; click Equa; click Implicit …

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• Another equation dialog box, but for implicit• Fill in x^2+y^2 = 4 (or xx+yy=4)• Choose a color; click ok

x^2+y^2=4

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• Note the new graph and the new inventory entry

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2-dimensional Plotting: Polar• Lastly we graph a polar equation; click Equa; click

Polar …

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2-dimensional Plotting: Polar• The equation dialog box for polar is displayed• The t value is theta; f(t) is the r value; that is, r=f(t)• Enter 1 for the f(t) value• Note that the t values range from 0 to 2pi• Choose a color; click ok

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2-dimensional Plotting: Polar• Note the fourth graph and the fourth inventory

entry

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2-dimensional Plotting: Table• Let’s look at the table of values for a few of the equations• All tables are accessed via the inventory button “table”• Highlight the inventory entry then click table• Each is shown on the following slides (no table for implicit)• Close the table by clicking Close

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2-dimensional Plotting: Table• y=sqrt(16-x^2); note undefined values; click Close

when done

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2-dimensional Plotting: Table• Table for parametric equations x=3cos(t), y=3sin(t)

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2-dimensional Plotting: Table• Table for polar equation r=1

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2-dimensional Plotting: Polar, Part 2

• We now graph a cardioid• Start with a clean 2-dim screen• We enter the polar equation r = 2 + 3 sin θ• Add grid lines, but use a polar grid• The next slide shows Winplot after Equa-

>Polar

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• Note: t instead of θ; t ranges from 0 to 2pi• Change pen width to 2; choose a color• Click ok

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• Zoom out: PgDn a few times; then View->Grid…

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2-dimensional Plotting: Polar, Part 2• Click polar (axis); polar sectors; 24; apply;

close

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2-dimensional Plotting: Polar, Part 2• Polar graph paper!

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2-dimensional Plotting: Calculus I

• The next example illustrates how an integral is approximated using Riemann sums

• The approximating rectangles are shown• The number of rectangles can be changed• The example also illustrates how to graph

the antiderivative and add explanatory text• Start with a new 2-dim screen• Begin by entering y=x^2 on Equa->Explicit

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• One->Measurement->Integrate

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• Set lower limit to 1, upper limit to 2• Set subintervals to 5• Check left endpoint; check overlay; choose a color• Click definite

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• Note new rectangles and new approximate value

• Click indefinite

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• Note new graph and new inventory entry• Highlight new inventory entry; click edit

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• Note that the f(x) value cannot be edited• Change the color; click ok

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• Not bad! Let’s add a few descriptive labels• First close the two dialog boxes by clicking close

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• Click Btns; note values; highlight or click Text• Position cursor to left of blue graph; right-click

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• Add what text you want to display• Change font/color; click font• The “tie text to” radio buttons associate the

text with one of three possibilities• If you don’t want the text to move when you

zoom in and out, check the frame button

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• Change font/font style/size• Change color of font• Click OK; Font dialog ends; click ok; edit text dialog ends

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• After adding a second label for the antiderivative• Left-click and drag text box to fine-tune position

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2-dimensional Plotting: Animation

• Next we will see the power of Winplot• We construct an example that illustrates slope• The example is dynamic• The dynamics are done using Winplot’s

animation• Animation is done with parameters A-W• X, Y, and Z are reserved for functions• We start with a clean 2-dim screen• We add the grid lines as before• We enter the explicit function m*x+b• Example taken from Steve Simonds’ videos

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2-dimensional Plotting: Animation• The initial parameter values are all 0, so

y=0

y=m*x+b = 0

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• Anim->Individual->B …• Repeat for M

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• Note initial M and B values; then slide M right

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• Note new M and new line; slide B left (down)

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• Note new B and new line position

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• Now we have an animated line• Next we want to illustrate slope• Add two points to the line (P and P+ΔP)• Add the “rise” and “run” segments

– That is, we add the “slope triangle”

• Points are added via the Equa menu item

• Segments are added the same way• The points and segments will be

animated

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• The first point is (p,m*p+b)• The second point is (p+d, m*(p+d)+b)• The parameter values P and D animate the

points• Plot the points and open the animation

boxes

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• Equa->Point->(x,y) …

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• Set x to p; set y to m*p+b• Select solid• Set dot size to 4• Choose a color for the point• Click ok when done

x=py=m*p+b

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• Note inventory; P=0, so the point is (0,B)

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• Follow the same steps to add the second point

• The x-coordinate of the point is p+d• The y-coordinate of the point is m*(p+d)

+b• Use a different color for this point• Finally, display the animation boxes for P

and D• Resulting graph is shown on the next slide

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• Note inventory; since D=0, the points coincide

Both points

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• Slide D to the right so points don’t coincide

(p, m*p+b)

(p+d, m*(p+d)+b)

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• Now the “rise” and “run” must be added• The “run” is the horizontal segment

joining (p, m*p+b) to (p+d, m*p+b)• The “rise” is the vertical segment

joining (p+d, m*p+b) to (p+d, m*(p+d)+b)

• Segments are added via Equa• The adding of the first segment is

shown on the next few slides

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• Equa->Segment->(x,y) …

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• Dialog box for the segment is displayed• Set x1 = p, y1 = m*p+b• Set x2 = p+d, y2 = m*p+b• Set pen width to 3 (thicker line

segment)• Choose a color• Click ok• Similar for “rise”

– x1 = p+d, y1 = m*p+b– x2 = p+d, y2 = m*(p+d)+b

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• We have one small item to fix

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• The “rise” and “run” terminate at the points• Because of the colors, we can see the

segments• We must delete and add back the two points• Use the inventory dupl button to duplicate

each point; the duplicated point appears at the bottom of the inventory

• Use the inventory delete button to delete the original two points

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2-dimensional Plotting: Animation• Note the points are now on top of the

segments

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• Now “animate” several of the values– Make M a little smaller– Make B a little larger– Slide P to the left (move first point down)

• Result shown on next slide

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2-dimensional Plotting: Animation• How about that!!!

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• The next 2-dimensional example is optional• The example illustrates “epsilon-delta” for

the “limit of f(x) as x approaches a” for a continuous function f

• Explicit and implicit shading is illustrated• The example uses e for epsilon and d for

delta• Animation is used to independently change

a, e, and d• Appendix A1 contains the instructions to

build the example• The next slide shows the example

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2-dimensional Plotting: Calculus II

• The final 2-dimensional example is optional

• The example illustrates the polar equation of a conic

• The example uses e for the eccentricity and d for the directrix

• Animation is used to independently change e and d

• A point on the conic is auto-animated using u to show how the conic is drawn

• Appendix A2 contains the instructions to build the example

• The next slide shows the example

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2-dimensional Plotting: Calculus II

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3-dimensional Plotting• Start at the Winplot main screen; click Window;

click 3-dim

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3-dimensional Plotting• Note similarities to 2-dim; click Equa

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3-dimensional Plotting• Note similarities to 2-dim

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3-dimensional Plotting

• The initial two screens are similar to 2-dim

• Equa and Anim are present• Equa has some additional values

– cylindrical and spherical– curve– plane

• Some 3-dim graphs produce undesirable results; must redraw using one of the other options

• Our first example uses Equa->Explicit to draw a hemisphere

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3-dimensional Plotting• Equa->Explicit …

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3-dimensional Plotting• Note the dialog box is for a function in

two variables: z=f(x,y)• Want to draw the upper hemisphere• The sphere is x^2+y^2+z^2=4• Set z=sqrt(4-x^2-y^2)• Set x lo = -2 = y lo, x hi = 2 = y hi• Choose a color; click ok

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3-dimensional Plotting• No axes; what is the planar part?

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3-dimensional Plotting• Display the axes: View->Axes->Axes

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3-dimensional Plotting• The axes are shown; slightly hidden

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3-dimensional Plotting• View; uncheck Hide segments

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3-dimensional Plotting• Hidden lines are now visible

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• The planar “tags” are due to what Winplot uses for the domain of the function

• The Winplot domain is [-2,2] x [-2,2]– Look back at the Equa->Explicit dialog box

• There are points in the Winplot domain that are not in the actual domain

• Winplot sets z to 0 for these points• These points make up the planar “tags”

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• The sphere can be drawn using spherical coordinates; ρ=2 is x^2+y^2+z^2=4

• Delete the first attempt from the inventory

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3-dimensional Plotting• Equa->Spherical …

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• The equation dialog box for spherical is displayed

• The r value is the ρ value; enter 2 there• The t value is the θ value; note that it

ranges from 0 to 6.28319 = 2π• The u value is the Φ value; note that it

ranges from 0 to 3.14159 = π• Choose a color• Click ok

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3-dimensional Plotting• Display the axes again; much better!

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3-dimensional Plotting• All the quadric surfaces can be drawn

– Ellipsoid– Elliptic paraboloid– Hyperbolic paraboloid– Hyperboloids with one and two sheets

• Equa->Explicit doesn’t always yield good results– Use parametric or cylindrical instead

• Cross-sections can be added using planes– Animation can be used to show the level curves

• The next example shows a hyperboloid with one sheet and its three cross-sections

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3-dimensional Plotting• Note inventory; animate on B,C,D; rotate graph

AnimParameters A-W

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• We next look at a space curve and its four related vectors: r=position vector, T=unit tangent vector, N=unit normal vector, and B=unit binormal vector

• To make things interesting, we animate a point, showing all the values as the point moves along the curve

• The space curve is a variation of the “twisted cubic”

• The animation gives visual feedback about why it is called “twisted”

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3-dimensional Plotting• An initial view of the graph; includes

labels

Slide notes area shows the inventory

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• A final 3-dimensional graph is taken from a problem in James Stewert’s “Calculus, Early Transcendentals” text. It graphically shows a 3-dimensional solid bounded by several curves and planes.

• You can use the arrow keys to rotate the solid to see it from just about any angle.

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3-dimensional Plotting• Rotate the graph to “look inside”

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Copying Graphs to Other Applications

• As a final illustration, we show how easy it is to copy a Winplot graph into a Word document

• We copy the 3-dimensional graph on the previous slide into a Word document

• In Winplot click on File• Click on Copy to clipboard (or Control-C)• Switch to your open Word document• Position where you want the graph• Click Edit; Paste (or Control-V)• That’s it! Result shown on next slide• The only recommendation is to do any fixing

up in Winplot before doing the copy and paste

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Copying Graphs to Other Applications

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Sources of Documentation• The web

– Use your favorite search engine

• The Winplot home page Supplemental link– Tutorials and examples in many languages– The two highlighted ones are especially good

• The Help menu items found throughout Winplot– While somewhat terse, there is good information

there

• The tips shown when Winplot is started– Reading through these provides lots of useful

information

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Summary• Winplot is a free tool used to graph functions • Both 2-dimensional and 3-dimensional graphs• In this introduction we’ve only touched on some of

the many functions provided by Winplot• With some thought, a lot of helpful animations can

be created to illustrate concepts to your students • The Winplot author is very receptive to feedback

and fixes problems almost as soon as they’re reported

• Check the Winplot home page often to be sure your version is current– Always backup your current version before you replace it

• A special thanks to Richard Parris, the author of Winplot, and Al Lehnen, a contributor to the Winplot supplemental materials, for their help with my many questions

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Appendix

• Appendix 1 (A1) contains the 2-dimensional “epsilon-delta” example

• Appendix 2 (A2) contains the 2-dimensional polar conic example

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A1: Epsilon-Delta• The example illustrates how epsilon and

delta interact with respect to a fixed function f and an x value of a

• The function f is defined as a user function• Epsilon is represented by e, delta by d• Point P (a,f(a)) is on the graph of f• Points Q (a,0) and R (0,f(a)) are on the

axes• Dashed lines connect P to the axis points• The epsilon and delta “bands” are shaded• The a, e, and d values are animated• Next slide shows the end result

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A1: Epsilon-Delta

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A1: Epsilon-Delta• Overview of steps follows• Start with a new 2-dim graph• Add the function f as a user function• Add the a, d, and e animate dialog

boxes• Add the points P, Q, and R• Add the dashed lines PQ and PR• Add “band” horizontal and vertical lines• Add shading• Add labels

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A1: Epsilon-Delta• Equa->User functions …

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A1: Epsilon-Delta• Fill in function name; fill in function• Click Enter; note function; click close• Note: name must be at least 2

characters

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A1: Epsilon-Delta• Equa->Explicit …

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A1: Epsilon-Delta• Set f(x)=ff(x)• Set pen width=2; set color; click ok

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A1: Epsilon-Delta• Graph is displayed; next add animation

boxes

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A1: Epsilon-Delta• Anim->Individual->A …

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A1: Epsilon-Delta• Note value is zero; note scroll bar in middle• Set left (lower) and right (upper) bounds for a• Enter -10; click set L (left bound); scroll bar at

left

• Enter 10; click set R (right bound); scroll bar at right

• Scroll A to 1

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A1: Epsilon-Delta• Repeat the steps for d and e• Set both lower bounds to zero• Set both upper bounds to 2• Scroll both so that the values are 1• Next slide shows results

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A1: Epsilon-Delta• We add P, Q, and R next

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A1: Epsilon-Delta• P is (a,ff(a))• Q is (a,0)• R is (0,ff(a))• Details for P follow• Details for Q and R are not shown; similar

to P

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A1: Epsilon-Delta• Equa->Point->(x,y) …

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A1: Epsilon-Delta

• Set x to a; set y to ff(a)• Select solid• Choose a color for the point• Click ok when done• Next slide shows P, Q, and R

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A1: Epsilon-Delta• Add dashed lines PQ and PR next

R

P

Q

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A1: Epsilon-Delta• Equa->Segment->(x,y) …

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A1: Epsilon-Delta• Instructions for PQ follow• Set x1=0, y1=ff(a)• Set x2=a, y2=ff(a)• Set color; click dotted; click ok• PR is similar; use dupl, then edit• Dupl P then delete first P• Next slide shows both segments; P is above

both

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A1: Epsilon-Delta• Next add the lines that bound the

“bands”

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A1: Epsilon-Delta• The “epsilon band” lines are y=ff(a)-e

and y=ff(a)+e• These are added as explicit functions• The “delta band” lines are x=a-d and

x=a+d• These are added as lines• The addition of one of each is shown on

the next few slides

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A1: Epsilon-Delta• Equa->Explicit …

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A1: Epsilon-Delta• Add the bottom line• Set f(x) to ff(a)-e; set color; click ok• Repeat for top line; not shown (use dupl)• Set f(x) to ff(a)+e; click ok• Next slide shows the two lines

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A1: Epsilon-Delta• The vertical lines are done next

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A1: Epsilon-Delta• Equa->Line …

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A1: Epsilon-Delta• Add the left vertical line• Set a=1, b=0, c=a-d; change color;

click ok• Use dupl for right vertical line (not

shown)• Set a=1, b=0, c=a+d; click ok• Next slide shows the two lines

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A1: Epsilon-Delta• One more item before we shade the

“bands”

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A1: Epsilon-Delta• Equa; note “Shade explicit inequalities

…” is available but “Shade implicit inequalities …” is grayed out

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A1: Epsilon-Delta• The “epsilon band” is shaded explicitly• The “delta band” is shaded implicitly• We need to add two implicit values so

that “Shade implicit inequalities …” is available

• The next few slides do this

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A1: Epsilon-Delta• Equa->Implicit …

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A1: Epsilon-Delta• Fill in x=a-d; set color; click ok• Use dupl to add second implicit (not

shown)• Fill in x=a+d; click ok• Click the graph button for these two

items in the inventory so that they are hidden

• Next slide shows the results

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A1: Epsilon-Delta• We’re ready to do the shading now

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A1: Epsilon-Delta• Equa->Shade explicit inequalities …

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A1: Epsilon-Delta• First dropdown; select y=ff(a)-e• Click between radio button• Second dropdown; select y=f(a)+e• Select color; click shade; note values; click

close

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A1: Epsilon-Delta• Equa->Shade implicit inequalities …

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A1: Epsilon-Delta• Click x=a-d; click change = to >; change color• Click x=a+d; click change = to <• Insure shading is correct; click close

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A1: Epsilon-Delta• Almost done! (Now is a good time to

save)

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A1: Epsilon-Delta

• The last items to add are the labels• The addition of one label is shown• The remaining labels are added in a

similar manner

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A1: Epsilon-Delta• Btns->Text

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A1: Epsilon-Delta• Right click near where you want the

label• Fill in text; optionally change font• Click tie text to frame; click ok• Repeat process for all the labels• Right click inside one to edit it• Click and drag them to fine-tune

position• Final result shown on next slide

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A1: Epsilon-Delta• Note the labels; (save the graph again)

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A1: Epsilon-Delta• Time to use the example• Set a to a particular value, say 1• Set e to a particular value, say 1• Scroll d until the graph, restricted to the

vertical band, is bounded by the horizontal band (within the intersection rectangle)

• Setting e to a particular value corresponds to “for every epsilon …”

• Scrolling d until the graph lies within the intersection rectangle corresponds to “there is a delta …”

• One possibility is shown on the next slide

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A1: Epsilon-Delta• Looks like delta=0.36 works for

epsilon=1

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A1: Epsilon-Delta• Play some more• Change e; does d need to change?• Change a, leaving e as before; does d

need to change?• Try changing the user-defined function;

does anything else need to change?• This concludes the example

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A2: Polar Conic• Recall that a conic is the set of points P

whose distance from a fixed point F (the focus) are a constant multiple (the eccentricity) of the distance from P to a fixed line L (the directrix); that is, |PF| = e|PL|

• The polar equation r = ed/(1+e*cos(θ)) is a conic with focus F at the pole and directrix L a vertical line that intersects the polar axis

• Our next example illustrates F, L, P, PF, PL, and how P changes as the parameter value θ changes

• The next slide shows the final result

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A2: Polar Conic

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A2: Polar Conic

• The example illustrates how a graph can do an “active” animation

• The eccentricity and directrix are animated

• The example also illustrates how to use a “User Function”, thus making the Inventory somewhat “dynamic”

• Start with a new 2-dim screen• Building this example takes some work,

but is worth it

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A2: Polar Conic• Equa->User functions …

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A2: Polar Conic• Type conic in name, ed/(1+ecos(x)) in

name(x)

• Click Enter; note value; click close

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A2: Polar Conic• Equa->Polar …

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A2: Polar Conic• Replace f(t) with conic(t)• Note low, high t are correctly set to 0,

2pi• Set pen width to 2• Set color• Click ok

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A2: Polar Conic• Can’t see graph because d and e are

zero!!!• Next open the d and e animate boxes

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A2: Polar Conic• Anim->Individual->D …

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A2: Polar Conic• Note value is zero; note scroll bar in middle• Set left (lower) and right (upper) bounds for d• Click set L (left bound); scroll bar now at left


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A2: Polar Conic• Still no graph, this time because d is 10• Lower the d value to 2; click or drag

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A2: Polar Conic• Hyperbolas appear! • Open and set animation for e

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A2: Polar Conic• Note value is 2.71828; note scroll bar• Set left (lower) and right (upper) bounds for e• Enter 0; click set L; scroll bar at left


• No change in graph; lower the e value to 2

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A2: Polar Conic• Still a hyperbola since e > 1

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A2: Polar Conic• Directrix is next; Equa->Line …

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A2: Polar Conic• Note a, b, c values• Set a=1, b=0, c=d; change pen width to

2; change color; click ok

x=d

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A2: Polar Conic• Now we see the directrix; next is the

focus

x=d

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A2: Polar Conic• Equa->Point->(x,y) …

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A2: Polar Conic• Set x=0, y=0• Click solid• Set dot size to 3• Set color• Click ok

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A2: Polar Conic• Now we see the focus

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A2: Polar Conic• The point P on the conic is now added• Anticipating that we want to animate P to

see it move along the conic, we define it using a parameter, u– P has polar coordinates (conic(u),u)

• A second point, D (on the directrix), is added; the distance from P to the directrix is |PD|; the point D is also defined in terms of u– D has rectangular coordinates (d, conic(u)sin(u))

• The next three slides show how P is added• We do not show the addition of D since it is

similar to what was done for the focus

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A2: Polar Conic• Add point P: Equa->Point->(r,t) …

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A2: Polar Conic• Set r=conic(u), t=u• Click solid• Set dot size to 3• Set color• Click ok• Next slide shows both P and D

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A2: Polar Conic• Red point is P; green point on directrix

is D• Note that u is initially zero

P D

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A2: Polar Conic• Add the animation dialog box for u• Proceed as we did for d and e• Set lower bound to 0 and upper bound to

2pi• Move the scroll bar so that u is greater

than zero• Result shown on next slide

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A2: Polar Conic• Note that P and D have moved

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A2: Polar Conic• Almost done!• What’s left is to add the line segment from

the focus, F, to P and the line segment from P to D

• We use rectangular coordinates for both• The endpoints of PF are

(conic(u)cos(u),conic(u)sin(u)) and(0,0)• The endpoints of PD are

(conic(u)cos(u),conic(u)sin(u)) and (d,conic(u)sin(u))

• The next four slides show the addition of PD• The addition of PF is similar so is not shown

183

A2: Polar Conic• Equa->Segment->(x,y) …

184

A2: Polar Conic• Set x1=conic(u)cos(u), y1=conic(u)sin(u)• Set x2=d, y2=conic(u)sin(u)• Click dotted• Set color• Click ok• Next slide shows both segments

185

A2: Polar Conic• Highlight P in inventory; dupl; delete

original

186

A2: Polar Conic• Graph is done! (Now is a good time to

save it)

187

A2: Polar Conic• Time to play!• The next few slides simulate the playing• You can do better• We show e=1 (parabola) and e<1

(ellipse)• It’s much more fun to watch the graph

change as you move the scroll bar for e• We wrap up the example by showing how

you can auto-animate P

188

A2: Polar Conic• Parabola (e=1)

189

A2: Polar Conic• Ellipse (e<1)

190

A2: Polar Conic• Hyperbola (e>1)

191

A2: Polar Conic• Our last illustration with this example is

actually why the example was created• When the graph is drawn, it is drawn so

fast that you can’t tell the direction drawn

• We get around this by auto-animating u• Close or move the e and d dialog boxes• Zoom out (PgDn a few times)• Close or move the inventory dialog box• Reset the u value to zero

192

A2: Polar Conic• Click autocyc

193

A2: Polar Conic• Click Q to quit, F to speed up, S to slow

down

194

A2: Polar Conic• Do the same auto-animation for a

parabola• Do the same auto-animation for an

ellipse• This completes the polar conic example

Documents

Introduction to Winplot Richland College Spring 2012 John Ganci [email protected]