Script Lesson 9

7/29/2019 Script Lesson 9

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Scripting Tutorial - Lesson 9

Scripting Tutorial - Lesson 9: Graphical ShapeNumbers

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It is time to try and put together everythingthat we have learned so far. In this lesson andlesson 10 we will use Lua's graphic commandsalong with many of the enhancements wehave learned to create documents that areboth useful, clear and easy to use. We willbegin with the graphical display of shapenumbers - square, rectangular and triangularnumbers.

Take amoment towatch theaccompanyingmovie andthen have aplay with thisdocumentusing the

Player to get afeel for thepossibilitiesand for someof the designchoices thathave beenmade. Forexample,while it isgreat to usearrow keysand enter,escape andeven tab keys


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to makecontrol bybothcomputer andhandheldeasy, if wewant ourdocuments to

be usable withthe Playerthen it isworth leavingin the sliders.

In theexampleshown,pressing upand down

arrowscontrols thevalue ofn,increasinganddecreasingthe numberbeing studied.Left and rightarrows show

the threeoptions -square,rectangularand triangularnumbers.Pressing entershowsdifferentviews - the

shape createdusing circles,with a border,and usingsquares.finally,pressing thetab key stepsthrough thebuilding up ofthat pattern,

making it easyto see therelationshipsinvolved -

Click anywhere on this image for a video demonstration


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squarenumbers arethe sums ofodd numbers,rectangularnumbers thesum of evennumbers, and

because everyrectangle isdouble thecorrespondingtriangle, thetriangularnumbers arebuilt byadding thecountingnumbers.Pressingescape takesyou backthrough thisprogression.

Lesson 9.1: Building a Grid Pattern

We will beginby usingdrawLine tocreate asquare gridcorrespondingto the currentvalue ofn. But

first, somepracticalconsiderations- plan yourdesign andlayout! Wewould like ourgrid to liecentered onthe page. We

know how todo that. Butwe would alsolike it if the


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size of ourgrid remainedwithin thevisible page,with a bit ofwhite spacearound it. Sowe could

divide thewidth andheight of thepage up bythe value ofn(and a bitmore forwhite space).Will also needa slider for n(and moresliders tofollow!). Soset up a splitpage with aGeometrywindow andslider on oneside and ourscript windowfor the main

window.

Look closelyat the codehere. Wedefine afunction(drawArray)that takes asits arguments

the currentvalue ofn, thex and ycoordinates ofthe startingposition, andthe length andwidth of eachcell.

You will see

that thedrawLinefunction takesfour

function drawArray(number, x, y, length,height, gc)

for k = 0, number do

for m = 0, number do

gc:drawLine(

x,

y + height *m,

x + length *number,

y + height *m)

gc:drawLine(

x + length *k,

y,


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arguments:the x and ycoordinates ofstart and endpoints. We willuse onevariable (m) todefine the

horizontallines and theother (k) forthe verticallines. Again,study thecode providedto see oneway in whichto achievewhat wedesire.

Once thefunction isdefined, weneed to paintthe screen toactually see it.here wechoose to

define therequiredvariableswithin theon.paintfunction.Hence wedefine thewindow widthand height,

recall thecurrent valueofn and use itto calculatethe x and ycoordinatesfor thestarting point,and the widthand length ofthe cells. Forthe lattervalues, wedivide thewindow

x + length *k,

y + height *number)

end

end

end

function on.paint(gc)

w = platform.window:width()

h = platform.window:height()

num = var.recall("n") or 1

xval = math.floor(w/(num+4))

yval = math.floor(h/(num+4))

x = w/2 - num * xval / 2

y = h/2 - num * yval / 2

gc:setPen("thin", "smooth")

gc:setColorRGB(165,42,42)

drawArray(num, x, y, xval, yval,gc)

end


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dimensions bythe value of n(and a littlemore), thentake thelowest integervalue. Thiswill ensure

that ourmodel alwaysremainswithin thescreendimensions.Finally, we setthe color andthe pen valuesand call ourfunction,drawArray.

This producesa dynamicsquare grid,as required,controlled bythe currentvalue of avariable n

within TI-Nspire.

Lesson 9.2: Varying our Grid Pattern

So we havea squaregrid - wewould liketo have twovariationson this

theme: arectangulargrid (withone side


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than theother) anda triangulargrid. Wewill controlthese witha slidervariable we

will calltype.

First, therectangularnumbers:essentiallythe samescript asfor thesquarenumbers,but withonevariableone morethan theother.

Recall thevalue of

variabletype at thestart of ourdrawArrayfunction,then use itas the basisof a test: iftype == 1then (the

squareroutine)elseif type== 2 then(rectangles)else(triangles)end.

Thetriangle

elseif types == 2 then

for k = 0, number + 1 do

for m = 0, number do

gc:drawLine(

x,

y + height *m,

x + length *(number + 1),

y + height *m)

gc:drawLine(

x + length *


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follows -the mainvariationfrom thetwopreviousforms isthat,

instead ofthe secondvariablerunningfrom 0 or1, it beginsat thecurrentvalue for k,thus

indentingeach line toform thetriangle. Inorder toclose thefigure, itwasnecessaryto add anadditionalline at topandanother atthe rightside -hence thefour linesin thisscriptwhere the

others hadonly two.

Add theline whichdefines thevariabletypes fromtype andthe firstcondition

,

y,

x + length *k,

y + height *number)

endend

else

gc:drawLine(x, y, x + length * (number+1) -length, y )

gc:drawLine(x + length * number, y, x +length * number, y + height * number)

for k = 1, number do

for m = k, number do

gc:drawLine(x+ length*(m-1), y + height* m, x +length *number, y +

height * m)

gc:drawLine(x+ length * (k-1), y, x +length * (k-1), y + height* k)

end

end

end


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(if types== 1 then)at the startof thefunctiondefinition,and thisscript will

deliver thethreeshapesdrawnusing agrid.

In the finaltutorial inthis series

this scriptis furtherenhancedusingcircles todynamicallybuild eachof thepatterns,and ourusual arrow

keycontrolswill beadded.

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Lesson 9

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