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title: getSequence Function -- author: JoaoPauloVF -- desc: a function that creates numeric sequences -- script: lua -- input: mouse, keyboard -- version: 0.2 -- license: MIT -- github: https://github.com/JoaoPauloVF/My-TIC-Cartridges#readme --[[ ----Summary---- (ctrl+f and search for the chapter) Description....................:-1- getSequence :-2- Paraments......................:-3- How To Use :-4- Constants Function Code..................:-5- Demo Code :-6- Math Functions Graph Code Scales Sequence Functions List Current Sequence renderGraph() Texts Code printWithRect() printTexts() ]]-- --[[ -1--Description---- This function returns a numeric array based on a math function. -2--getSequence---- getSequence (mathFunc, [lenght=1]) --> numeric array getSequence (mathFunc, min, max, [step=1]) --> numeric array -3--Paraments---- mathFunc: A function that serves as a math function. It must get and return a number. For example, these are valid functions: function f(num) return num+1 end function f(num) return num*3 - 1 end function f(num) return 8 end lenght: The number of input values to the math function, that starts from one. For example, in the following code: f = function(num) return num*2 end list = getSequence(f, 5) the variable list will get {2, 4, 6, 8, 10} from the function. min, max, step: You also can set the starting(min), ending(max), and the increment(step) of the sequence. For instance, altering the before code: f = function(num) return num*2 end list = getSequence(f, 4, 0, -1) list will have {8, 6, 4, 2, 0} as value. -4--How To Use---- You can copy the function, bellow the following constants, to your code and use it. You can see the demo code, after the function code, for some insights too. ]]-- ----Constants---- WIDTH = 240 HEIGHT = 136 x50 = WIDTH*0.5 y50 = HEIGHT*0.5 FONT_H = 6 --Buttons UP = 0 DOWN = 1 LEFT = 2 RIGHT = 3 Z = 4 --Colors background = 15 xColor = 6 yColor = 10 pointColor = 12 tutTexts = { "LEFT/RIGHT: alter the function", "UP/DOWN: alter scale", "Z: hide or show texts" } --5--- Function Code function getSequence(mathFunc, min, max, step) local seq = {} step = step or 1 min = min or 1 if not(max) then min, max = max, min min = 1 end for num=min, max, step do table.insert(seq, mathFunc(num)) end return seq end --6--Demo Code---- --[[ Here, it stays the demo code. It consists in showing the texts and the graph of some math functions. ]]-- ----Math Functions---- --[[ The math functions in the demo. They get and returns a number. If the input number lets to an error, like zero division, the function returns nil. ]]-- function linear(num) return num end function square(num) return num*num end function cube(num) return num^3 end function squareRoot(num) if num < 0 then return nil end return math.sqrt(num) end function logarithm(num) if num < 0 then return nil end return math.log(num) end function inverse(num) if num == 0 then return nil end return 1/num end function module2(num) return num%2 end function sine(num) return math.sin(num/8) end function arcSine(num) if (num/8) > 1 and (num/8) < -1 then return nil end return math.asin(num/8) end function sineSum(num) return math.sin(num/8) + math.sin(num/4) end function cosine(num) return math.cos(num/8) end function tangent(num) return math.tan(num/8) end function randomSum(num) return math.random()+math.random() end function baseTwo(num) return 2^num end ----Graph Code---- ----Scales Sequence---- --[[ It holds the different scales applied to the graph. ]]-- scales = getSequence(baseTwo, -8, 7, 1) --#scales == 15 currScale = 8 --Update the scale function updateScale() if btnp(UP, 0, 10) or currFunc~=lastFunc then currScale = math.min(funcs[currFunc].maxSc, currScale+1) end if btnp(DOWN, 0, 10) or currFunc~=lastFunc then currScale = math.max(funcs[currFunc].minSc, currScale-1) end end ----Functions List---- --[[ It lists info to make the current graph on the screen(label, starting, ending, math function, etc.). ]]-- funcs = { { label = "f(num) = (num)", func = linear, maxSc = #scales-3, minSc = #scales//2 - 1, minNum = -x50, maxNum = x50 }, { label = "f(num) = (num*num)", func = square, maxSc = #scales//2, minSc = 1, minNum = -x50, maxNum = x50 }, { label = "f(num) = (num^3)", func = cube, maxSc = #scales//2, minSc = 1, minNum = -x50, maxNum = x50 }, { label = "f(num) = 2^num", func = baseTwo, maxSc = #scales//2, minSc = 1, minNum = 0, maxNum = x50*2 }, { label = "f(num) = sqrt(num)", func = squareRoot, maxSc = #scales-4, minSc = #scales//2, minNum = 0, maxNum = x50*2 }, { label = "f(num) = log(num)", func = logarithm, maxSc = #scales-3, minSc = #scales//2, minNum = 1, maxNum = x50*2+1 }, { label = "f(num) = (1/num)", func = inverse, maxSc = #scales, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = (num%2)", func = module2, maxSc = #scales-1, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = (sin(num/8))", func = sine, maxSc = #scales, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = (cos(num/8))", func = cosine, maxSc = #scales, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = (tan(num/8))", func = tangent, maxSc = #scales, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = (asin(num/8))", func = arcSine, maxSc = #scales, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = (sin(num/8)+sin(num/4))", func = sineSum, maxSc = #scales, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = 1", func = function(num)return 1 end, maxSc = #scales-1, minSc = #scales//2, minNum = -x50, maxNum = x50 }, { label = "f(num) = random()", func = function(num)return math.random() end, maxSc = #scales, minSc=#scales//2, minNum = -x50, maxNum = x50 }, { label="f(num) = (random()+random())", func=randomSum, maxSc=#scales, minSc=#scales//2, minNum = -x50, maxNum = x50 } } currFunc = 1 lastFunc = nil function updateCurrFunc() if btnp(RIGHT, 0, 10) then currFunc = math.min(#funcs, currFunc+1) end if btnp(LEFT, 0, 10) then currFunc = math.max(1, currFunc-1) end end ----Current Sequence---- --[[ It is created from the info of the previous list. The numbers of this sequence form the graph points. ]]-- currSeq = nil function updateSeq() currSeq = lastFunc~=currFunc and getSequence(funcs[currFunc].func, funcs[currFunc].minNum, funcs[currFunc].maxNum) or currSeq end updateSeq() ----renderGraph()---- --[[ It draws the horizontal and vertical axes and the sequence points. ]]-- function renderGraph(seq) local margin = 2 --Render horizontal line, subtitle, and numbers line( 0, y50, WIDTH, y50, xColor ) print( "num", margin, y50 - FONT_H, xColor ) for i=0, 2 do local x = i*x50+margin if i == 2 then x = x - 18 end local numValue = (i*x50)+funcs[currFunc].minNum print( string.format("%i", numValue), x, y50 + FONT_H/2, xColor, false, 1, true ) end --Render vertical line, subtitle, and numbers line( x50, 0, x50, HEIGHT, yColor ) print( "f(num)", x50 + margin, margin, yColor ) for i=0, 2 do local y = (2-i)*y50 if i == 0 then y = y - (FONT_H+margin) end print( (i-1)*HEIGHT//2, x50-12, y+margin, yColor, false, 1, true ) end --Render graph points for index, num in pairs(seq) do local x = (index-1) local y = HEIGHT/2 if num then --If num is equal nil, f(num) could allow a crash. local numScaled = num*scales[currScale] pix( x, y-numScaled, pointColor ) end end end ---Texts Code---- ----showTexts---- --[[ It shows/hides the text when pressing "Z". ]]-- showTexts = true function updateShowText() if btnp(Z, 0, 10) then showTexts = not(showTexts) end end ----printWithRect()---- --[[ This function highlights texts by printing them in a black rectangle. The text can be a string or a list of strings(to multiple-lines texts). ]]-- function printWithRect(text, x, y) --Get the text width local biggerW = nil if type(text) == "table" then biggerW = print(text[1], 0, -FONT_H) for i=2, #text do local w = print(text[i], 0, -FONT_H) biggerW = w > biggerW and w or biggerW end end local textW = biggerW or print(text, 0, -FONT_H) --Internal rectangle margin local margin = 3 local rectW = textW + 2*margin local rectH = type(text)=="table" and 1.5*(#text*FONT_H+(#text+1)*margin) or FONT_H + 2*margin --Render the rectangle rect( x, y, rectW, rectH, 0 ) --Print the text if type(text)=="table" then for i=1, #text do print( text[i], x+margin, y+1.5*(margin*i+FONT_H*(i-1)), 12 ) end else print( text, x+margin, y+margin, 12 ) end end ----printTexts()---- --It prints all the texts. function printTexts() if showTexts then --Function Label text = funcs[currFunc].label.."*"..tostring(scales[currScale]) printWithRect(text, WIDTH*0.015, HEIGHT*0.03) --Tutorial printWithRect(tutTexts, WIDTH*0.015, HEIGHT*0.6) end end ----TIC() Function---- function TIC() updateCurrFunc() updateScale() updateSeq() updateShowText() lastFunc = currFunc cls(background) renderGraph(currSeq) printTexts() end