init: tool for graphing functions and slope fields in love2d
This commit is contained in:
Devyn Freet
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{
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"runtime.version": "LuaJIT",
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"workspace.library": ["../love2d"],
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"runtime.special": {
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"love.filesystem.load": "loadfile"
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}
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}
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local function getPixelPosition(point, minPoint, maxPoint, drawBounds)
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if
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point[1] < minPoint[1]
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or point[1] > maxPoint[1]
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or point[2] < minPoint[2]
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or point[2] > maxPoint[2]
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then
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error("Point ("..point[1]..", "..point[2]..") outside the bounds ("
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..minPoint[1]..", "..minPoint[2]..") to ("..maxPoint[1]..", "..maxPoint[2]..")")
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end
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local pointBound = {maxPoint[1] - minPoint[1], maxPoint[2] - minPoint[2]}
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local pointOffset = {point[1] - minPoint[1], -point[2] - minPoint[2]}
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local position = {
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(pointOffset[1] / pointBound[1]) * drawBounds.width + drawBounds.x,
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(pointOffset[2] / pointBound[2]) * drawBounds.height + drawBounds.y
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}
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return position[1], position[2]
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end
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function GraphFunction(x, y, width, height, func)
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local points = {}
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local origin = {x = (width + x) / 2, y = (height + y) / 2}
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local neg_x, neg_y = -math.floor(origin.x), -math.floor(origin.y)
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local pos_x, pos_y = math.floor(origin.x), math.floor(origin.y)
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for i = neg_x, pos_x, 1 do
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local j = math.floor(func(i))
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if j > neg_y and j < pos_y then
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local k, l = getPixelPosition({i,j}, {neg_x,neg_y}, {pos_x,pos_y},
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{x=x,y=x,width=width,height=height})
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table.insert(points, k)
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table.insert(points, l)
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end
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end
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return points
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end
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function GetLineFromSlope(midpoint, slope, length, color)
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color = color or {1, 1, 1}
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local delta_x, delta_y
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if slope == nil then
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delta_x, delta_y = 0, length
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else
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delta_x = math.sqrt((length ^ 2) / (1 + slope ^ 2))
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delta_y = -(slope * delta_x)
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end
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local x1 = midpoint.x - delta_x / 2
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local y1 = midpoint.y - delta_y / 2
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local x2 = x1 + delta_x
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local y2 = y1 + delta_y
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return {
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p1 = {x = x1, y = y1},
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p2 = {x = x2, y = y2},
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midpoint = midpoint,
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color = color
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}
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end
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@@ -0,0 +1,15 @@
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local function factorial(n)
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if n <= 2 then
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return n
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end
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return n * factorial(n-1)
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end
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local function calculate_e(terms)
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local e = 1
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for i = 1, terms do
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e = e + 1 / factorial(i)
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end
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return e
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end
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return calculate_e(10)
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@@ -0,0 +1,165 @@
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local utf8 = require("utf8")
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require("coordinates")
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-- to use with functions involving e
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--local e = require("eulerNumber")
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local function differential(x, y)
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return 2*y
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end
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local function loadWindow()
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love.window.setTitle("Slope Fields")
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love.keyboard.setKeyRepeat(true)
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end
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love.load = loadWindow
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local function drawLine(line)
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love.graphics.setColor(unpack(line.color))
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love.graphics.line(line.p1.x, line.p1.y, line.p2.x, line.p2.y)
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love.graphics.circle("fill", line.midpoint.x, line.midpoint.y, 4)
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end
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local width, height = love.window.getMode()
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local boxMargin = 10
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local boxHeight = math.max(height / 12, 20)
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local textbox = {
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x = boxMargin,
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y = height - (boxHeight + boxMargin),
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width = width - 2 * boxMargin,
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height = boxHeight,
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padding = 5,
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text = 'x',
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active = false,
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colors = {
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background = {0.2, 0.2, 0.2},
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text = {0.9, 0.9, 0.9}
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}
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}
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local graphbox = {
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x = boxMargin,
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y = boxMargin,
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width = width - 2 * boxMargin,
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height = textbox.y - 2 * boxMargin,
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colors = {
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background = {0.2, 0.2, 0.2}
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}
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}
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local center = {
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x = graphbox.x + graphbox.width / 2,
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y = graphbox.y + graphbox.height / 2
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}
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local scale = 5
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local xScale, yScale
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local step
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if graphbox.width <= graphbox.height then
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step = graphbox.width / (2 * (scale+1))
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xScale = scale
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yScale = math.floor(graphbox.height / (2 * step)) - 1
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else
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step = graphbox.height / (2 * (scale+1))
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yScale = scale
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xScale = math.floor(graphbox.width / (2 * step)) - 1
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end
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local lines = {
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grid = {},
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axes = {
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x = GetLineFromSlope(center, 0, graphbox.width),
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y = GetLineFromSlope(center, nil, graphbox.height)
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},
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field = {}
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}
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local xpos, ypos = graphbox.x, graphbox.y + graphbox.height
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for y = -yScale, yScale, 1 do
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ypos = ypos - step
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lines.grid[{y=y}] = GetLineFromSlope({x = center.x, y = ypos}, 0, graphbox.width, {0.3, 0.3, 0.3})
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end
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for x = -xScale, xScale, 1 do
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xpos = xpos + step
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lines.grid[{x=x}] = GetLineFromSlope({x = xpos, y = center.y}, nil, graphbox.height, {0.3, 0.3, 0.3})
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ypos = graphbox.y + graphbox.height
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for y = -yScale, yScale, 1 do
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ypos = ypos - step
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lines.field[{x, y}] = GetLineFromSlope({x = xpos, y = ypos}, differential(x,y), 50, {0, 0.5, 1})
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end
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end
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local function func(x)
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return x^2
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end
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local points = GraphFunction(graphbox.x, graphbox.y, graphbox.width, graphbox.height, func)
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local function drawScene()
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love.graphics.setColor(unpack(graphbox.colors.background))
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love.graphics.rectangle('fill',
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graphbox.x, graphbox.y,
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graphbox.width, graphbox.height,
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4, 4)
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love.graphics.setColor(unpack(textbox.colors.background))
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love.graphics.rectangle('fill',
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textbox.x, textbox.y,
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textbox.width, textbox.height,
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4, 4)
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love.graphics.setColor(unpack(textbox.colors.text))
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love.graphics.printf(textbox.text,
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textbox.x + textbox.padding, textbox.y + textbox.padding,
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textbox.width, 'left', 0, 2, 2)
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for _, line in pairs(lines.grid) do
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drawLine(line)
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end
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for _, line in pairs(lines.axes) do
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drawLine(line)
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end
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for _, line in pairs(lines.field) do
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drawLine(line)
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end
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if points ~= nil then
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love.graphics.setColor(0,1,0)
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love.graphics.points(points)
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end
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end
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love.draw = drawScene
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local function textboxinput(text)
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if textbox.active and string.match(text,"[xy+%-%/*%^%d()]") then
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textbox.text = textbox.text .. text
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end
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end
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love.textinput = textboxinput
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local function keypress(key)
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if key == "backspace" then
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local byteoffset = utf8.offset(textbox.text, -1)
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if byteoffset then
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textbox.text = string.sub(textbox.text, 1, byteoffset - 1)
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end
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return
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end
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if key == "return" then
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textbox.active = false
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end
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end
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love.keypressed = keypress
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local function mousepress(x, y)
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if
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x >= textbox.x and
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x <= textbox.x + textbox.width and
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y >= textbox.y and
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y <= textbox.y + textbox.height
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then
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textbox.active = true
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elseif textbox.active then
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textbox.active = false
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end
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end
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love.mousepressed = mousepress
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