-- bezier curve drawing functions for playdate lua
-- these are based on de Casteljau's algorithm
-- this site has a nice interactive demo to compare both types of curve: https://pomax.github.io/bezierinfo/#flattening

-- Original code source: https://gist.github.com/jaames/5de95dd62d4522b86b8409f095b3925f

-- draws a curve starting at x1,y1, ending at x3,y3, with x2,y2 being a control point that "pulls" the curve towards it
-- steps is the number of line segments to use, lower is better for performance, higher makes your curve look smoother
-- the playdate is kinda slow, so it's recommended to find a relatively low step number that looks passable enough!
function drawQuadraticBezier(x1, y1, x2, y2, x3, y3, steps)
  steps = steps or 8
  local d = 1 / steps
  local prevX = x1
  local prevY = y1
  local x, y
  for t = d, 1, d do
	x = (1 - t) ^ 2 * x1 + 2 * (1 - t) * t * x2 + t ^ 2 * x3
	y = (1 - t) ^ 2 * y1 + 2 * (1 - t) * t * y2 + t ^ 2 * y3
	playdate.graphics.drawLine(prevX, prevY, x, y)
	prevX = x
	prevY = y
  end
end

-- Create an array of lineSegments and return it, instead of drawing it 
function buildQuadraticBezier(x1, y1, x2, y2, x3, y3, steps)
  steps = steps or 8
  local lineSegments = {}
  local d = 1 / steps
  local prevX = x1
  local prevY = y1
  local x, y
  for t = d, 1, d do
	x = (1 - t) ^ 2 * x1 + 2 * (1 - t) * t * x2 + t ^ 2 * x3
	y = (1 - t) ^ 2 * y1 + 2 * (1 - t) * t * y2 + t ^ 2 * y3
	local lineSegment = playdate.geometry.lineSegment.new(prevX, prevY, x, y)
	table.insert(lineSegments, lineSegment)
	prevX = x
	prevY = y
  end
  
  return lineSegments
end

-- draws a curve starting at x1,y1, ending at x4,y4, with x2,y2 and x3,y3 being a control point that "pulls" the curve towards them
-- (nb: this is the kind of curve you make using the pen tool in vector drawing apps like Adobe Illustator!)
-- steps is the number of line segments to use, lower is better for performance, higher makes your curve look smoother
-- the playdate is kinda slow, so it's recommended to find a relatively low step number that looks passable enough!
function drawCubicBezier(x1, y1, x2, y2, x3, y3, x4, y4, steps)
  steps = steps or 12
  local d = 1 / steps
  local prevX = x1
  local prevY = y1
  local x, y
  for t = d, 1, d do
	x = (1 - t) ^ 3 * x1 + 3 * (1 - t) ^ 2 * t * x2 + 3 * (1 - t) * t ^ 2 * x3 + t ^ 3 * x4
	y = (1 - t) ^ 3 * y1 + 3 * (1 - t) ^ 2 * t * y2 + 3 * (1 - t) * t ^ 2 * y3 + t ^ 3 * y4
	playdate.graphics.drawLine(prevX, prevY, x, y)
	prevX = x
	prevY = y
  end
end

-- example usage:
function playdate.update()
  -- curves are just drawn as a bunch of lines, so you can tweak line settings like width, cap, color, etc
  gfx.setLineWidth(2)
  drawQuadraticBezier(
	10, 80,  -- curve start x,y coordinate
	200, 50, -- control x,y coordinate - your curve will be "pulled" towards this point
	390, 80, -- curve end x,y coordinate
	8 -- number of line segments used to draw the curve, 8 is probably plenty to get a smooth curve
  )
  drawCubicBezier(
	10, 160,  -- curve start x,y coordinate
	100, 110, -- first control x,y coordinate
	300, 210, -- seccond control x,y coordinate
	390, 160, -- curve end x,y coordinate
	12 -- number of line segments used to draw the curve
  )
end