bezier.lua

bezier.lua

--[[---------------------------------------------------------
	Name: BezierLerp( frac, points )
	Desc: Lerp point between points with bezier algorithms
-----------------------------------------------------------]]

function math.BezierLerp( frac, points )
	local mu = frac * frac
	local mum = 1 - frac
	local mum2 = mum * mum

	if ( points[4] ) then -- Cubic
		return mum2 * mum * points[1] + 3 * mum2 * frac * points[2] + 3 * mum * mu * points[3] + mu * frac * points[4]
	elseif ( points[3] ) then -- Quadratic
		return mum2 * points[1] + 2 * mum * frac * points[2] + mu * points[3]
	else -- Linear
		return mum * points[1] + frac * points[2]
	end
end

--[[---------------------------------------------------------
	Name: BezierSpline( points, steps, spline )
	Desc: Calc spline between points with bezier algorithms
-----------------------------------------------------------]]

do
	local function GetDistance( p1, p2 )
		return math.sqrt( ( p2.x - p1.x ) ^ 2 + ( p2.y - p1.y ) ^ 2 )
	end

	local bezierStepSize = 1 / ( math.pi * 10 )

	function math.BezierSpline( points, steps, spline )
		if steps == nil then
			local distance = GetDistance( points[1], points[2] )
			if points[3] then
				distance = distance + GetDistance( points[2], points[3] )
			end
			if points[4] then
				distance = distance + GetDistance( points[3], points[4] )
			end

			steps = math.max( 1, math.floor( distance * bezierStepSize ) )
		end

		spline = spline or {}
		local i = 1

		for frac = 0, 1, 1 / steps do
			spline[ i ] = math.BezierLerp( frac, points )
			i = i + 1
		end

		return spline
	end
end

local function bbox(points)
	local mins, maxs = Vector(math.huge, math.huge), Vector()

	for _, point in ipairs(points) do
		mins.x, mins.y = math.min(mins.x, point.x), math.min(mins.y, point.y)
		maxs.x, maxs.y = math.max(maxs.x, point.x), math.max(maxs.y, point.y)
	end

	return mins, maxs - mins
end

local function test(name, points)
	local spline = math.BezierSpline(points)

	return function()
		local mins, maxs = bbox(points)
		draw.SimpleText(name, "DermaDefault", mins.x + maxs.x * 0.5, mins.y, nil, TEXT_ALIGN_CENTER, TEXT_ALIGN_BOTTOM)

		-- draw bbox
		surface.SetDrawColor(0, 0, 0, 150)
		surface.DrawRect(mins.x, mins.y, maxs.x, maxs.y)

		-- draw points
		surface.SetDrawColor(0, 255, 0)

		for i, point in ipairs(points) do
			surface.DrawRect(point.x - 4, point.y - 4, 8, 8)
			draw.SimpleText(i, "DermaDefault", point.x + 4, point.y + 4)
		end

		-- draw spline
		surface.SetDrawColor(255, 0, 0)

		for _, point in ipairs(spline) do
			surface.DrawRect(point.x - 2, point.y - 2, 4, 4)
		end

		-- draw moving point
		local frac = RealTime() % 1
		local point = math.BezierLerp(frac, points)

		surface.SetDrawColor(255, 255, 0)
		surface.DrawRect(point.x - 4, point.y - 4, 8, 8)
	end
end

do -- tests
	local x, y = 32, 32

	local Cubic = test("Cubic", {
		Vector(x, y),
		Vector(x + 256, y),
		Vector(x + 256, y + 256),
		Vector(x, y + 256),
	})

	x = x + 320

	local Quadratic = test("Quadratic", {
		Vector(x, y),
		Vector(x + 256, y),
		Vector(x, y + 256)
	})

	x = x + 320

	local Linear = test("Linear", {
		Vector(x, y),
		Vector(x + 256, y + 256)
	})

	hook.Add("HUDPaint", "bezier tests", function()
		Cubic()
		Quadratic()
		Linear()
	end)
end