Bezier

--[[
    Class: Bezier
    Author: Me a.k.a. Creator
]]--

local Internal, Nano, NanoPath, ApplicationPath, ClassPath = ...

local function Bezier(x1,y1,x2,y2,x3,y3)
    --Private
    local x1 = x1
    local y1 = y1
    local x2 = x2
    local y2 = y2
    local x3 = x3
    local y3 = y3

    local maxY = y1 > y2 and (y1 > y3 and y1 or y3) or y2 > y3 and y2 or y3
    local minY = y1 < y2 and (y1 < y3 and y1 or y3) or y2 < y3 and y2 or y3

    local maxX = x1 > x2 and (x1 > x3 and x1 or x3) or x2 > x3 and x2 or x3
    local minX = x1 < x2 and (x1 < x3 and x1 or x3) or x2 < x3 and x2 or x3

    local xa = (x3 - 2*x2 + x1)
    local xb = 2*(x2 - x1)
    local ya = (y3 - 2*y2 + y1)
    local yb = 2*(y2 - y1)

    --Public
    local self = {}

    --Render
    self.render = function(resolution)
        local path = {}
        local num = 1
        for index=0, 1, 1/resolution do
            path[num] = {(1-index)^2*x1+2*(1-index)*index*x2+index^2*x3, (1-index)^2*y1+2*(1-index)*index*y2+index^2*y3}
            num = num + 1
        end
        return path
    end
    --Point
    function self.point(index)
        return {(1-index)^2*x1+2*(1-index)*index*x2+index^2*x3, (1-index)^2*y1+2*(1-index)*index*y2+index^2*y3}
    end
    --Get x of patricular y
    function self.getX(y,a,b)
        if maxY == minY and y == minY then
            return minX, maxX
        end
        local a = ya
        local b = yb
        local c = (y1 - y)
        local discriminant = b^2 - 4*a*c
        if discriminant < 0 then
            return
        else
            local aByTwo = 2*a
            local theSQRT = math.sqrt(discriminant)
            --print("Discriminant: ",discriminant)
            if discriminant == 0 then
                local index1 = -b/aByTwo
                --print("Incides (1): ",index1)
                return (1-index1)^2*x1+2*(1-index1)*index1*x2+index1^2*x3
            else
                local index1, index2 = (-b - theSQRT)/aByTwo, (-b + theSQRT)/aByTwo
                --print("Incides (2): ",index1,index2)
                return (1-index1)^2*x1+2*(1-index1)*index1*x2+index1^2*x3, (1-index2)^2*x1+2*(1-index2)*index2*x2+index2^2*x3
            end
        end
    end
    --Get y of patricular x
    function self.getY(x,a,b)
        if maxX == minX and x == minX then
            return minY, maxY
        end
        local a = xa
        local b = xb
        local c = (x1 - x)
        local discriminant = b^2 - 4*a*c
        if discriminant < 0 then
            return
        else
            local aByTwo = 2*a
            local theSQRT = math.sqrt(discriminant)
            if discriminant == 0 then
                local index1 = -b/aByTwo
                return (1-index1)^2*y1+2*(1-index1)*index1*y2+index1^2*y3
            else
                local index1, index2 = (-b - theSQRT)/aByTwo, (-b + theSQRT)/aByTwo
                return (1-index1)^2*y1+2*(1-index1)*index1*y2+index1^2*y3, (1-index2)^2*y1+2*(1-index2)*index2*y2+index2^2*y3
            end
        end
    end
    --Scanline render
    function self.scanRender()
        local path = {}
        local counter = 1
        local fX, sX
        local a = (y3 - 2*y2 + y1)
        local b = 2*(y2 - y1)
        for i=minY, maxY do
            fX, sX = self.getX(i,a,b)
            if fX then
                path[counter] = fX
                path[counter+1] = i
                counter = counter + 2
                if sX then
                    path[counter] = sX
                    path[counter+1] = i
                    counter = counter + 2
                end
            end
        end
        return path
    end
    --More efficient
    --Self
    return self
end

if not Internal.Graphics then
    Internal.Graphics = {}
end

Internal.Graphics.Bezier = Bezier

Nano.Bezier = Bezier