Bezier Stuff

--[[
    Class: Bezier
    Author: Wasil Janssen a.k.a. Creator
]]--

local Engine = ...

function splineMax(Sx, helpA, Ex)

    helpC = Sx - helpA
    helpD = helpC + Ex - helpA
    max=Sx

    if Ex>Sx then
        max = Ex
    end
    if helpD ~= 0 then
        F=helpC/helpD
        if F>0 and F<1 then
            X=Sx-helpC*F;
            if X>max then max=X end
        end
    end
    return max
end

function splineMin(Sx, helpA, Ex)

    helpC = Sx - helpA
    helpD = helpC + Ex - helpA
    max=Sx

    if Ex<Sx then
        max = Ex
    end
    if helpD ~= 0 then
        F=helpC/helpD
        if F>0 and F<1 then
            X=Sx-helpC*F;
            if X<max then max=X end
        end
    end
  return max
end

--print = Internal.Debug.print

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

    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 bMaxY = splineMax(y1,y2,y3)
    local bMinY = splineMin(y1,y2,y3)

    local bMaxX = splineMax(x1,x2,x3)
    local bMinX = splineMin(x1,x2,x3)

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

    --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
    self.getX = ya ~= 0 and function(y)
        if y > maxY or y < minY then
            return
        end
        if y == y1 or y == bMaxY or y == bMinY or y == y3 then
            y = y + 0.001
        end
        local c = y1 - y
        local b = yb
        local a = ya
        local discriminant = (b^2 - 4*a*c )

        if discriminant < 0 then
            return
        else
            if discriminant == 0 then
                local index1 = -b/yaByTwo
                if 0 < index1 and index1 < 1 then
                    return (1-index1)^2*x1+2*(1-index1)*index1*x2+index1^2*x3
                end
            else
                local theSQRT = math.sqrt(discriminant)
                local index1, index2 = (-b -theSQRT)/yaByTwo, (-b +theSQRT)/yaByTwo
                if 0 < index1 and index1 < 1 then
                    if 0 < index2 and index2 < 1 then
                        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
                    else
                        return (1-index1)^2*x1+2*(1-index1)*index1*x2+index1^2*x3
                    end
                elseif 0 < index2 and index2 < 1 then
                    return (1-index2)^2*x1+2*(1-index2)*index2*x2+index2^2*x3
                end
            end
        end
    end or function(y)
        if y > maxY or y < minY or yb == 0 then
            return
        end
        if y == y1 or y == bMaxY or y == bMinY or y == y3 then
            y = y + 0.001
        end
        index1 = -(y1-y)/yb
        if 0 < index1 and index1 < 1 then
            return (1-index1)^2*x1+2*(1-index1)*index1*x2+index1^2*x3
        end
    end
    --Get y of patricular x
    function self.getY(x)
        if x > maxX or x < minX then
            return
        end
        if maxX == minX and x == minX then
            return minY, maxY
        end
        local index1, index2, buffer1, buffer2
        local a = (x1 - x)
        if a == 0 then
            return
        end
        local b = xb
        local c = xc
        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

    function self.ind(u)
        ind = u
    end

    function self.info()
        print("maxY",maxY)
        print("minY",minY)
        print("yb",yb)
        print("ya",ya)
        print("x1",x1,"y1",y1)
        print("x2",x2,"y2",y2)
        print("x3",x3,"y3",y3)
        print("bMaxY",bMaxY)
        print("bMinY",bMinY)
        print("maxDiscri",yb^2 - 4*ya*(y1 - bMaxY))
        print("minDiscri",yb^2 - 4*ya*(y1 - bMinY))
    end
    --Self
    return self
end

return Bezier