a function to draw a triangle from three vertexs, don't to traversal every point restrict in the rectangle

draw_triangle_shape.lua

--[[
计算斜率：0和无穷大的情况简化处理了
]]
function get_slope(nPosX1, nPosY1, nPosX2, nPosY2, nPosX3, nPosY3)
	local nSlope1, nSlope2, nSlope3
	if nPosX1 == nPosX2 then
		nSlope1 = 99999999  --设置一个近似无穷斜率
	else
		nSlope1 = (nPosY1 - nPosY2) / (nPosX1 - nPosX2)
	end
	if nPosX2 == nPosX3 then
		nSlope2 = 99999999
	else
		nSlope2 = (nPosY2 - nPosY3) / (nPosX2 - nPosX3)
	end
	if nPosX3 == nPosX1 then
		nSlope3 = 99999999
	else
		nSlope3 = (nPosY3 - nPosY1) / (nPosX3 - nPosX1)
	end
	if nSlope1 == 0 then
		nSlope1 = 0.0000001
	end
	if nSlope2 == 0 then
		nSlope2 = 0.0000001
	end
	if nSlope3 == 0 then
		nSlope3 = 0.0000001
	end
	return nSlope1, nSlope2, nSlope3
end
--[[
获取最长边对应的顶点以及边判断的顺序
]]
function get_max_angle_pos(tbLine1, tbLine2, tbLine3)
	local nMaxLine = math.max(tbLine1[1], tbLine2[1], tbLine3[1])
	local tbStartPos = {}
	local tbSlopeJudge = {}
	if nMaxLine == tbLine1[1] then
		tbStartPos = tbLine1[2]
		table.insert(tbSlopeJudge, tbLine2[3])  --后期简化代码
		table.insert(tbSlopeJudge, tbLine3[3])
		table.insert(tbSlopeJudge, tbLine1[3])
	elseif nMaxLine == tbLine2[1] then
		tbStartPos = tbLine2[2]
		table.insert(tbSlopeJudge, tbLine1[3])
		table.insert(tbSlopeJudge, tbLine3[3])
		table.insert(tbSlopeJudge, tbLine2[3])
	else
		tbStartPos = tbLine3[2]
		table.insert(tbSlopeJudge, tbLine1[3])
		table.insert(tbSlopeJudge, tbLine2[3])
		table.insert(tbSlopeJudge, tbLine3[3])
	end
	return tbStartPos, tbSlopeJudge
end
--[[
获取起始点对应的增长方向
]]
function get_add_dir(tbStartPos, nMaxX, nMinX, nMaxY, nMinY)
	local nAddX = 0
	local nAddY = 0
	if tbStartPos[1] == nMaxX then
		nAddX = -1
	elseif tbStartPos[1] == nMinX then
		nAddX = 1
	end
	if tbStartPos[2] == nMaxY then
		nAddY = -1
	elseif tbStartPos[2] == nMinY then
		nAddY = 1
	end
	return nAddX, nAddY
end
--[[
神奇的函数：计算出对应点与三角形三条线相交的交点，并决定正确的范围
]]
function getIntersection(tbSlopeJudge, nPoint, nDir, nMin, nMax)
	local tbLimit = {}
	local nMinC, nMaxC
	local nC1, nC2, nC3 --交点
	if (nDir == 1) or (nDir == 2) then  --x
		nC1 = math.floor(tbSlopeJudge[1][1] * nPoint + tbSlopeJudge[1][2])
		nC2 = math.floor(tbSlopeJudge[2][1] * nPoint + tbSlopeJudge[2][2])
		nC3 = math.floor(tbSlopeJudge[3][1] * nPoint + tbSlopeJudge[3][2])
	elseif (nDir == 3) or (nDir == 4) then  --y
		nC1 = math.floor((nPoint - tbSlopeJudge[1][2]) / tbSlopeJudge[1][1])
		nC2 = math.floor((nPoint - tbSlopeJudge[2][2]) / tbSlopeJudge[2][1])
		nC3 = math.floor((nPoint - tbSlopeJudge[3][2]) / tbSlopeJudge[3][1])
	end
	nMinC, nMaxC = math.min(nC1, nC2), math.max(nC1, nC2)
	--用矩形范围加以限制，保证点不超出矩形区域
	nMinC = math.max(nMinC, nMin)
	nMaxC = math.min(nMaxC, nMax)
	--与发散点所对的边的交点如果在这个限制范围内，就截短范围
	if (nC3 >= nMinC) and (nC3 < nMaxC) then
		if tbSlopeJudge[3][1] > 0 then   --正斜率且正向增长就替换最大范围，负斜率负向增长就替换最小范围
			if math.fmod(nDir, 2) == 1 then
				nMinC = nC3
			else
				nMaxC = nC3
			end
		elseif tbSlopeJudge[3][1] < 0 then
			if math.fmod(nDir, 2) == 1 then
				nMaxC = nC3
			else
				nMinC = nC3
			end
		end
	end
	table.insert(tbLimit, nMinC)
	table.insert(tbLimit, nMaxC)
	return tbLimit
end
--[[
按照方向来填充三角形所包含的点
]]
function fill_triangle_point(nAddX, nAddY, tbStartPos, tbSlopeJudge, nMinY, nMaxY, nMinX, nMaxX)
	local tbTrianglePos = {}
	local nDir = 0
	if nAddX ~= 0 then
		--决定x的扩展范围
		local nLimitX = 0
		if nAddX > 0 then
			nLimitX = nMaxX
			nDir = 1
		elseif nAddX < 0 then
			nLimitX = nMinX
			nDir = 2
		end
		for x = tbStartPos[1], nLimitX, nAddX do
			--找出x增加后y被三角形所夹的范围，范围内的点都在三角形内
			local tbNode = getIntersection(tbSlopeJudge, x, nDir, nMinY, nMaxY)
			for y = tbNode[1], tbNode[2] do
				table.insert(tbTrianglePos, {x, y})
			end
		end
	elseif nAddY ~= 0 then
		--决定y的扩展范围
		local nLimitY = 0
		if nAddY > 0 then
			nLimitY = nMaxY
			nDir = 3
		elseif nAddY < 0 then
			nLimitY = nMinY
			nDir = 4
		end
		for y = tbStartPos[2], nLimitY, nAddY do
			--找出y增加后x被三角形所夹的范围，范围内的点都在三角形内
			local tbNode = getIntersection(tbSlopeJudge, y, nDir, nMinX, nMaxX)
			for x = tbNode[1], tbNode[2] do
				table.insert(tbTrianglePos, {x, y})
			end
		end
	end
	return tbTrianglePos
end
--[[
绘制三角形区域
]]
function create_triangle(tbPos1, tbPos2, tbPos3)
	local nPosX1, nPosY1 = unpack(tbPos1)
	local nPosX2, nPosY2 = unpack(tbPos2)
	local nPosX3, nPosY3 = unpack(tbPos3)
	--找出包围三角形的最小矩形
	local nMaxX = math.max(nPosX1, nPosX2, nPosX3)
	local nMinX = math.min(nPosX1, nPosX2, nPosX3)
	local nMaxY = math.max(nPosY1, nPosY2, nPosY3)
	local nMinY = math.min(nPosY1, nPosY2, nPosY3)
	--求出每条边的斜率并处理斜率为无穷和0的情况（有优化的方案可以减小此情况下的计算量）
	local nSlope1, nSlope2, nSlope3 = get_slope(nPosX1, nPosY1, nPosX2, nPosY2, nPosX3, nPosY3)
	--直线方程：y = kx + b
	local nB1 = nPosY1 - nSlope1 * nPosX1
	local nB2 = nPosY2 - nSlope2 * nPosX2
	local nB3 = nPosY3 - nSlope3 * nPosX3
	--计算每条边的长度
	local nLine1 = math.sqrt((nPosY2 - nPosY1)^2 + (nPosX2 - nPosX1)^2) --pos3
	local nLine2 = math.sqrt((nPosY3 - nPosY2)^2 + (nPosX3 - nPosX2)^2) --pos1
	local nLine3 = math.sqrt((nPosY1 - nPosY3)^2 + (nPosX1 - nPosX3)^2) --pos2
	--找到最长边对应的那个顶点作为发散起始点
	local tbStartPos, tbSlopeJudge = get_max_angle_pos({nLine1, tbPos3, { nSlope1, nB1 }},
	               {nLine2, tbPos1, { nSlope2, nB2 }},
	               {nLine3, tbPos2, { nSlope3, nB3 }})
	--判断起始点所处的位置，决定发散的方向
	local nAddX, nAddY = get_add_dir(tbStartPos, nMaxX, nMinX, nMaxY, nMinY)
	--终于到正文了，根据发散方向依次计算在三角形内的点
	return fill_triangle_point(nAddX, nAddY, tbStartPos, tbSlopeJudge, nMinY, nMaxY, nMinX, nMaxX)
end