这个需求来自于工作中的一个需求
两个城池之间的路径是美术事先画好的,武将需要沿着画好的曲线行进
经过查找资料,发现了这篇文章
用到了下面这个公式：
阶贝塞尔曲线可如下推断。给定点P0、P1、…、Pn，其贝塞尔曲线即
高阶曲线为建构高阶曲线，便需要相应更多的中介点。对于三次曲线，可由线性贝塞尔曲线描述的中介点Q0、Q1、Q2，和由二次曲线描述的点R0、R1所建构：
三次贝塞尔曲线
对于四次曲线，可由线性贝塞尔曲线描述的中介点Q0、Q1、Q2、Q3，由二次贝塞尔曲线描述的点R0、R1、R2，和由三次贝塞尔曲线描述的点S0、S1所建构：
四次贝塞尔曲线
更复杂的:
五次贝塞尔曲线
以下为lua的实现方式,参考了上文中的c++算法,并没有考虑在极为高阶的情况下的性能问题
代码基于quick-cocos2d-x 2.2.5编写(谁叫他快呢)
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-- -- Author: superyyl -- Date: 2014-08-22 17:31:48 -- tool = {} -- float to int function tool.toint(n) local s = tostring(n) local i, j = s:find('%.') if i then return tonumber(s:sub(1, i-1)) else return n end end -- 获取在ccnode屏幕的位置 function tool.getPositionInScreen(node) if not node then return 0,0 end local x,y = node:getPosition() local parent = node:getParent() while parent do local px,py = parent:getPosition() if not parent:isIgnoreAnchorPointForPosition() then local anchorPoint = parent:getAnchorPointInPoints() px = px - anchorPoint.x py = py - anchorPoint.y end x =x + px y = y + py parent = parent:getParent() end return x, y end -- 检查触摸x,y是否在摸个node上 function tool.checkIfTouch(sprite, x, y) if not sprite then return false end local px, py = tool.getPositionInScreen(sprite) local anchorPoint = sprite:getAnchorPointInPoints() local px = px - anchorPoint.x local py = py - anchorPoint.y local w = sprite:getContentSize().width local h = sprite:getContentSize().height local boundingBox = CCRect:new(px,py,w,h) if boundingBox:containsPoint(ccp(x,y)) then return true else return false end end --阶乘 function factorial(n) local result = 1 for i=1,n,1 do result = result * i end return result end --杨辉三角 function pascalTriangleRatio(n,i) return factorial(n)/(factorial(i)*factorial(n-i)) end --x的y次幂 function powf(x,y) if y == 0 then return 1 end local result = 1 for i=1,y,1 do result = result * x end return result end --贝塞尔 --[[ @param p 控制点table @param t ]] function bezieerat(p,t) local px,py = 0,0 local n = #p - 1 for i=0,n do local ratio = pascalTriangleRatio(n,i) px = px + ratio * p[i+1].x * powf(t,i) * powf(1-t, n-i) py = py + ratio * p[i+1].y * powf(t,i) * powf(1-t, n-i) end return ccp(px,py) end |
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-- -- Author: superyyl -- Date: 2014-08-27 11:44:08 -- local General = class("General",function() return display.newSprite("res/ui/circle.png") end) General.STATE = { IDLE = 0, MOVE = 1 } function General:ctor() self:registerScriptHandler(function(e) if e == "enter" then self:onEnter() elseif e == "exit" then self:onExit() end end) self.state = General.STATE.IDLE end function General:startAction(p,t) self.controlPos = {} self.totalTime = t self.state = General.STATE.MOVE for idx,pos in pairs(p) do local newPos = ccp(pos.x,pos.y) self.controlPos[#self.controlPos+1] = newPos end self.number = #self.controlPos self.t = 0 end function General:update(dt) if self.state == General.STATE.MOVE then self.t = self.t + dt local p = bezieerat(self.controlPos, self.t/self.totalTime) self:setPosition(p) if self.t > self.totalTime then self.state = General.STATE.IDLE self:startAction(self.controlPos, self.totalTime) end end end function General:onEnter() self.updateSchedulerEntry = CCDirector:sharedDirector():getScheduler():scheduleScriptFunc(handler(self,self.update), 0, false) end function General:onExit() if self.updateSchedulerEntry then CCDirector:sharedDirector():getScheduler():unscheduleScriptEntry(self.updateSchedulerEntry) end end return General |
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-- -- Author: superyyl -- Date: 2014-08-27 10:20:02 -- local TestScene = class("TestScene", function() return display.newScene("TestScene") end) function TestScene:ctor() self.layer = CCLayerColor:create(ccc4(255, 255, 255, 255)) self:addChild(self.layer) self.pos = {} self.points = {} self.layer:registerScriptTouchHandler(handler(self,self.onTouch), false) self.layer:setTouchEnabled(true) local delete = CCControlButton:create( CCLabelTTF:create("删除最后一个节点", "Thonburi", 24), CCScale9Sprite:create("res/ui/btn_default_normal.png") ) delete:setPreferredSize(CCSize(200, 80)) delete:setPosition(120,display.height-60) delete:addHandleOfControlEvent( handler(self,self.onDeleteClick), CCControlEventTouchUpInside ) self:addChild(delete) end function TestScene:onDeleteClick() table.remove(self.pos,#self.pos) self:refresh() end function TestScene:onTouch(e,x,y) if e == "began" then self.touchLocation = ccp(x,y) self.dragPoint = nil self.dragIndex = nil for idx,point in pairs(self.points) do if tool.checkIfTouch(point,x,y) then self.dragPoint = point self.dragIndex = idx print("self.dragIndex",self.dragIndex) end end return true elseif e == "moved" then if self.dragPoint then local sprite = self.dragPoint local pos = ccp(sprite:getPositionX()+x-self.touchLocation.x,sprite:getPositionY()+y-self.touchLocation.y) self.dragPoint:setPosition(pos) self.touchLocation = ccp(x,y) end elseif e == "ended" then if self.dragPoint then self.pos[self.dragIndex] = ccp(x,y) self.dragPoint = nil self.dragIndex = nil self:refresh() else local pos = ccp(x,y) local distance = ccpDistance(self.touchLocation, pos) if distance < 25 then self.pos[#self.pos+1] = pos end self:refresh() end end end function TestScene:refresh() self.layer:removeAllChildrenWithCleanup(true) self.points = {} for i,pos in pairs(self.pos) do local point = CCSprite:create("res/ui/point.png") point:setPosition(pos) self.layer:addChild(point) local label = CCLabelTTF:create(tostring(i), "Thonburi", 20) label:setColor(ccc3(0, 0, 0)) label:setPosition(point:getContentSize().width/2,point:getContentSize().height+10) point:addChild(label) self.points[#self.points+1] = point end if #self.pos > 1 then self.general = require("app.models.General").new() self.general:setPosition(self.pos[1]) self.layer:addChild(self.general) self.general:startAction(self.pos, 4) local controlPos = {} for idx,pos in pairs(self.pos) do local newPos = ccp(pos.x,pos.y) controlPos[#controlPos+1] = newPos end local node = CCDrawNode:create() self.layer:addChild(node) local tracePoints = {} for t=0,1,0.001 do local point = bezieerat(controlPos, t) node:drawDot(point, 2, ccc4f(0, 255, 0, 128)) tracePoints[#tracePoints+1] = {} tracePoints[#tracePoints].point = point tracePoints[#tracePoints].percent = t end local distance = 0 for i=1,#tracePoints-1,1 do local p1 = tracePoints[i] local p2 = tracePoints[i+1] local d = ccpDistance(p1.point, p2.point) distance = distance + d end local len = 30 local pointInfo = {} local count = tool.toint(distance / len) local mod = distance % len len = len + mod / count pointInfo[1] = tracePoints[1] local remain = len for i=1,#tracePoints-1,1 do local p1 = tracePoints[i] local p2 = tracePoints[i+1] local d = ccpDistance(p1.point, p2.point) remain = remain - d if remain <= 0 then pointInfo[#pointInfo+1] = p2 remain = remain + len end end for idx,p in pairs(pointInfo) do local point = CCSprite:create("res/ui/trace.png") point:setPosition(p.point) print("percent:"..p.percent) self.layer:addChild(point) end print(string.format("长度:%s#%s#%s#%s",distance,count,mod,len)) end end return TestScene |
最后放一张效果图
