415 lines
15 KiB
Plaintext
415 lines
15 KiB
Plaintext
/*
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文件名:MathClass.nut
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路径:System/BaseTool/MathClass.nut
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创建日期:2024-05-10 16:02
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文件用途:数学库
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*/
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class Math {
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function getDirectionToTargetX(objX, x) {
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if (objX > x)
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return 0;
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else
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return 1;
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}
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/*
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* @函数作用: 取随机值 左闭右闭
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* @参数 name
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* @返回值
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*/
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function Rand(Min, Max) {
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local In = rand();
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local Ret = (Min + (Max - Min + 1) * (In / (RAND_MAX + 1).tofloat())).tointeger();
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return Ret;
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}
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function getCollisionByObjBox(obj, box) {
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local x = obj.X;
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local y = obj.Y;
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local z = obj.Z;
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local ArrBuf = [];
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if (obj.Direction == 1) {
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local pleft = [x + box[0], y + box[1], z + box[2]];
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local pright = [x + box[0] + box[3], y + box[1] + box[4], z + box[2] + box[5]];
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ArrBuf.extend(pleft);
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ArrBuf.extend(pright);
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} else {
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local pleft = [x - box[0], y + box[1], z + box[2]];
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local pright = [x - box[0] - box[3], y + box[1] + box[4], z + box[2] + box[5]];
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ArrBuf.extend(pleft);
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ArrBuf.extend(pright);
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}
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return ArrBuf;
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}
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function GetDistancePos(startX, direction, offsetX) {
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if (direction == 0)
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return startX - offsetX;
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return startX + offsetX;
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}
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//通过坐标获得两点旋转角度
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function getRorateAngleByCurrentPos(x1, y1, z1, x2, y2, z2) {
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return 0;
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}
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//贝塞尔曲线构造的抛物线运动，支持开始z轴(obj,curT,lastZ,moveT)
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function sq_BParabola(currentT, maxT, initZPos, jumpHeight, lastZPos) {
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local z = getBeizeri(currentT, maxT, initZPos, initZPos + jumpHeight, initZPos + jumpHeight, lastZPos);
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return z.tointeger();
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}
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//获得抛物线(不支持开始z轴)
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function sq_Parabola(x, b, c) {
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local a = (-b.tofloat() * 4) / (c.tofloat() * c.tofloat());
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return a.tofloat() * (x.tofloat() - c.tofloat() / 2) * (x.tofloat() - c.tofloat() / 2) + b.tofloat();
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}
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//获得两点之间平面的距离.
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function Get2D_Distance(x1, y1, x2, y2) {
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local offsetX = x1 - x2;
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local offsetY = (y1 - y2) * 0.29;
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return sqrt(offsetX * offsetX + offsetY * offsetY);
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}
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//判断给定的角度是否在startA和endA角度之间(startA与endA形成的锐角内)
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function CheckAngleIsInArea(judge, startA, endA) {
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if (startA< 0)
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startA = startA + 360.0;
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if (endA< 0)
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endA = endA + 360.0;
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if (startA > 360.0)
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startA = startA - 360.0;
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if (endA > 360.0)
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endA = endA - 360.0;
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if (startA > 0 && startA< 90 && endA > 270 && endA< 360) {
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if (judge > 270 && judge< 360) {
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if (endA< judge && judge< startA + 360)
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return true;
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} else if (judge< 90) {
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if (endA< judge + 360 && judge + 360< startA + 360)
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return true;
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}
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} else {
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if (endA > judge && judge > startA)
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return true;
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}
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return false;
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}
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//弧度制转为角度制
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function toDegree(x) {
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return x * 57.29577;
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}
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//角度转为弧度
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function toRadian(x) {
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return x * 0.01745;
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}
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//立方体与立方体之间碰撞 暂未测试
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function CubeAndCubeCollection(c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ) {
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if (pointIsInCubeArea(c1StartX, c1StartY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, c1StartY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1StartX, c1EndY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, c1EndY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1StartX, c1StartY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, c1StartY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1StartX, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, c2StartY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, c2StartY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, c2EndY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, c2EndY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, c2StartY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, c2StartY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, c2EndY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, c2EndY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1StartY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1EndY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1StartY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1StartX, (c1StartY + c1EndY) / 2, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1StartX, (c1StartY + c1EndY) / 2, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, (c1StartY + c1EndY) / 2, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, (c1StartY + c1EndY) / 2, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1StartX, c1StartY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1StartX, c1EndY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, c1StartY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea(c1EndX, c1EndY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2StartY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2EndY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2StartY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2EndY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, (c2StartY + c2EndY) / 2, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, (c2StartY + c2EndY) / 2, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, (c2StartY + c2EndY) / 2, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, (c2StartY + c2EndY) / 2, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, c2StartY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2StartX, c2EndY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, c2StartY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea(c2EndX, c2EndY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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if (pointIsInCubeArea((c1StartX + c1EndX) / 2, (c1StartY + c1EndY) / 2, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
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return true;
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if (pointIsInCubeArea((c2StartX + c2EndX) / 2, (c2StartY + c2EndY) / 2, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
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return true;
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return false;
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}
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//判断该点是否在给定参数的立方体内
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function pointIsInCubeArea(px, py, pz, startX, startY, startZ, endX, endY, endZ) {
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local cubeCenterX = (startX + endX) / 2;
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local cubeXLen = abs(startX - endX) / 2;
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local cubeCenterY = (startY + endY) / 2;
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local cubeYLen = abs(startY - endY) / 2;
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local cubeCenterZ = (startZ + endZ) / 2;
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local cubeZLen = abs(startZ - endZ) / 2;
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if (abs(px - cubeCenterX) <= cubeXLen && abs(py - cubeCenterY) <= cubeYLen && abs(pz - cubeCenterZ) <= cubeZLen)
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return true;
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return false;
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}
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//判断(px,py)是否在这个四边形内，如果在就返回true，否则返回false,
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//一定要注意，1，2，3，4的坐标必须能首尾组成四边形，不能跳坐标！！！！否则判断会直接失效！！！
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function pointIsIn4PointArea(px, py, x1, y1, x2, y2, x3, y3, x4, y4) {
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local area = get4PointArea(x1, y1, x2, y2, x3, y3, x4, y4);
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local pointArea1 = get3PointArea(x1, y1, x2, y2, px, py);
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local pointArea2 = get3PointArea(x2, y2, x3, y3, px, py);
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local pointArea3 = get3PointArea(x3, y3, x4, y4, px, py);
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local pointArea4 = get3PointArea(x4, y4, x1, y1, px, py);
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if (abs(area - pointArea1 - pointArea2 - pointArea3 - pointArea4)< 10.0)
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return true;
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return false;
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}
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//判断一个点是否存在于一个矩形中
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function PointIsInSquare(x1, y1, SquareArr) {
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return Sq_Is_Point_In_Square(x1, y1, SquareArr);
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}
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//判断一个点是否存在于一个矩形中 返回是哪一个矩形
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function PointIsInWhichRectangle(x1, y1, SquareArr) {
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return Sq_Is_Point_In_WhichRectangle(x1, y1, SquareArr);
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}
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//获得给定4个点形成的四边形面积
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function get4PointArea(x1, y1, x2, y2, x3, y3, x4, y4) {
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local area1 = get3PointArea(x1, y1, x2, y2, x3, y3)
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local area2 = get3PointArea(x2, y2, x3, y3, x4, y4)
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return area1 + area2;
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}
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//获得给定3个点形成的三角形面积
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function get3PointArea(x1, y1, x2, y2, x3, y3) {
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return abs(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2;
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/*
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local l1 = sqrt(pow((x1- x2), 2) + pow((y1- y2), 2));
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local l2 = sqrt(pow((x1- x3), 2) + pow((y1- y3), 2));
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local l3 = sqrt(pow((x2- x3), 2) + pow((y2- y3), 2));
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return sqrt((l1 + l2 + l3) * (l1 + l2- l3) * (l1- l2 + l3) * (l2 + l3- l1)) / 4;
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*/
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}
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//获得该数的符号
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function getSign(var) {
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if (var< 0)
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return 1;
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else if (var > 0)
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return -1;
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return 0;
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}
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//简便性能高的开平方
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function sqrt(sum) {
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local i = (sum / 2).tofloat();
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local isb = 0;
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for (isb = 0; isb< 10; isb++) {
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i = (i - ((i * i - sum) / (2 * i))).tofloat();
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}
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return i;
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}
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//四舍五入
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function Round(var) {
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local v =
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var -
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var.tointeger();
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if (v< 0.5)
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return var.tointeger();
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return var.tointeger() + 1;
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}
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//currentRate 越接近maxRate ,返回值由sv越接近ev
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function getUniformVelocity(sv, ev, currentRate, maxRate) {
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local rate = currentRate.tofloat() / maxRate.tofloat();
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local varyValue = ev - sv;
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return sv + varyValue * rate;
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}
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function sq_GetAccel(sv, ev, currentRate, maxRate, increaseFeature) {
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local rate = currentRate.tofloat() / maxRate.tofloat();
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local varyValue = ev - sv;
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local increaseRate = 1.0;
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if (increaseFeature) {
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increaseRate = pow(50, rate) / 50; //慢->快
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} else {
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// 修正后的减速逻辑计算，例如采用线性变换结合幂次运算来实现更合理的减速效果
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// 先将rate映射到一个更合适的范围（这里从[0,1]映射到[0.1, 1]，可调整）
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local mappedRate = rate * 0.9 + 0.1;
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increaseRate = pow(mappedRate, 2); // 幂次可调整，这里取2来让减速更明显，可根据实际情况修改
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}
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return sv + varyValue * increaseRate;
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}
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function Max(a, b) {
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if (a< b)
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return b;
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return a;
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}
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function Min(a, b) {
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if (a > b)
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return b;
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return a;
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}
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//获得贝塞尔曲线(2阶)
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function getBeizeri(var1, var2, p0, p1, p2, p3) {
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local t = var1.tofloat() / var2.tofloat();
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local t1 = 1.0 - t;
|
||
|
||
local v1 = t1 * t1 * t1;
|
||
local v2 = t1 * t1;
|
||
local v3 = t1;
|
||
local v4 = t * t * t;
|
||
|
||
local ret = p0 * v1;
|
||
ret = ret + 3.0 * p1 * t * v2;
|
||
ret = ret + 3.0 * p2 * t * t * v3;
|
||
ret = ret + p3 * v4;
|
||
|
||
return ret;
|
||
}
|
||
|
||
//获得贝塞尔曲线角度
|
||
function getBeizeriAngle(var1, var2, p0, p1, p2, p3) {
|
||
|
||
|
||
local t = var1.tofloat() / var2.tofloat();
|
||
local t1 = 1.0 - t;
|
||
|
||
local v1 = t1 * t1;
|
||
local v2 = t1;
|
||
local v3 = t1;
|
||
local v4 = t * t;
|
||
|
||
local ret = 2.0 * p0 * v1;
|
||
ret = ret + 6.0 * p1 * t * v2;
|
||
ret = ret + 6.0 * p2 * t * v3;
|
||
ret = ret + 2.0 * p3 * v4;
|
||
|
||
return ret;
|
||
|
||
|
||
}
|
||
|
||
function IsIntersectRect(x1, y1, width1, height1, x2, y2, width2, height2) {
|
||
// 计算矩形1的边界
|
||
local right1 = x1 + width1;
|
||
local bottom1 = y1 + height1;
|
||
// 计算矩形2的边界
|
||
local right2 = x2 + width2;
|
||
local bottom2 = y2 + height2;
|
||
// 检查是否有重叠
|
||
return !(right1< x2 || bottom1< y2 || x1 > right2 || y1 > bottom2);
|
||
}
|
||
}
|
||
//初始化随机数
|
||
srand(time());
|
||
Math.Rand(0, 1); |