DOF/sqr/Core/BaseTool/Math.nut

/*
文件名:MathClass.nut
路径:System/BaseTool/MathClass.nut
创建日期:2024-05-10	16:02
文件用途:数学库
*/
class Math {

    function getDirectionToTargetX(objX, x) {
        if (objX > x)
            return 0;
        else
            return 1;
    }


    /*
     * @函数作用: 取随机值 左闭右闭
     * @参数 name
     * @返回值
     */
    function Rand(Min, Max) {
        local In = rand();
        local Ret = (Min + (Max - Min + 1) * (In / (RAND_MAX + 1).tofloat())).tointeger();
        return Ret;
    }


    function getCollisionByObjBox(obj, box) {
        local x = obj.X;
        local y = obj.Y;
        local z = obj.Z;

        local ArrBuf = [];
        if (obj.Direction == 1) {
            local pleft = [x + box[0], y + box[1], z + box[2]];
            local pright = [x + box[0] + box[3], y + box[1] + box[4], z + box[2] + box[5]];

            ArrBuf.extend(pleft);
            ArrBuf.extend(pright);
        } else {
            local pleft = [x - box[0], y + box[1], z + box[2]];
            local pright = [x - box[0] - box[3], y + box[1] + box[4], z + box[2] + box[5]];

            ArrBuf.extend(pleft);
            ArrBuf.extend(pright);
        }
        return ArrBuf;

    }

    function GetDistancePos(startX, direction, offsetX) {
        if (direction == 0)
            return startX - offsetX;

        return startX + offsetX;
    }

    //通过坐标获得两点旋转角度
    function getRorateAngleByCurrentPos(x1, y1, z1, x2, y2, z2) {
        return 0;
    }

    //贝塞尔曲线构造的抛物线运动，支持开始z轴(obj,curT,lastZ,moveT)
    function sq_BParabola(currentT, maxT, initZPos, jumpHeight, lastZPos) {
        local z = getBeizeri(currentT, maxT, initZPos, initZPos + jumpHeight, initZPos + jumpHeight, lastZPos);
        return z.tointeger();
    }

    //获得抛物线(不支持开始z轴)
    function sq_Parabola(x, b, c) {
        local a = (-b.tofloat() * 4) / (c.tofloat() * c.tofloat());
        return a.tofloat() * (x.tofloat() - c.tofloat() / 2) * (x.tofloat() - c.tofloat() / 2) + b.tofloat();
    }

    //获得两点之间平面的距离.
    function Get2D_Distance(x1, y1, x2, y2) {
        local offsetX = x1 - x2;
        local offsetY = (y1 - y2) * 0.29;

        return sqrt(offsetX * offsetX + offsetY * offsetY);

    }

    //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)
    function CheckAngleIsInArea(judge, startA, endA) {

        if (startA< 0)
            startA = startA + 360.0;

        if (endA< 0)
            endA = endA + 360.0;

        if (startA > 360.0)
            startA = startA - 360.0;

        if (endA > 360.0)
            endA = endA - 360.0;

        if (startA > 0 && startA< 90 && endA > 270 && endA< 360) {
            if (judge > 270 && judge< 360) {
                if (endA< judge && judge< startA + 360)
                    return true;
            } else if (judge< 90) {
                if (endA< judge + 360 && judge + 360< startA + 360)
                    return true;
            }

        } else {
            if (endA > judge && judge > startA)
                return true;
        }

        return false;
    }

    //弧度制转为角度制
    function toDegree(x) {
        return x * 57.29577;
    }

    //角度转为弧度
    function toRadian(x) {
        return x * 0.01745;
    }

    //立方体与立方体之间碰撞 暂未测试
    function CubeAndCubeCollection(c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ) {

        if (pointIsInCubeArea(c1StartX, c1StartY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, c1StartY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1StartX, c1EndY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, c1EndY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1StartX, c1StartY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, c1StartY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1StartX, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, c2StartY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, c2StartY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, c2EndY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, c2EndY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, c2StartY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, c2StartY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, c2EndY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, c2EndY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1StartY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1EndY, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1StartY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea((c1StartX + c1EndX) / 2, c1EndY, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1StartX, (c1StartY + c1EndY) / 2, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1StartX, (c1StartY + c1EndY) / 2, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, (c1StartY + c1EndY) / 2, c1StartZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, (c1StartY + c1EndY) / 2, c1EndZ, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1StartX, c1StartY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1StartX, c1EndY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, c1StartY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea(c1EndX, c1EndY, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2StartY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2EndY, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2StartY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea((c2StartX + c2EndX) / 2, c2EndY, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, (c2StartY + c2EndY) / 2, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, (c2StartY + c2EndY) / 2, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, (c2StartY + c2EndY) / 2, c2StartZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, (c2StartY + c2EndY) / 2, c2EndZ, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, c2StartY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2StartX, c2EndY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, c2StartY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea(c2EndX, c2EndY, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;
        if (pointIsInCubeArea((c1StartX + c1EndX) / 2, (c1StartY + c1EndY) / 2, (c1StartZ + c1EndZ) / 2, c2StartX, c2StartY, c2StartZ, c2EndX, c2EndY, c2EndZ))
            return true;
        if (pointIsInCubeArea((c2StartX + c2EndX) / 2, (c2StartY + c2EndY) / 2, (c2StartZ + c2EndZ) / 2, c1StartX, c1StartY, c1StartZ, c1EndX, c1EndY, c1EndZ))
            return true;

        return false;

    }


    //判断该点是否在给定参数的立方体内
    function pointIsInCubeArea(px, py, pz, startX, startY, startZ, endX, endY, endZ) {

        local cubeCenterX = (startX + endX) / 2;
        local cubeXLen = abs(startX - endX) / 2;

        local cubeCenterY = (startY + endY) / 2;
        local cubeYLen = abs(startY - endY) / 2;

        local cubeCenterZ = (startZ + endZ) / 2;
        local cubeZLen = abs(startZ - endZ) / 2;

        if (abs(px - cubeCenterX) <= cubeXLen && abs(py - cubeCenterY) <= cubeYLen && abs(pz - cubeCenterZ) <= cubeZLen)
            return true;

        return false;

    }

    //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,
    //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！！！
    function pointIsIn4PointArea(px, py, x1, y1, x2, y2, x3, y3, x4, y4) {
        local area = get4PointArea(x1, y1, x2, y2, x3, y3, x4, y4);
        local pointArea1 = get3PointArea(x1, y1, x2, y2, px, py);
        local pointArea2 = get3PointArea(x2, y2, x3, y3, px, py);
        local pointArea3 = get3PointArea(x3, y3, x4, y4, px, py);
        local pointArea4 = get3PointArea(x4, y4, x1, y1, px, py);

        if (abs(area - pointArea1 - pointArea2 - pointArea3 - pointArea4)< 10.0)
            return true;

        return false;

    }

    //判断一个点是否存在于一个矩形中
    function PointIsInSquare(x1, y1, SquareArr) {
        return Sq_Is_Point_In_Square(x1, y1, SquareArr);
    }

    //判断一个点是否存在于一个矩形中 返回是哪一个矩形
    function PointIsInWhichRectangle(x1, y1, SquareArr) {
        return Sq_Is_Point_In_WhichRectangle(x1, y1, SquareArr);
    }


    //获得给定4个点形成的四边形面积
    function get4PointArea(x1, y1, x2, y2, x3, y3, x4, y4) {
        local area1 = get3PointArea(x1, y1, x2, y2, x3, y3)
        local area2 = get3PointArea(x2, y2, x3, y3, x4, y4)
        return area1 + area2;
    }

    //获得给定3个点形成的三角形面积
    function get3PointArea(x1, y1, x2, y2, x3, y3) {

        return abs(x1 * (y2 - y3) + x2 * (y3 - y1) + x3 * (y1 - y2)) / 2;

        /*
        local l1 = sqrt(pow((x1- x2), 2) + pow((y1- y2), 2));
        local l2 = sqrt(pow((x1- x3), 2) + pow((y1- y3), 2));
        local l3 = sqrt(pow((x2- x3), 2) + pow((y2- y3), 2));

        return sqrt((l1 + l2 + l3) * (l1 + l2- l3) * (l1- l2 + l3) * (l2 + l3- l1)) / 4;
        */
    }



    //获得该数的符号
    function getSign(var) {
        if (var< 0)
            return 1;
        else if (var > 0)
            return -1;
        return 0;
    }

    //简便性能高的开平方
    function sqrt(sum) {
        local i = (sum / 2).tofloat();

        local isb = 0;
        for (isb = 0; isb< 10; isb++) {
            i = (i - ((i * i - sum) / (2 * i))).tofloat();
        }
        return i;

    }

    //四舍五入
    function Round(var) {
        local v =
            var -
            var.tointeger();
        if (v< 0.5)
            return var.tointeger();
        return var.tointeger() + 1;

    }

    //除以两个值并四舍五入
    function DivideAndRound(var1, var2) {
        local ret = var1.tofloat() / var2.tofloat();
        return Round(ret);
    }

    //总是舍去
    function Floor(var) {
        return var.tointeger();
    }

    //currentRate 越接近maxRate ,返回值由sv越接近ev
    function getUniformVelocity(sv, ev, currentRate, maxRate) {

        local rate = currentRate.tofloat() / maxRate.tofloat();

        local varyValue = ev - sv;

        return sv + varyValue * rate;
    }

    function sq_GetAccel(sv, ev, currentRate, maxRate, increaseFeature) {
        local rate = currentRate.tofloat() / maxRate.tofloat();
        local varyValue = ev - sv;

        local increaseRate = 1.0;
        if (increaseFeature) {
            increaseRate = pow(50, rate) / 50; //慢->快
        } else {
            // 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
            // 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）
            local mappedRate = rate * 0.9 + 0.1;
            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
        }

        return sv + varyValue * increaseRate;
    }

    //根据原数值 浮动比例 最终倍率 获得最终值
    function getFinalValueByFloatRate(originalValue, floatRate, finalRate) {
        // 计算 Value 的 15%
        local fifteenPercent = originalValue * 0.15;
        // 计算浮动范围的下限和上限
        local lowerBound = originalValue - fifteenPercent;
        local upperBound = originalValue + fifteenPercent;
        // 根据 Rate 计算最终值
        local finalValue = lowerBound + floatRate * (upperBound - lowerBound);
        return finalValue;
    }


    function Max(a, b) {
        if (a< b)
            return b;
        return a;
    }


    function Min(a, b) {
        if (a > b)
            return b;
        return a;
    }

    //获得贝塞尔曲线(2阶)
    function getBeizeri(var1, var2, p0, p1, p2, p3) {
        local t = var1.tofloat() / var2.tofloat();
        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);