参考：https://blog.csdn.net/weixin_39383896/article/details/99615371和https://blog.csdn.net/qq_15821883/article/details/117421400

代码逻辑思路：
1、获取向量AB、BC的坐标。
2、计算向量AB、BC的长度。
3、根据点乘获取cosθ大小。
4、根据cosθ大小判断夹角为钝角还是锐角。
5、如果小于等于90度，根据缩放距离、夹角和等间距求缩放后的点位置。
6、如果大于90度，根据叉积公式判断多边形为凸边形还是凹变形。
7、判断凸凹边形后，根据缩放距离、夹角和等间距求缩放后的点位置。
实现结果：

Qt实现代码：

QVector<QPointF> Widget::calcPoint(const QVector<QPointF> &datas, int sec_dis)
{QVector<double> x;QVector<double> y;int number = datas.size();if (number < 3){return QVector<QPointF>();}for (int i = 0; i < number; ++i){x.append(datas[i].x());y.append(datas[i].y());}QVector<QPointF> points;for (int i = 0; i < number; ++i){// 向量ABdouble x1 = x[i % number] - x[(i - 1 + number) % number];double y1 = y[i % number] - y[(i - 1 + number) % number];// 向量BCdouble x2 = x[i % number] - x[(i + 1)% number];double y2 = y[i % number] - y[(i + 1)% number];// 求线段的长度double d1 = sqrt(x1*x1 + y1 * y1);double d2 = sqrt(x2*x2 + y2 * y2);// 点乘double ab = x1 * x2 + y1 * y2;// cosθ = A * B / (|A| * |B|)double cosA = ab / (d1 * d2);// 求sinAdouble sinA;if (cosA  > 0) // 表示夹角0-90度 锐角{sinA = sqrt(1 - cosA * cosA);double dv1 = sec_dis / sinA;// # 向量V1,V2的坐标double v1_x = (dv1 / d1) * x1;double v1_y = (dv1 / d1) * y1;double v2_x = (dv1 / d2) * x2;double v2_y = (dv1 / d2) * y2;double PiQi_x = v1_x + v2_x;double PiQi_y = v1_y + v2_y;double Qi_x = PiQi_x + x[i];double Qi_y = PiQi_y + y[i];points.append(QPointF(Qi_x, Qi_y));}else if(cosA < 0) // 钝角  钝角分为外钝角和 内钝角{// 判断凹凸点（叉积）double P1P3_x = x[(i + 1) % number] - x[i];double P1P3_y = y[(i + 1) % number] - y[i];double P1P2_x = x[i] - x[(i - 1 + number) % number];double P1P2_y = y[i] - y[(i - 1 + number) % number];double P = (P1P3_y*P1P2_x) - (P1P3_x*P1P2_y);// 为凹if (P < 0){sinA = -sqrt(1 - cosA * cosA);double dv1 = sec_dis / sinA;double v1_x = (dv1 / d1) * x1;double v1_y = (dv1 / d1) * y1;double v2_x = (dv1 / d2) * x2;double v2_y = (dv1 / d2) * y2;double PiQi_x = v1_x + v2_x;double PiQi_y = v1_y + v2_y;double Qi_x = PiQi_x + x[i];double Qi_y = PiQi_y + y[i];points.append(QPointF(Qi_x, Qi_y));}else if (P > 0) // 为凸{sinA = -sqrt(1 - cosA * cosA);double dv1 = -sec_dis / sinA;double v1_x = (dv1 / d1) * x1;double v1_y = (dv1 / d1) * y1;double v2_x = (dv1 / d2) * x2;double v2_y = (dv1 / d2) * y2;double PiQi_x = v1_x + v2_x;double PiQi_y = v1_y + v2_y;double Qi_x = PiQi_x + x[i];double Qi_y = PiQi_y + y[i];points.append(QPointF(Qi_x, Qi_y));}else // error{return QVector<QPointF>();}}else if(cosA == 0){sinA = 1;double dv1 = sec_dis / sinA;double v1_x = (dv1 / d1) * x1;double v1_y = (dv1 / d1) * y1;double v2_x = (dv1 / d2) * x2;double v2_y = (dv1 / d2) * y2;double PiQi_x = v1_x + v2_x;double PiQi_y = v1_y + v2_y;double Qi_x = PiQi_x + x[i];double Qi_y = PiQi_y + y[i];points.append(QPointF(Qi_x, Qi_y));}}return points;
}