diff --git a/experiment_data/analysis_state/~$peak.xlsx b/experiment_data/analysis_state/~$peak.xlsx
deleted file mode 100644
index d4a5841..0000000
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diff --git a/experiment_data/analysis_state/玻璃化转变.xlsx b/experiment_data/analysis_state/玻璃化转变.xlsx
new file mode 100644
index 0000000..8ad172a
Binary files /dev/null and b/experiment_data/analysis_state/玻璃化转变.xlsx differ
diff --git a/src/data/pointcalculate.cpp b/src/data/pointcalculate.cpp
index 8a36033..62d30ca 100644
--- a/src/data/pointcalculate.cpp
+++ b/src/data/pointcalculate.cpp
@@ -363,7 +363,7 @@ QPair<float,float> PointCalculate::getCurveInflectionPointTangent(const float x1
             dataVtr.push_back(ed.sampleTemp);
         }
     }
-    //
+    // 5
     std::vector<float> processedVtr = movingAverage(dataVtr,5);
 
     // find max slope.
@@ -387,7 +387,7 @@ QPair<float,float> PointCalculate::getCurveInflectionPointTangent(const float x1
 
     return qMakePair<float,float>(maxSlope,b);
 }
-QPointF PointCalculate::getIntersectionBySlope(const LineStruct& line1, const LineStruct& line2) {
+QPointF PointCalculate::getIntersection(const Line& line1, const Line& line2) {
     float x = (line2.intercept - line1.intercept) / (line1.slope - line2.slope);
     float y = line1.slope * x + line1.intercept;
     //    return {x, y};
@@ -541,3 +541,81 @@ QVector<Global::ExperimentData> PointCalculate::getDataInXRange(const float x1,
 
     return targetVtr;
 }
+
+QVector<QPointF> PointCalculate::getNearbyPointGroupByX(const float targetX)
+{
+    const int conCount = 10;
+    QVector<QPointF> tmpPointVtr,targetPointVtr;
+    float minDiff = std::numeric_limits<float>::max();
+
+    for(Global::ExperimentData &ed:_dataVtr){
+        float diff = std::abs(ed.sampleTemp - targetX);
+        if(diff > 10){
+            continue;
+        }
+
+        tmpPointVtr.push_back({ed.sampleTemp,ed.dsc});
+
+        if (diff < minDiff) {
+            minDiff = diff;
+
+            targetPointVtr = QVector<QPointF>(tmpPointVtr.end() - conCount, tmpPointVtr.end());
+        }
+    }
+
+
+    return targetPointVtr;
+}
+
+// 计算两点之间的斜率
+double PointCalculate::calculateSlope(double x1, double y1, double x2, double y2) {
+    return (y2 - y1) / (x2 - x1);
+}
+
+// 寻找第一个拐点
+QVector<double> PointCalculate::findInflectionPoints(
+        const QVector<double>& x, const QVector<double>& y) {
+    QVector<double> inflectionPointsX;
+    for (int i = 2; i < x.size() - 2; ++i) {
+        double d1 = calculateSlope(x[i - 2], y[i - 2], x[i - 1], y[i - 1]);
+        double d2 = calculateSlope(x[i - 1], y[i - 1], x[i], y[i]);
+        double d3 = calculateSlope(x[i], y[i], x[i + 1], y[i + 1]);
+        double d4 = calculateSlope(x[i + 1], y[i + 1], x[i + 2], y[i + 2]);
+
+        // 检查二阶导数的符号变化
+        if (((d2 - d1) * (d3 - d2) < 0) && ((d3 - d2) * (d4 - d3) < 0)) {
+            inflectionPointsX.append(x[i]);
+        }
+    }
+    return inflectionPointsX;
+}
+
+// 计算切线方程
+QMap<double, PointCalculate::Line>  PointCalculate::calculateTangentLine(
+        const QVector<double>& x, const QVector<double>& y) {
+    QMap<double, Line> tangentLines;
+    QVector<double> inflectionPointsX = findInflectionPoints(x, y);
+
+    for (double xInflection : inflectionPointsX) {
+        int i = std::distance(x.begin(), std::find(x.begin(), x.end(), xInflection));
+        double slope = calculateSlope(x[i - 1], y[i - 1], x[i + 1], y[i + 1]);
+        double yInflection = y[i];
+        double intercept = yInflection - slope * xInflection;
+        tangentLines[xInflection] = {slope, intercept};
+    }
+
+    return tangentLines;
+}
+QVector<QPointF> PointCalculate::getPointVtrInXRange(const float x1, const float x2)
+{
+    QVector<QPointF> targetVtr;
+    for(const Global::ExperimentData &ed : _dataVtr) {
+        if(x1 < ed.sampleTemp && ed.sampleTemp < x2){
+            targetVtr.push_back({ed.sampleTemp,ed.dsc});
+        }else if (ed.sampleTemp > x2){
+            break;
+        }
+    }
+
+    return targetVtr;
+}
diff --git a/src/data/pointcalculate.h b/src/data/pointcalculate.h
index ce4750b..7a08b0e 100644
--- a/src/data/pointcalculate.h
+++ b/src/data/pointcalculate.h
@@ -10,9 +10,13 @@ void setExperimentData(const QVector<Global::ExperimentData>&);
 
 QPair<QPointF,QPointF> getStartAndEndPoint();
 QVector<Global::ExperimentData> getDataInXRange(const float, const float);
+QVector<QPointF> getPointVtrInXRange(const float, const float);
 
 void setRegionPointX(const float,const float);
+
 QPointF getClosestPointByX(const float);
+QVector<QPointF> getNearbyPointGroupByX(const float);
+
 QPointF getClosestPointByY(const float left,const float right,const float valueY);
 QPointF getPeakPoint();
 QPair<float, float>  getMaxMinValue();
@@ -32,11 +36,14 @@ QString textFormatGlassTranstion(const float t1,const float tg,const float t2);
 
 // glass transition
 QPair<float,float> getCurveInflectionPointTangent(const float,const float);
-struct LineStruct {
-    float slope; //
-    float intercept; //
+struct Line {
+    double slope; //
+    double intercept; //
 };
-QPointF getIntersectionBySlope(const LineStruct& line1, const LineStruct& line2);
+QPointF getIntersection(const Line& line1, const Line& line2);
+double calculateSlope(double x1, double y1, double x2, double y2) ;
+QVector<double> findInflectionPoints(const QVector<double>& x, const QVector<double>& y) ;
+QMap<double, Line>  calculateTangentLine(const QVector<double>& x, const QVector<double>& y) ;
 
 //private
 void updateStartEndPoint();
diff --git a/src/ui/centralwidget.cpp b/src/ui/centralwidget.cpp
index a120b4d..32694c3 100644
--- a/src/ui/centralwidget.cpp
+++ b/src/ui/centralwidget.cpp
@@ -352,7 +352,8 @@ void CentralWidget::slotAnalysisSettingApply()
     }
     case AnalysisMode::GlassTransition:
     {
-        glassTransitionHandle();
+        //        glassTransitionHandle();
+        glassTransitionHandle2();
         //
         break;
     }
@@ -452,7 +453,7 @@ void CentralWidget::glassTransitionHandle()
     _customPlot->replot();
 #endif
     //
-    PointCalculate::LineStruct lineStrc1,lineStrc2,tangetLineStrc;
+    PointCalculate::Line lineStrc1,lineStrc2,tangetLineStrc;
 
     lineStrc1.slope = 0.0;
     lineStrc1.intercept = point1.y();
@@ -464,8 +465,8 @@ void CentralWidget::glassTransitionHandle()
     tangetLineStrc.slope = tangentLinePair.first;
     tangetLineStrc.intercept = tangentLinePair.second;
 
-    QPointF intersection1 = PointCalculate::getIntersectionBySlope(tangetLineStrc,lineStrc1);
-    QPointF intersection2 = PointCalculate::getIntersectionBySlope(tangetLineStrc,lineStrc2);
+    QPointF intersection1 = PointCalculate::getIntersection(tangetLineStrc,lineStrc1);
+    QPointF intersection2 = PointCalculate::getIntersection(tangetLineStrc,lineStrc2);
 
     //    logde<<"intersection1 x:"<<intersection1.x();
     //    logde<<"intersection2 x:"<<intersection2.x();
@@ -487,8 +488,37 @@ void CentralWidget::glassTransitionHandle()
     QString str = PointCalculate::textFormatGlassTranstion(intersection2.x(),
                                                            averagePoint.x(),
                                                            intersection1.x());
+    //draw line
+    ///line1
+    QVector<double> xVtr,yVtr;
+    xVtr.push_back(intersection1.x());
+    xVtr.push_back(point1.x());
+
+    yVtr.push_back(intersection1.y());
+    yVtr.push_back(point1.y());
+
+    QCPGraph *lineGraph1 = _customPlot->addGraph();
+    lineGraph1->setData(xVtr, yVtr);
+    _customPlot->replot();
+
+    ///line2
+    QVector<double> xVtr2,yVtr2;
+    xVtr2.push_back(intersection2.x());
+    xVtr2.push_back(point2.x());
+
+    yVtr2.push_back(intersection2.y());
+    yVtr2.push_back(point2.y());
+
+    QCPGraph *lineGraph2 = _customPlot->addGraph();
+    lineGraph2->setData(xVtr2, yVtr2);
+    _customPlot->replot();
+
+    //draw text
     drawText(averagePoint,str);
 
+    _customPlot->replot();
+
+
 #if 0
     // 创建一个圆形绘图项
     QCPItemEllipse *circle = new QCPItemEllipse(_customPlot);
@@ -515,6 +545,192 @@ void CentralWidget::glassTransitionHandle()
 #endif
 }
 
+void CentralWidget::glassTransitionHandle2()
+{
+    QPointF point1 = PointCalculate::getClosestPointByX(_line1->point1->coords().x());
+    QPointF point2 = PointCalculate::getClosestPointByX(_line2->point1->coords().x());
+
+    logde<<"point1:"<<point1.x()<<","<<point1.y();
+    logde<<"point2:"<<point2.x()<<","<<point2.y();
+
+    QVector<QPointF> point1Vtr = PointCalculate::getNearbyPointGroupByX(point1.x());
+    QVector<QPointF> point2Vtr = PointCalculate::getNearbyPointGroupByX(point2.x());
+
+    QVector<double> xVtr,yVtr;
+    for(QPointF &p:point1Vtr){
+        xVtr.append(p.x());
+        yVtr.append(p.y());
+    }
+
+    PointCalculate::Line line1 =  calculateLinearRegression(xVtr,yVtr);
+
+#if 1
+    ///line1
+    //    QVector<double> xVtr,yVtr;
+    xVtr.clear();
+    yVtr.clear();
+
+    xVtr.push_back(point1.x());
+    yVtr.push_back(point1.y());
+
+    xVtr.push_back(point1.x() + 10);
+    double y1 = line1.slope * (point1.x() + 10) + line1.intercept;
+    yVtr.push_back(y1);
+
+    QCPGraph *lineGraph1 = _customPlot->addGraph();
+    lineGraph1->setData(xVtr, yVtr);
+    QPen pen;
+    pen.setColor(Qt::darkGreen);
+    lineGraph1->setPen(pen);
+
+#endif
+
+    xVtr.clear();
+    yVtr.clear();
+    for(QPointF &p:point2Vtr){
+        xVtr.append(p.x());
+        yVtr.append(p.y());
+    }
+
+    PointCalculate::Line line2 =  calculateLinearRegression(xVtr,yVtr);
+
+#if 1
+    ///line2
+    QVector<double> xVtr2,yVtr2;
+    xVtr2.push_back(point2.x());
+    yVtr2.push_back(point2.y());
+
+    xVtr2.push_back(point2.x() - 10);
+    double y2 = line2.slope * (point2.x() - 10) + line2.intercept;
+    yVtr2.push_back(y2);
+
+    QCPGraph *lineGraph2 = _customPlot->addGraph();
+    lineGraph2->setData(xVtr2, yVtr2);
+    lineGraph2->setPen(pen);
+
+    _customPlot->replot();
+#endif
+
+    // inflection point.
+    QVector<QPointF> pointVtr = PointCalculate::getPointVtrInXRange(point1.x(),point2.x());
+
+    xVtr.clear();
+    yVtr.clear();
+    for(QPointF& p:pointVtr){
+        xVtr.append(p.x());
+        yVtr.append(p.y());
+    }
+    QMap<double, PointCalculate::Line>  tangentLines =
+            PointCalculate::calculateTangentLine(xVtr,yVtr);
+
+    double targetX = 0.0;
+    PointCalculate::Line targetLine;
+    double maxSlopeAbs = 0.0; // 初始化最大斜率绝对值为0
+    for (auto it = tangentLines.begin(); it != tangentLines.end(); ++it) {
+        if (std::fabs(it.value().slope) > maxSlopeAbs) {
+            maxSlopeAbs = std::fabs(it.value().slope); // 更新最大斜率绝对值
+
+            targetX = it.key();
+            targetLine = it.value();
+        }
+    }
+
+#if 1
+    QPointF intersection1 = PointCalculate::getIntersection(targetLine,line1);
+    QPointF intersection2 = PointCalculate::getIntersection(targetLine,line2);
+
+    // graph 3
+    xVtr.clear();
+    yVtr.clear();
+
+#if 0
+    xVtr.push_back(point1.x());
+    yVtr.push_back(point1.y());
+
+    xVtr.push_back(point1.x());
+    yVtr.push_back(point1.y());
+#endif
+#if 1
+    xVtr.push_back(intersection1.x());
+    yVtr.push_back(intersection1.y());
+
+    xVtr.push_back(intersection2.x());
+    yVtr.push_back(intersection2.y());
+#endif
+
+    QCPGraph *lineGraph3 = _customPlot->addGraph();
+    lineGraph3->setData(xVtr, yVtr);
+    lineGraph3->setPen(pen);
+#endif
+
+    _customPlot->replot();
+
+    // point value
+    double averageY = (point1.y() + point2.y()) / 2;
+
+    QPointF averagePoint = PointCalculate::getClosestPointByY(point1.x(),point2.x(),averageY);
+
+
+    QString str = PointCalculate::textFormatGlassTranstion(intersection2.x(),
+                                                           averagePoint.x(),
+                                                           intersection1.x());
+
+        drawText(averagePoint,str);
+
+}
+// 使用最小二乘法计算线性回归
+PointCalculate::Line CentralWidget::calculateLinearRegression(const QVector<double>& x, const QVector<double>& y) {
+    PointCalculate::Line line;
+    double sum_x = 0, sum_y = 0, sum_xy = 0, sum_xx = 0;
+    size_t n = x.size();
+
+    // 计算所需的总和
+    for (size_t i = 0; i < n; ++i) {
+        sum_x += x[i];
+        sum_y += y[i];
+        sum_xy += x[i] * y[i];
+        sum_xx += x[i] * x[i];
+    }
+
+    // 计算斜率和截距
+    double x_mean = sum_x / n;
+    double y_mean = sum_y / n;
+    double numerator = n * sum_xy - sum_x * sum_y;
+    double denominator = n * sum_xx - sum_x * sum_x;
+    line.slope = numerator / denominator;
+    line.intercept = y_mean - line.slope * x_mean;
+
+    return line;
+}
+
+// 二次多项式拟合函数
+void CentralWidget::quadraticFit(const QVector<QPointF>& points, double& a, double& b, double& c) {
+    int n = points.size();
+    if (n < 3) {
+        throw std::invalid_argument("At least three points are required for quadratic fit.");
+    }
+
+    double sumX = 0, sumY = 0, sumXX = 0, sumXY = 0, sumX2Y = 0;
+    for (const QPointF& p : points) {
+        sumX += p.x();
+        sumY += p.y();
+        sumXX += p.x() * p.x();
+        sumXY += p.x() * p.y();
+        sumX2Y += p.x() * p.x() * p.y();
+    }
+
+    double det = n * (sumXX * sumY - sumX * sumXY) - sumX * sumX * sumY + sumX * sumX2Y;
+    a = (sumXX * sumY - sumX * sumXY) / det;
+    b = (sumX2Y - n * sumXY) / det;
+    c = (sumY - a * sumX - b * sumX) / n;
+}
+
+// 计算二次多项式拟合曲线的导数（切线斜率）
+double CentralWidget::derivativeAt(const double a, const double b, const double x) {
+    return 2 * a * x + b;
+}
+
+
 void CentralWidget::setEventHandlerEnable(const bool flag)
 {
     logde<<"setEventHandlerEnable..."<<flag;
@@ -632,7 +848,7 @@ void CentralWidget::clearData(const CentralWidget::ClearDataMode mode)
     // Clear graph on plot.
     for (int i = _customPlot->graphCount() - 1; i >= 0; --i) {
         QCPGraph *graph = _customPlot->graph(i);
-            _customPlot->removeGraph(graph);
+        _customPlot->removeGraph(graph);
     }
 #endif
 
diff --git a/src/ui/centralwidget.h b/src/ui/centralwidget.h
index 5cc2e43..fabf77f 100644
--- a/src/ui/centralwidget.h
+++ b/src/ui/centralwidget.h
@@ -9,6 +9,7 @@
 #include "global.h"
 #include "eventhandler.h"
 #include "filemanager.h"
+#include "pointcalculate.h"
 
 class CentralWidget:public QWidget
 {
@@ -51,6 +52,13 @@ protected:
     void contextMenuEvent(QContextMenuEvent *event);
 private:
     void glassTransitionHandle();
+
+    void glassTransitionHandle2();
+    void quadraticFit(const QVector<QPointF>& points, double& a, double& b, double& c);
+    double derivativeAt(const double a, const double b, const double x);
+    PointCalculate::Line calculateLinearRegression(const QVector<double>& x, const QVector<double>& y);
+
+
     void setEventHandlerEnable(const bool);
     void drawText(const QPointF,const QString);
     void fillGraph(const double x1,const double x2);