improve 3

task3/src/main/java/org/example/Main.java

@@ -228,18 +228,14 @@ public class Main extends JFrame {
 
             for (List<Point> curve : bezierCurves) {
                 if (curve.size() >= 4) {
-                    int numSegments = 100;
+                    int numSegments = 500;
                     double[] xPoints = new double[numSegments + 1];
                     double[] yPoints = new double[numSegments + 1];
                     for (int i = 0; i <= numSegments; i++) {
                         double t = (double) i / numSegments;
-                        xPoints[i] = 0;
-                        yPoints[i] = 0;
-                        for (int j = 0; j < 4; j++) {
-                            double blend = blendFunction(3, j, t);
-                            xPoints[i] += blend * curve.get(j).getX();
-                            yPoints[i] += blend * curve.get(j).getY();
-                        }
+                        Point point = blendFunction(curve.get(0), curve.get(1), curve.get(2), curve.get(3), t);
+                        xPoints[i] = point.getX();
+                        yPoints[i] = point.getY();
                     }
                     for (int i = 1; i <= numSegments; i++) {
                         int x1 = (int) xPoints[i - 1];
@@ -252,10 +248,17 @@ public class Main extends JFrame {
             }
         }
 
-        private double blendFunction(int n, int i, double t) {
-            int k = n - i;
-            double binomialCoefficient = factorial(n) / (factorial(i) * factorial(k));
-            return binomialCoefficient * Math.pow(t, i) * Math.pow(1 - t, k);
+        private Point blendFunction(Point p0, Point p1, Point p2, Point p3, double t) {
+            double u = 1 - t;
+            double tt = t * t;
+            double uu = u * u;
+            double uuu = uu * u;
+            double ttt = tt * t;
+
+            double x = p0.getX() * uuu + 3 * p1.getX() * t * uu + 3 * p2.getX() * tt * u + p3.getX() * ttt;
+            double y = p0.getY() * uuu + 3 * p1.getY() * t * uu + 3 * p2.getY() * tt * u + p3.getY() * ttt;
+
+            return new Point(x,y);
         }
 
         private double factorial(int n) {