initial commit

BezierCurve.pde

@@ -0,0 +1,132 @@
+final float pointRadius = 5;
+final int pointAmount = 6;
+
+ArrayList<PVector> points = new ArrayList<PVector>();
+boolean dragging = false, showNormals = true, showHelp = true;
+int dragIndex = -1;
+int increment = 100;
+
+void setup() {
+  fullScreen();
+  
+  for (int i = 0; i < pointAmount; i++) {
+    points.add(
+      new PVector(
+        ((i + 1) * width) / (pointAmount + 1),
+        height / 2
+      )
+    );
+  }
+  
+  textSize(height / 32);
+}
+
+void draw() {
+  background(0);
+  if (showHelp) {
+    fill(255);
+    text("Press 's' to show the Green Point-Connections.\nPress 'a' to decrease the calculated intervals of the red line.\nPress 'd' to increase the calculated intervals of the red line.\nPress 'h' to display this message.",0,height / 32);
+  }
+  
+  if (dragging && dragIndex != -1) {
+    points.set(dragIndex, new PVector(mouseX, mouseY));
+  }
+  
+  if (showNormals) {
+    fill(255);
+    for (int i = 0; i < points.size(); i++) {
+      final PVector current = points.get(i).copy();
+      stroke(255);
+      circle(current.x, current.y, pointRadius);
+      if (i > 0) {
+        final PVector previous = points.get(i - 1).copy();
+        stroke(0, 255, 0);
+        line(current.x, current.y, previous.x, previous.y);
+      }
+    }
+  }
+  
+  noFill();
+  stroke(255, 0, 0);
+  PVector p = bezierCurve(0);
+  final float inc = (float)1 / increment;
+  for (float i = inc; i <= 1; i += inc) {
+    PVector n = bezierCurve(i);
+    line(p.x, p.y, n.x, n.y);
+    p = n.copy();
+  }
+  final PVector last = points.get(points.size()-1).copy();
+  line(p.x, p.y, last.x, last.y);
+}
+
+PVector bezierCurve(float t) {
+  final int n = points.size() - 1;
+  PVector newPoint = PVector.mult(points.get(0).copy(), pow(1 - t, n));
+  
+  for (int i = 1; i <= n; i++) {
+    final float factor = binomialCoefficient(n, i) * pow(1 - t, n - i) * pow(t, i);
+    final PVector nextPoint = PVector.mult(points.get(i).copy(), factor);
+    newPoint.add(nextPoint);
+  }
+  
+  return newPoint;
+}
+
+void mousePressed() {
+  dragging = true;
+  final PVector mouseVector = new PVector(mouseX, mouseY);
+  
+  int recordIndex = 0;
+  float recordDistance = PVector.dist(mouseVector, points.get(recordIndex));
+  for (int i = 1; i < points.size(); i++) {
+    final float distance = PVector.dist(mouseVector, points.get(i));
+    if (distance < recordDistance) {
+      recordIndex = i;
+      recordDistance = distance;
+    }
+  }
+  
+  if (recordDistance <= pointRadius * 4) {
+    dragIndex = recordIndex;
+  }
+}
+
+void mouseReleased() {
+  dragging = false;
+  dragIndex = -1;
+}
+
+void keyPressed() {
+  final char lk = lowerCaseChar(key);
+  if (lk == 's') {
+    showNormals = !showNormals;
+  } else if (lk == 'a' && increment > 0) {
+    increment -= 5;
+  } else if (lk == 'd' && increment < 100) {
+    increment += 5;
+  } else if (lk == 'h') {
+    showHelp = !showHelp;
+  }
+}
+
+char lowerCaseChar(char c) {
+  return str(c).toLowerCase().charAt(0);
+}
+
+float binomialCoefficient(int n, int k) {
+  return factorial(n) / (factorial(k) * factorial(n - k));
+}
+
+int factorial(int n) {
+  if (n == 0 || n == 1) {
+    return 1;
+  }
+  
+  int o = 2;
+  
+  for (int i = 3; i < n + 1; i++) {
+    o *= i;
+  }
+  
+  return o;
+}