A Java-based application to visualize mathematical curves in Cartesian and Polar (Radial) coordinate systems. The app uses sliders for real-time control over parameters like Amplitude (A), Frequency (W), and Phase Shift (PHI).
📈 Cartesian Curves (AppCartesian.java)
| Curve Name |
Graph Preview |
Formula Used |
| Sine Wave (Blue) |
 |
Math.sin(W * x + PHI) * A |
| Cosine Wave (Magenta) |
|
Math.cos(W * x + PHI) * A |
| Tangent Wave |
 |
Math.tan(W * x + PHI) * A * 0.1 |
| Triangle Wave |
 |
2 * A / π * asin(sin(W * x + PHI)) |
| Damped Sine |
 |
sin(W * x + PHI) * exp(-0.01 * x) * A |
| Pulse Train |
 |
(sin(W * x + PHI) > 0 ? 1 : 0) * A |
| Harmonic Blend |
 |
(sin(W * x + PHI) + sin(3W * x + PHI)) / 2 * A |
| Sine of Sine |
 |
sin(W * x + PHI) * sin(0.8W * x + PHI) * A |
🌀 Radial Curves (AppRadial.java)
| Curve Name |
Graph Preview |
Formula (r = ...) |
| Cardiod |
 |
(1 - sin(θ)) * 100 |
| Infinity (Lemniscate) |
 |
sqrt(10000 * cos(2θ)) |
| Rose Curve |
 |
100 * cos(4θ) |
| Archimedean Spiral |
 |
10 + 10 * θ |
| Fermat Spiral |
 |
10 * sqrt(θ) |
| Epicycloid |
 |
100 * (1 - cos(3θ)) |
| Logarithmic Spiral |
 |
10 * e^(0.15 * θ) |
🧮 Parametric Curves (AppParametric.java)
| Curve Name |
Graph Preview |
Formula (x(t), y(t)) |
| Lissajous Curve |
 |
x = A·sin(W·t + φ)
y = A·sin(2·W·t) |
| Parametric Archimedean Spiral |
 |
x = (t/30)·cos(W·t)
y = (t/30)·sin(W·t) |
| Hypotrochoid |
 |
x = (A - 20)·cos(W·t) + 40·cos(((A - 20)/20)·W·t)
y = (A - 20)·sin(W·t) - 40·sin(((A - 20)/20)·W·t) |
| Helix (3D) |
 |
x = A·cos(W·t)
y = A·sin(W·t)
z = t |
♾️ Mandelbrot Fractal (AppFractal.java)
c = x + iy (a point in the complex plane)z₀ = 0Recurrence: zₙ₊₁ = zₙ² + c
| Location |
Preview |
| Overview |
 |
| Left Zoom |
 |
| Left |
 |
| Center |
 |
| Bottom |
 |
The app provides interactive sliders to dynamically update curves:
int function(float x){
A = sliderA.getValue();
W = sliderW.getValue()/1000.0;
PHI = sliderPHI.getValue()/100.0;
return (int)(Math.sin(W * x + PHI) * A); // Sine Wave
}
public AppCartesian(){
points = new ArrayList<>();
new Timer(sliderDelay.getValue(), e -> {
x += (float)(sliderStep.getValue()/10f);
add -> points.add(new Point((int)x,function(x),(int)size,Color.BLUE));
repaint();
}).start();
}
