3D Function Plotter

BetaThis tool is in beta. Some features may change or have limited functionality.
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Plot and visualize 3D mathematical surfaces interactively. Enter any z = f(x, y) expression to generate beautiful surface plots with customizable domains, resolution, color mapping, and wireframe display. Supports trigonometric, exponential, and logarithmic functions.
z = f(x, y) =
to
to
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Functions

sin, cos, tan, asin, acos, atan
exp, log, log2, sqrt, abs
floor, ceil, round
min(a,b), max(a,b), pow(a,b)
Constants: PI, E
Operators: + - * / ^ %
Loading 3D scene...

Click and drag to rotate. Scroll to zoom. Right-click to pan.

Understanding 3D Function Plotting and Surface Visualization

A 3D function plotter visualizes mathematical functions of two variables, z = f(x, y), as surfaces in three-dimensional space. Each point (x, y) in the domain maps to a height z, creating a surface that reveals the function's behavior.

Common Surface Types

  • Paraboloid (x² + y²): A bowl-shaped surface that opens upward, commonly seen in optics and satellite dishes.
  • Saddle Point (x² - y²): A hyperbolic paraboloid that curves up in one direction and down in another, like a horse saddle.
  • Sinc Function (sin(r)/r): A radially symmetric surface with a central peak and concentric ripples, fundamental in signal processing.
  • Gaussian (e^-(x²+y²)): The bell curve extended to 3D, central to probability and statistics.

How It Works

The plotter evaluates the function at a grid of (x, y) points within the specified domain. These sample points are connected into triangles to form a mesh, and colors are mapped based on the z-value (height). The result is rendered using WebGL for smooth, hardware-accelerated 3D graphics.

Applications

3D surface plotting is essential in multivariable calculus, physics (potential fields, wave functions), engineering (stress analysis, terrain modeling), economics (utility functions), and data science (loss landscapes in machine learning).

Frequently Asked Questions

What mathematical functions can I use?
You can use standard arithmetic operators (+, -, *, /, ^), trigonometric functions (sin, cos, tan, asin, acos, atan), exponential and logarithmic functions (exp, log, log2), and utility functions (sqrt, abs, floor, ceil, round, min, max, pow). The constants PI and E are also available.
Why does my surface look jagged or blocky?
The surface quality depends on the resolution setting. Increase the resolution slider to sample more points, which produces a smoother surface. However, very high resolutions require more computation and may affect performance on older devices.
What does the color on the surface represent?
The colors represent the height (z-value) of the surface using a rainbow gradient. Blue indicates the lowest points, green represents middle values, and red marks the highest points. This color mapping makes it easy to identify peaks, valleys, and saddle points at a glance.
Can I plot functions with singularities or discontinuities?
Yes, but functions with singularities (like 1/x at x=0) may produce very tall spikes or missing regions. The plotter automatically handles undefined values (division by zero, logarithm of negative numbers) by treating them as gaps in the surface. Adjusting the domain to avoid singularities often gives better results.
How do I navigate the 3D view?
Click and drag to rotate the view around the surface. Use the scroll wheel to zoom in and out. Right-click and drag to pan the view. You can also enable auto-rotate to continuously spin the surface, which is useful for examining it from all angles.