1. What Is A 3D Function Plotter?

A 3D function plotter visualizes mathematical functions of the form z = f(x, y), creating three-dimensional surfaces and shapes. It helps in understanding complex mathematical relationships and spatial concepts.

2. How To Use This Calculator

Enter a function in terms of x and y, set the range for both variables, and the calculator will generate a 3D visualization of the function.

Function syntax examples:

• x^2 + y^2 (paraboloid)
• sin(x) + cos(y) (wave surface)
• sqrt(x^2 + y^2) (cone)
• x*y/(x^2 + y^2) (special function)

3. Understanding 3D Coordinates

In 3D plotting:

• X-axis: Horizontal direction (left-right)
• Y-axis: Depth direction (forward-backward)
• Z-axis: Vertical direction (up-down)

The function z = f(x, y) calculates the height (z) at each point (x, y) in the plane.

4. Examples Of 3D Functions

Common 3D surfaces:

• Planes: z = 2x + 3y + 1
• Spheres: z = sqrt(1 - x^2 - y^2)
• Paraboloids: z = x^2 + y^2
• Hyperbolic paraboloids: z = x^2 - y^2
• Torus: z = sqrt(1 - (sqrt(x^2 + y^2) - 2)^2)

5. Frequently Asked Questions

Q1: What types of functions can I plot?
A: You can plot any function that can be expressed as z = f(x, y), including polynomials, trigonometric functions, exponentials, and more.

Q2: Why can't I see the 3D plot?
A: This demonstration shows the interface. A full implementation would require JavaScript 3D libraries like Three.js, Plotly.js, or similar.

Q3: Can I rotate and zoom the 3D plot?
A: In a complete implementation, yes. You would typically be able to rotate, zoom, and pan to examine the 3D surface from different angles.

Q4: Are there limitations to what I can plot?
A: Complex functions with discontinuities or undefined regions may not render perfectly. The plotting range also affects visibility.

Q5: Can I plot multiple functions at once?
A: Advanced 3D plotters allow multiple surfaces to be displayed simultaneously, often with different colors for each function.