Use JavaScript syntax: Math.sin(x), Math.pow(x, 2), Math.sqrt(), Math.PI, etc.
Low (Fast)
Medium
High
Click 'Generate 3D Plot' to visualize the function.
function calculateAndGraph() {
var funcStr = document.getElementById("functionInput").value;
var xMin = parseFloat(document.getElementById("xMin").value);
var xMax = parseFloat(document.getElementById("xMax").value);
var yMin = parseFloat(document.getElementById("yMin").value);
var yMax = parseFloat(document.getElementById("yMax").value);
var resolution = parseInt(document.getElementById("resolution").value);
var errorDiv = document.getElementById("errorMessage");
errorDiv.style.display = "none";
if (isNaN(xMin) || isNaN(xMax) || isNaN(yMin) || isNaN(yMax)) {
errorDiv.innerText = "Error: Please enter valid numerical ranges.";
errorDiv.style.display = "block";
return;
}
var xValues = [];
var yValues = [];
var zValues = [];
var xStep = (xMax – xMin) / resolution;
var yStep = (yMax – yMin) / resolution;
try {
// Pre-calculate X and Y axes
for (var i = 0; i <= resolution; i++) {
xValues.push(xMin + (i * xStep));
yValues.push(yMin + (i * yStep));
}
// Generate Z data matrix
for (var j = 0; j <= resolution; j++) {
var row = [];
var y = yValues[j];
for (var k = 0; k <= resolution; k++) {
var x = xValues[k];
// Simple evaluation logic
// We use a Function constructor for safer, scoped evaluation
var z;
try {
var evalFunc = new Function('x', 'y', 'return ' + funcStr);
z = evalFunc(x, y);
} catch (e) {
throw new Error("Invalid mathematical expression.");
}
if (isNaN(z) || !isFinite(z)) {
row.push(null); // Handle undefined or infinite points
} else {
row.push(z);
}
}
zValues.push(row);
}
var data = [{
z: zValues,
x: xValues,
y: yValues,
type: 'surface',
colorscale: 'Viridis',
contours: {
z: {
show: true,
usecolormap: true,
highlightcolor: "#42f4f4",
project: {z: true}
}
}
}];
var layout = {
title: 'z = f(x, y)',
autosize: true,
margin: { l: 0, r: 0, b: 0, t: 40 },
scene: {
xaxis: { title: 'X Axis' },
yaxis: { title: 'Y Axis' },
zaxis: { title: 'Z Axis' }
}
};
var config = { responsive: true };
Plotly.newPlot('plotArea', data, layout, config);
} catch (err) {
errorDiv.innerText = "Computation Error: " + err.message;
errorDiv.style.display = "block";
}
}
// Initial load
window.onload = function() {
calculateAndGraph();
};
Understanding 3D Graphing and Surface Functions
3D graphing calculators are essential tools for visualizing multivariable functions, where the value of a dependent variable (usually z) is determined by two independent variables (x and y). Unlike traditional 2D Cartesian graphs that plot lines or curves, a 3D grapher produces a surface, allowing mathematicians and engineers to observe topological features like peaks, valleys, and saddle points.
How to Use the 3D Function Grapher
To generate a plot, you must define the relationship between the coordinates. The calculator accepts standard mathematical syntax. For example:
Paraboloid:Math.pow(x, 2) + Math.pow(y, 2)
Waves:Math.sin(x) * Math.cos(y)
Ripple Effect:Math.sin(Math.sqrt(x*x + y*y))
Key Concepts in Multivariable Calculus
When analyzing a 3D surface, several mathematical concepts become visually apparent:
Domain and Range: The X and Y ranges define the "floor" of the observation area, while the Z values represent the height of the surface at any given coordinate.
Partial Derivatives: These represent the slope of the surface when moving strictly along the X-axis or Y-axis. On a 3D plot, you can visualize this as the steepness of the terrain in a specific cardinal direction.
Extrema: Local maximums (peaks) and minimums (pits) are easily identified visually, which is crucial for optimization problems in physics and economics.
Practical Applications
Beyond pure mathematics, 3D graphing is used extensively in:
Engineering: Stress analysis on a flat plate can be modeled as a 3D surface where Z represents the magnitude of stress.
Meteorology: Pressure systems and temperature gradients across a geographic area are mapped using three-dimensional coordinates.
Data Science: Visualizing loss functions in machine learning helps developers understand how algorithms "descend" toward a global minimum during training.
Optimization Tip:
If you are graphing complex oscillating functions, increase the Resolution to "High". This adds more sample points to the grid, preventing "aliasing" where the graph appears jagged or omits critical details due to insufficient sampling.