Function Selection
Choose from preset mathematical functions to visualize
Dual View Visualization
Contour Map (Top View)
3D Surface
Level Curve Controls
View Controls
Understanding Level Curves
What are level curves?
Level curves (also called contour lines) are curves along which the function f(x,y) has a constant value. Each curve represents points where z = c for some constant c. On a topographic map, these would be lines of constant elevation.
Level curves (also called contour lines) are curves along which the function f(x,y) has a constant value. Each curve represents points where z = c for some constant c. On a topographic map, these would be lines of constant elevation.
Reading the contour map:
• Closely spaced curves indicate steep slopes
• Widely spaced curves indicate gentle slopes
• Concentric circles usually indicate peaks or valleys
• Saddle points show curves crossing in an X pattern
• The direction of steepest ascent is perpendicular to the level curves
• Closely spaced curves indicate steep slopes
• Widely spaced curves indicate gentle slopes
• Concentric circles usually indicate peaks or valleys
• Saddle points show curves crossing in an X pattern
• The direction of steepest ascent is perpendicular to the level curves
Connection to the 3D surface:
The contour map on the left shows what you would see looking down from above the surface. Each colored curve on the contour map corresponds to a "slice" of the 3D surface at a specific height. Think of cutting the surface with horizontal planes at different z-values.
The contour map on the left shows what you would see looking down from above the surface. Each colored curve on the contour map corresponds to a "slice" of the 3D surface at a specific height. Think of cutting the surface with horizontal planes at different z-values.
Key Insight: The contour map contains all the information needed to reconstruct the 3D surface. By looking at the spacing and shape of level curves, you can visualize hills, valleys, saddle points, and slopes without seeing the 3D surface.
Mouse Controls: Click and drag to rotate in 3D view, Scroll to zoom, Right-click drag to pan. The contour map can also be rotated to see from different angles.