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3D Graphing

In this manual, we’ll explore how to visualize mathematical functions in three dimensions. We’ll cover the basics of coordinate systems and show you how to create, manipulate, and interpret 3D graphs of functions.

3d graph of sin(x)*cos(y)

Getting Started

Inputting 3D functions

The CalcES calculator accepts f(x,y) as 3D function.

Examples:

sin(x)+sin(y)

This function represents the sum of sine functions of x and y.

This function represents the sum of sine functions of x and y.

x∗sin(y)

This function is the product of x and the sine of y.

This function is the product of x and the sine of y

2x+2y−3

This function represents a linear plane in three-dimensional space with a slope of 2 in both the x and y directions and an intercept of -3.

This function is the product of x and the sine of y

Accessing the 3D graphing mode

To enter the 3D graphing mode on CalcES calculator, follow these steps:

  1. Input the f(x,y) function: sin(x)+sin(y):

    sin(x)+sin(y)

  2. Tap the GRAPH button to show graph options dialog

    Tap the `GRAPH` button

  3. Select the 3D Graphing option to open 3D graphing screen

    Select the 3D Graphing option

  4. The 3D Graphing screen is displayed

    3D Graphing of sin(x)+sin(y)

Adjusting viewing parameters (zoom, rotation)

Adjusting viewing parameters allows you to manipulate the perspective and orientation of the graph, providing a clearer understanding of the plotted functions. Here’s how you can adjust viewing parameters on CalcES calculator:

Zoom

Control the zoom level to change the scale of the graph. Zooming in brings objects closer and magnifies details, while zooming out provides a broader view of the graph. Use the zoom-in and zoom-out functions to adjust the magnification as needed.

Zoom control Zoom control

Rotation

Rotate the graph to view it from different angles. Rotating the graph allows you to explore its structure from various perspectives, helping you gain insights into its shape and behavior. Use the rotation controls to rotate the graph horizontally, vertically, or around its axis.

Zoom control

Color and style options

In 3D graphing, color and style options play a crucial role in enhancing the visual clarity and aesthetic appeal of plotted functions. Here’s how you can utilize color and style options on CalcES calculator to customize the appearance of your graphs:

Plot modes:

  • 3D Surface: Renders the function in three-dimensional space, displaying it as a continuous surface.
3D Surface of sin(x)+sin(y)
  • 3D Wireframe: Presents the function as a wireframe mesh in three-dimensional space, providing a skeletal representation of the surface.
3D Wireframe of sin(x)+sin(y)
  • 2D Density: Visualizes the density of the function in a two-dimensional plane, with color gradients indicating varying levels of density.
2D Density of sin(x)+sin(y)
  • 2D Contour: Displays contour lines representing constant values of the function in a two-dimensional plane, facilitating the visualization of level sets and isolines.
2D Contour of sin(x)+sin(y)

Colors modes:

  • Color Spectrum: Utilizes a spectrum of colors to represent the function, with distinct hues indicating different function values. This mode provides a visually vibrant representation of the function.
Color Spectrum of sin(x)+sin(y)
  • Dual Shade: Renders the function using two contrasting shades, typically alternating between light and dark tones. This mode offers a clear and easy-to-read visualization of the function.
Dual Shade of sin(x)+sin(y) and cos(xy)
  • Gray Scale: Displays the function using varying shades of gray, with lighter shades representing higher function values and darker shades representing lower function values. This mode provides a monochromatic representation of the function.
Gray Scale of sin(x)+sin(y) and cos(xy)
  • Fog: Applies a fog effect to the graph, with closer objects appearing clearer and distant objects appearing more obscured. This mode enhances depth perception and realism in the visualization of the function.
Fog of sin(x)+sin(y)

These color modes offer different aesthetic styles and visualizations, allowing users to choose the most suitable color representation based on their preferences and requirements.

By leveraging color and style options effectively, you can create visually appealing and informative 3D graphs that effectively convey the underlying mathematical concepts. Experiment with different combinations to find the optimal settings that suit your preferences and facilitate a deeper understanding of plotted functions.

Example Problems

Example Problems

Plot the function x2+y2 in the 3D graphing mode of CalcES calculator.

  • Input the equation x2+y2 into the calculator.
  • Tap the GRAPH to show graph options dialog
  • Select the 3D Graphing option to open 3D graphing screen
  • Adjust viewing parameters to visualize the function from different angles
3D graphing of x^2+y^2