3D Graphics View

Perspectives algebra 3Dgraphics.svg 3D Graphics View User Interface

By default, the Perspectives algebra 3Dgraphics.svg 3D Graphics View is opened next to the Algebra View Algebra View. In addition, either the Input Bar is displayed at the bottom of the GeoGebra window (GeoGebra Desktop), or an Input Field is integrated directly in the Algebra View Algebra View (GeoGebra Web and Tablet Apps). The 3D Graphics View Toolbar is displayed at the top of the GeoGebra window, with the Menu-edit-undo.svgMenu-edit-redo.svg Undo / Redo buttons in the top right corner.

3D-Graphics-View.png

3D Graphics View

The Perspectives algebra 3Dgraphics.svg 3D Graphics View is part of the Perspectives algebra 3Dgraphics.svg 3D Graphics Perspective, although you may add a Perspectives algebra 3Dgraphics.svg 3D Graphics View window to any Perspective at any time by using the Menu-view.svg View Menu or the Stylingbar dots.svg Views button in the Style Bar.

Customizing the 3D Graphics View

You can customize the Perspectives algebra 3Dgraphics.svg 3D Graphics View according to the mathematical topic you want to work with. The basic setup can be changed using the 3D Graphics View Style Bar (e.g. display of coordinate axes, xOy-plane, grid). In addition, the Preferences Dialog provides more options to customize the Perspectives algebra 3Dgraphics.svg 3D Graphics View. You may also change the layout of GeoGebra’s user interface according to your needs.

Creating Mathematical Objects

Constructions with the Mouse

Using the construction Tools available in the 3D Graphics View Toolbar you can create geometric constructions in the Perspectives algebra 3Dgraphics.svg 3D Graphics View with the mouse. Select any construction tool from the 3D Graphics View Toolbar and read the tooltip provided in the Perspectives algebra 3Dgraphics.svg 3D Graphics View in order to find out how to use the selected Tool.

Any object you create in the Perspectives algebra 3Dgraphics.svg 3D Graphics View also has an algebraic representation in the Algebra View Algebra View.

Select the Mode sphere2.svg Sphere with Center through Point Tool and click in the 3D Graphics View twice. The first click creates the center point while the second click creates a sphere and a point on the sphere.

Note Hint: In order to create a new point in the 3-dimensional space, you need to…​

  • click and hold the mouse key (tap and hold) in order to define it’s x- and y-coordinate, then

  • drag the point up or down in order to change the z-coordinate and

  • release the click (tap) once you reached the desired coordinates.

3D Graphics View Toolbar

The 3D Graphics View Toolbar provides a wide range of Tools that can be operated with the mouse and allow you to create the three-dimensional graphical representations of objects directly in the Perspectives algebra 3Dgraphics.svg 3D Graphics View. Every icon in the Toolbar represents a Toolbox that contains a selection of related construction Tools. In order to open a Toolbox, you need to click on the corresponding default Tool shown in the 3D Graphics View Toolbar (GeoGebra Web and Tablet Apps) or on the small arrow in the lower right corner of the Toolbar icon (GeoGebra Desktop).

3D Graphics Tools

The Tools of the 3D Graphics View Toolbar are organized by the nature of resulting objects or the functionality of the Tools. You will find Tools that create different types of planes in the Mode planethreepoint.svg Planes Toolbox or Tools that allow you to create geometric solids in the Mode pyramid.svg Geometric Solids Toolbox.

Direct Input using the Input Bar

GeoGebra’s Perspectives algebra 3Dgraphics.svg 3D Graphics View supports points, vectors, lines, segments, rays, polygons, and circles in a three-dimensional coordinate system. You may either use the Tools provided in the 3D Graphics View Toolbar, or directly enter the algebraic representation of these objects in the Input Bar or Input Field of the Algebra View Algebra View (GeoGebra Web and Tablet Apps).

Enter A=(5, -2, 1) into the Input Bar or Input Field of the Algebra View Algebra View in order to create a point in the three-dimensional coordinate system.

Furthermore, you may now create surfaces, planes, as well as geometric solids (pyramids, prisms, spheres, cylinders, and cones).

Enter f(x, y)=sin(x*y) in order to create the corresponding surface.

Commands

In addition to the wide range of /Category:Commands.adoc[Commands] available for the other Views of GeoGebra, there also is a selection of 3D Commands specifically for the 3D Graphics View.

Let A=(2, 2, 0), B=(-2, 2, 0), C=(0, -2, 0), and D=(0, 0, 3). Input the command Pyramid[A, B, C, D] and hit the Enter key in order to create the pyramid with base ABC and apex D.

Moving Mathematical Objects in 3D

Move Tool

Using the Move Tool Move Tool you may drag and drop Free Points in the Perspectives algebra 3Dgraphics.svg 3D Graphics View. In order to move a point in the three-dimensional coordinate system, you can switch between two modes by clicking on the point:

  • Mode xOy-plane: You may move the point parallel to the xOy-plane without changing the z-coordinate.

  • Mode z-axis: You may move the point parallel to the z-axis without changing the x- and y-coordinates.

Moving Objects using Keyboard Shortcuts

In the Perspectives algebra 3Dgraphics.svg 3D Graphics View, you may use the Page Up key in order to move a selected object up and the Page Down key in order to move a selected object down.

Display of Mathematical Objects

Translation of the Coordinate System

You may translate the coordinate system by using the Mode translateview.svg Move Graphics View Tool and dragging the background of the Perspectives algebra 3Dgraphics.svg 3D Graphics View with your pointing device. Thereby, you can switch between two modes by clicking on the background of the Perspectives algebra 3Dgraphics.svg 3D Graphics View:

  • Mode xOy-plane: You may translate the scene parallel to the xOy-plane.

  • Mode z-axis: You may translate the scene parallel to the z-axis.

Alternatively you can hold the Shift key and drag the background of the Perspectives algebra 3Dgraphics.svg 3D Graphics View in order to translate the coordinate system. Again, you need to click in order to switch between the two modes while holding the Shift key.

You can go back to the default view by selecting the button Stylingbar graphicsview standardview.svg Back to Default View in the 3D Graphics View Style Bar.

Rotation of the Coordinate System

You may rotate the coordinate system by using the Rotate 3D Graphics View Tool Rotate 3D Graphics View Tool and dragging the background of the Perspectives algebra 3Dgraphics.svg 3D Graphics View with your pointing device.

Alternatively you can right-drag the background of the Perspectives algebra 3Dgraphics.svg 3D Graphics View in order to rotate the coordinate system.

If you want to continue the rotation of the coordinate system when the mouse is released, you may use the option Stylingbar graphics3D rotateview play.svg Start Rotating the View and Stylingbar graphics3D rotateview pause.svg Stop Rotating the View in the 3D Graphics View Style Bar.

You can go back to the default rotation by selecting the button Stylingbar graphics3D standardview rotate.svg Rotate back to default view in the 3D Graphics View Style Bar.

Viewpoint in front of an Object

You may use the Mode viewinfrontof.svg View in front of Tool in order to view the coordinate system from a viewpoint in front of the selected object.

Zoom

You may use the Mode zoomin.svg Zoom In Tool and Mode zoomout.svg Zoom Out Tool in order to zoom in the Perspectives algebra 3Dgraphics.svg 3D Graphics View.

Note Hint: You may also use the wheel of your mouse to zoom.

3D Graphics View Style Bar

The 3D Graphics View Style Bar contains buttons to

  • Stylingbar graphics3D axes plane.svg show / hide the coordinate axes, Stylingbar graphics3D plane.svg the xOy-plane, and a Stylingbar graphicsview show or hide the grid.svg grid in the xOy-plane

  • go Stylingbar graphicsview standardview.svg back to default view

  • change the Stylingbar graphicsview point capturing.svg Point Capturing settings

  • Stylingbar graphics3D rotateview play.svg start / stop rotating the view automatically

  • adjust the Stylingbar graphics3D view xy.svg view direction

  • Stylingbar graphics3D view orthographic.svg choose the type of projection

  • open the Menu-options.svg Properties Dialog (GeoGebra Web and Tablet Apps)

  • display additional Stylingbar dots.svg Views in the GeoGebra window (GeoGebra Web and Tablet Apps)

Style Bar for Tools and Objects

Depending on the Tool or object you select, the buttons in the Style Bar adapt to your selection. Please see Style Bar Options for Tools and Objects for more information.