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GeoGebraGeoGebra Classroom

Understanding Multiple Vanishing Points

A Vanishing Point in a 2-dimensional composition is a point in the 2-dimensional media where parallel lines of the 3-dimensional subject converge in the 2-dimensional composition. For example, the vanishing point of the parallel lines in Raphael's School of Athens is behind Plato and Aristotle.  The presence of a vanishing point or vanishing points creates the illusion of 3 dimensions in 2-dimensional media. This illusion is sometimes called perspective. When creating a 2-dimensional perspective composition, it can be challenging to understand how to intentionally locate vanishing points in your 2-dimensional media to accurately depict your 3-dimensional subject. The applet below helps you understand the process of selecting the location of vanishing points based on information about your subject. To get started: Move the point MyEye in the left window around the 3-dimensional cube. The point represents your point of view of the cube in 3 dimensions. As you move MyEye, the blue canvas--which represents your 2-dimensional canvas--automatically draws a perspective drawing of the cube from the point of view of MyEye with three vanishing points. The drawing is displayed on the right.
  • Click the button on the bottom to toggle on/off aids in locating vanishing points.
  • If you get "lost", click the circular arrows in the top right of bottom pane.
  • Click on MyEye to toggle between lateral/vertical movement.
  • You may need to pan or zoom in the right pan if motion of MyEye takes your drawing out of frame.
After exploring with the applet, consider the following rule about how to locate a vanishing point of a set of parallel lines : Vanishing Point Rule: The location of the vanishing point in a 2-dimensional media for a set of parallel lines is the intersection of the line L and the 2-dimensional media, where line L is the unique line through MyEye and which is parallel to the lines . In the applet, there are three sets of parallel lines in the cube, and therefore there are three vanishing points. There is no limit to the number of vanishing points in a perspective drawing, however because a cube has only three sets of parallel lines, only three vanishing points are required to properly illustrate the cube with perspective. Can you use this rule to create your own multiple vanishing point perspective drawing of a 3-dimensional subject?