Abstract

Art, Math and Science at first seem like very different subjects, but they are related in variety of ways. Experience the relationship between math and art by creating a miniature world inside a box and learn how linear perspective works.

Diorama (Creating illusion of depth using perspective)

Why do things further away look smaller?  Why we cannot see objects that are behind other objects?  Learn how we perceive depth and make a miniature world inside a box.

Objectives:

  • Notice various depth cues we use to perceive distance.
  • Understand why the distance affects the apparent size of objects.
  • Understand why the closer objects block the view of objects in distance.
  • Experience the connection between art and math (perspective art and projective geometry).

Materials:

  • Box
  • Everyday craft supply (construction paper, craft foam sheets, tissue paper, pompoms, etc.)
  • Glue (hot glue works well for this project)
  • Sample Picture (Depth Cue) (included in this document)
  • “Perspective Projection Principle” image (included in this document)

Tools:

  • Pencils
  • Scissors
  • Markers

Activity 1

Artists use various depth cues to create an illusion of depth.  Perspective is one of them. It is a technique to change the size and position of objects in relation to each other to make objects appear closer or farther away.  Examine the picture below to see how we perceive a sense of depth.

Here are some of the things you might notice looking at this picture.

  • Parallel lines meet at a point on the horizon.
  • Things farther away appear smaller.
  • Straight lines remain straight but angles of objects may change when photographed.
  • Closer objects block the view of farther away objects on the same sight line.
  • Objects closer to the horizon are farther away from the viewer.
  • There are other depth cues such as outline, texture, color and brightness.

Note: When we look at real three dimensional objects or sceneries, we also get depth cues from using  two eyes together (binocular vision).

Additional Information

Why do things further away look smaller?

When viewing an object, the light rays from the top and bottom of the object determine the size of the image projected on the picture plane.  A picture plane is an imaginary plane between the viewer’s eye and the various objects.  The projected image gets larger as an object moves closer to the eye, and it gets smaller as an object moves further away.  This is the basic idea artists use to create perspective drawings.

Why can’t we see the objects that are behind other objects?

The line of sight is a line that connect a distant point and an observer’s eye.

All points that lie along the same line of sight connect to a single point on the picture plane. If there are two points that lie along the same line of sight, the point nearer to the observer blocks the light from the point farther away.

Image Credit: https://commons.wikimedia.org/wiki/File:Perspective_Projection_Principle.jpg

Perspective uses mathematical rules.

Artists use perspective to draw realistic objects or scenery on a flat surface.  It is a systematic technique to create illusion of distance and depth by projecting three dimensional objects onto two dimensional surfaces.

The development of perspective in art  during the Renaissance era lead to renewed interest in projective geometry, a branch of mathematics that focuses on the geometry of projected space.

Geometry is a study of shapes in space and how they are related.  The size and shape of objects may change when they are projected onto a different space, but some properties stay the same. Projective geometry deals with the properties and invariants of geometric figures under projection.  For example, now we know why straight lines stay straight when photographed, although the shapes of objects may be deformed in the picture.  We study mathematics to advance the understanding of the world we live in. 

Activity 2

Create the diorama using perspective and other depth cues.

Now you are ready to create your own diorama.  Before you start you might want to find images of dioramas on the internet to see how artists use various depth cues to create the scenery.   The American Museum of Natural History has many beautiful dioramas.

Step 1: Choose your theme

Think of a scene you would like to create inside the box.  It can be an imaginary forest, underwater world, a scene from a book you read, a place you visited, etc.  Incorporate various objects at different distances to enhance the 3D effect.

Step 2: Gather materials

Find a box and gather materials you can use to create your diorama.  If you can not find suitable box, you can make one from scrap cardboard.

Step 3: Create the background and cover the ground

Glue a sheet of paper or a picture inside the back panel of the box. Extend the background to cover the ground.  Think of the vanishing point and adjust the height of the horizon as necessary.

Step 4:  Add layers and  objects to the scene. 

Make far away objects smaller, and closer objects larger to create a sense of depth.  Use other cues to add more depth information.

References and Resources:

http://www.marthastewart.com/910338/how-make-forest-diorama

http://peabody.yale.edu/james-perry-wilson

Fleet Science Center

 

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