Geometry

Representing Solids

Big Picture

There are four main ways to visualize a three-dimensional figure in two dimensions: isometric view, orthographic view, cross-sectional view, and a net.

Key Terms

Perspective: Artistic illusion used to make things in the distance look smaller by using a vanishing point where parallel lines converge.

Isometric View: Three-dimensional view of a solid that does not typically include perspective.

Orthographic Projection: A view that shows a flat representation of each side of the figure’s sides.

Cross Section View: A slice of a three-dimensional figure.

Net: A two-dimensional figure that can be folded into a geometric solid.

Isometric View

Isometric View

The  perspective view looks more “real” to the eye, but isometric view is more useful for measuring and comparing distances. It is often shown in a transparent form; shading and coloring can also be applied to make the figure look more realistic.

Isometric View

Orthographic View

How to show a figure in an orthographic projection:

  • Place it in an imaginary box.
  • Project each side of the figure out to each of the walls of the box.
  • The image of the side will be on each of the six walls of the box.

For example:

Orthographic View

Geometry

Representing Solids Cont.

Cross Section View

Cross Section View






This is similar to slicing a 3-dimensional figure into a series of thin slices. Each slice will show a cross section view. Depending on the angle at which we slice the figure, there are many possible cross sections that we can get.

Net

Nets are just another way to model a figure. If a net is cut out, it can be folded into a model of a figure. A single figure can have multiple possible nets.

Nets

Notes