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
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.
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:
