RepresentingSolids
LearningObjectives
- Identifyisometric,orthographic,cross-sectionalviewsof solids.
- Drawisometric,orthographic,cross-sectionalviewsof solids.
- Identify, draw, and constructnets for solids.
Introduction
The best way to representa three-dimensionalfigureis to use a solidmodel.Unfortunately, modelsare
sometimesnot available.Thereare four primarywaysto representsolidsin two dimensionson paper. These
are:
- An isometric(or perspective)view.
- An orthographicor blow-upview.
- A cross-sectionalview.
- A net.
IsometricView
The typicalthree-dimensionalview of a solidis theisometricview. Strictlyspeaking,an isometricview of
a solid doesnot includeperspective.Perspectiveis the illusionusedby artiststo makethingsin the distance
look smallerthan thingsnearbyby usinga vanishingpointwhereparallellines converge.
The figuresbelowshowthe differencebetweenan isometricand perspectiveview of a solid.
As you can see, the perspectiveview looksmore“real”to the eye, but in geometry, isometricrepresentations
are usefulfor measuringand comparingdistances.
The isometricview is oftenshownin a transparent“see-through”form.