Orthographic Views

Matching 3D objects with their top, front, or side projections.

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Matching 3D objects with their top, front, or side projections.

View matching involves identifying how a 3D object appears when projected onto a 2D plane from different directions. Orthographic projection shows top, front, and side views without perspective distortion. This is fundamental in technical drawing, engineering, and architecture.

view = project(3d_object, viewing_direction)

Top view shows which cells have any blocks
Front view shows the maximum height in each column
Side view shows the height profile from the left or right

How to recognize it

For top view: look straight down, note which positions have blocks
For front view: look from front, trace the highest visible point in each column
For side view: look from side, trace the profile
Hidden blocks behind visible ones don't change the view

Common mistakes

Confusing which direction each view comes from
Not considering that multiple heights project to same position
Forgetting that views show silhouettes, not internal structure

Step-by-step walkthrough

A staircase made of blocks goes up from left to right (heights 1, 2, 3). What does the front view look like?

Position yourself viewing from the front, looking at the staircase head-on.
From the front, you see each column of blocks at its full height.
The left column has height 1, middle has height 2, right has height 3.
Front view shows these as a staircase silhouette stepping up left to right.
The view is a stepped profile: 1 block, 2 blocks, 3 blocks from left to right.

Answer: A stepped silhouette rising from 1 block on the left to 3 blocks on the right

Practice guidance

Spatial Reasoning