Orthographic Views: Top, Front and Side
Three flat pictures can describe a 3D shape well enough to build it. Here is how to read them, and how to go from the views back to the solid.
What orthographic projection is
Orthographic projection draws an object as if you were looking at it from very far away, straight on to one side. There is no perspective: parallel edges stay parallel, and every square face stays a true square. Each picture made this way is an orthographic view. Engineers, architects and CAD programs describe parts with a set of these views because, unlike a photo, every measurement can be read straight off the drawing.
The three views
- Top view: looking down from above. The front edge is at the bottom of the picture.
- Front view: standing in front, where the arrow points. Left is left and the ground is at the bottom.
- Left side view: standing on the left. The front is on your right, the back on your left.
Many engineering drawings use a right side view instead. The book THINK IN 3D and our puzzles use the left side view, so that is what you will see here. Always check which side a view was drawn from before you read it.
Lines show depth
A filled square means something solid is on that line of sight. A thick line inside a view means the surface you see steps nearer or further away at that line. No line means one flat face. So the lines tell you about depth, even though each view on its own is flat.
Some cubes can hide completely behind others. When the views cannot tell whether a cube is there, the book's rule is "hidden means solid": treat it as solid. Our puzzles follow the same rule, so every question has exactly one answer.
From the views to the solid, step by step
- Find the front. Everything depends on it. In our drawings an arrow under the solid marks the front.
- Use the top view for the footprint. It shows which squares of the floor have at least one cube, and its lines show where neighbouring stacks have different heights.
- Use the front view for heights left to right. Each column of the front view is as tall as the tallest stack in that column of the footprint. Thick lines show which stacks stand further back.
- Use the left side view for heights front to back. Read it from right (front) to left (back): each column is as tall as the tallest stack in that row.
- Combine them. A stack can be no taller than both its front view column and its side view column. Where the two limits meet, a tall stack must stand.
- Check all three views. Build the solid in your head, then draw each view from it, lines included. If one view differs, a stack is in the wrong place.
The common traps
- The mirror image. A view flipped left to right looks almost right. Check which side the tall part is on.
- Reading the wrong side. The left side view has the front on the right. Mixing that up is the most common mistake.
- Ignoring the lines. Two views with the same outline can have different inner lines, and only one matches.
- Two views match, one does not. On Medium and harder, every wrong answer matches two of the three views. Never stop after two checks.
Isometric vs orthographic drawing
The solids on this page are isometric drawings. Isometric drawing shows the top, the front and one side together in a single picture. The three edges of every cube are drawn the same length and 120 degrees apart, so the cube looks solid without any perspective. Orthographic views show one side at a time instead.
The two go together. Reading a set of orthographic views and sketching the solid on isometric grid paper is exactly the skill engineering drawing classes and spatial reasoning tests practise. To sketch one: draw the footprint from the top view as a diamond grid, raise each stack to its height from the front and side views, then darken the visible edges.
Practise it
Reading views gets quicker with practice. The 3D spatial reasoning puzzles give you a new five-question test every day and unlimited rounds at four levels, with the reason each wrong option fails.