Orthographic projection – three views of a solid
Mathematics3D GeometryAges 16–17
Use it with your class: students open it from a link or a QR code, with no account needed.
Next in 3D Geometry
Build a solid from unit cubes (click the grid to raise or lower each column) or pick a preset shape, rotate it to look around, and see the three orthographic views – front, top, and side – laid out by first-angle projection, with solid lines for visible edges and dashed lines for hidden edges. The 2D | 3D button shows the actual solid in the corner of the three projection planes (front plane behind, top plane below, side plane on the right), with projection rays and each view drawn on its plane, and the scene can be rotated.
Lesson: Elements of technical drawing
What it shows
Orthographic projection represents a 3D object by 2D views drawn at right angles to it. Here the solid is built from unit cubes, and its front, top and side views are generated and laid out by first-angle projection, the convention used in Europe and much of Asia: the top view sits below the front view and the side view to its right. Visible edges are solid lines and hidden edges are dashed, which is why a concealed slot or hole must still appear in the drawing. The 3D mode shows the solid in the corner of the three projection planes, with projection rays.
How to use
Pick a Sample solid and ask students to sketch the three views before looking at the result. Change the Viewing rotation angle to look around the solid, compare each view with the drawing, and switch Show hidden lines on and off. Next, build a new solid by clicking grid cells to raise each column, or reverse the task: show only the three views and have students reconstruct the solid. Use 3D and Reset view to see how each view lands on its plane.
Parameters you can change
- Sample solid L-block, Step block, Slotted block, Support bracket
- Viewing rotation angle 0–355 °
Questions to explore
- Which two dimensions of the solid can you read from the top view?
- When is an edge drawn as a dashed line in a view?
- Can two different solids have the same front view, and how would you build an example on the grid?
Common questions
What is orthographic projection, and how is it different from a perspective drawing?
Orthographic projection draws a solid with parallel rays perpendicular to a plane, so a face parallel to that plane keeps its true size and shape, whereas a perspective drawing uses rays meeting at the eye, so distant parts look smaller. Orthographic views are harder to picture at first, but lengths can be measured directly from them, which is why engineers use them.
How do you draw the three views of a solid built from cubes?
Look straight along each direction and draw one square for every position where you can see material, however far away it is, keeping the views on the same grid with the top view below the front view and the side view to its right. Then add any edges hidden behind material as dashed lines.
How can you work out the shape of a solid from its three views?
Read the views together, never just one, following the alignment lines: a feature in the front view lies directly above its position in the top view and level with its position in the side view. Start from the outline in one view, use the other two to find depth and height, and check that dashed lines match hidden slots or holes.
