Representation of 3D figures on 2D

We have already seen in the previous sections, how when depicting real life 3-D objects on a piece of paper, often the diagram becomes two dimensional. However, using visual illusion, we can draw a solid shape so that the diagram is distorted to look like a three-dimensional object.

There are two techniques for doing this, which we will look into now.

Oblique Sketches

Here, we have a diagram of a cube. What can be said about it? It gives a clear depiction of how a cube looks like when viewes from the front. We also do not see certain faces. In the diagram drawn here, the lengths are not necessarily equal as they should be in a cube, yet we are able to recognise the object as a cube. Such a sketch of a solid is called an oblique sketch of that solid.

Cube Oblique Sketch

In the oblique sketch we make the following observations:

• The sizes of the front face and its opposite face are the same

• The edges, which are all equal in a cube, appear so in the sketch. However, the actual measures of edges are not taken into consideration.

Similarly, we can make one for a cuboid:

Cuboid Oblique Sketch

Continue

Isometric Sketches

The second type of sketch for making 3-D depictions of objects is using an isometric sheet. On these sheets, we draw sketches where the measurements agree with that of the real-life measurement values of the object. These sketches are called isometric sketches.

Let us try to draw an isometric sketch of a cuboid of dimensions 4 × 2 × 2 i.e. length, breadth and height are 4, 2, 2 units respectively.

The diagram drawn will look something like the following:

Cuboid with actual measurements

Isometric Cuboid

The process would look something like this:

Continue

Let's Solve

On isometric dot paper, make the isometric sketches for the following given shapes:

(a)

(b)

(c)

(d)

Make the oblique sketches for each one of the given isometric shapes:

(a)

(b)