How to visualize 3-D shapes from 2-D drawings ?

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Visualization is the key part of an Architect which helps him/her to eye for the detail.Often people find it difficult to visualize 3-d objects from 2-d drawings or vice-versa. Well this article explains various types of drawings and provides information on how to visualize objects and draw their faces. So before visualizing part begins lets focus on what does a 2-d or 2-d geometry means.

  • 2-dimensional Shape

Any shape that can be laid flat on a piece of paper or any mathematical plane. A 2D shape is any shape that has two dimensions.In mathematics, a flat surface is called a plane. A plane is one example of a two-dimensional shape.Examples of 2D shapes include rectangles, octagons,squares,circles.

2-dimensional Shape is a shape that does not have a parameter of depth attached to it. This is the reason why we can draw a 2-d shape on a plane because plane itself is only 2-dimensional having parameters of length and breadth.

cylinder

Cylinder- Top and Front Face

The above image describes how an 2-d face of a cylinder is crated by simply taking projections from it.Try the exercise below to make a 2-d shape of any object around you.

Exercise – Take out a piece of paper, and place it on your desk. Now take any nearby object, place it  on the  paper, and trace around it. The shape formed will be 2-dimensional. 

  • 3-dimensional Shape

When an object has a all the three parameters of length, breadth and height attached to it the shape formed is a 3-dimensional .For example, a box is three-dimensional; it is solid. It has volume, a top and bottom, left and right (sides), as well as a front and back.

A dimension is measurable in inches, microns, miles, kilometers, or any other unit of length.The three dimensions are often called length (or depth), width (or breadth), and height.

The image below will give you a clear idea about  3-dimensional Shapes-

3-d- space

Now moving towards visualizing a 3-d object. First let us consider a part of a staircase to begin with. The image below contains a 3-d image of stairs with its faces. Try to figure out which face is of the top, side and front. Go on –

stairs

This is a very important question considering the JEE and NATA exam format. Many questions in aptitude section are of this type.If you are looking for the answer of the above question here it is –

Answer – Bottom Left Image (Side Face of staircase )  , Bottom Right Image (Front face or Risers of staircase), Top Left Image (Top Face or Tread of staircase)

The complexity of the same can be increased but the principles are simple.

example

These images show the relation between an 2-d and 2-d image. When we look at any object its each surface is a 2-d plane. All together an 3-d object is formed by multiple 2-d surfaces. Once you get a hang of what an 2-d surface means and how it corresponds with 3-d object you can easily think of its different faces.

  • Orthographic projection is a way of showing a 3D object in 2D. It is a form of parallel projection, where the view direction is orthogonal to the projection plane. As shown in figure- “Cylinder- Top and Front Face” above orthogonal projections are used to show 2-d surfaces of a object. 

Below are some questions that came in the exam. Try attempting it. The answer will be in the end of this article.

JEE -MAINS- 2014

JEE MAINS Question

Interestingly an 3-d object can be viewed in different ways. It depends on angle with which we view its surfaces. Given below are some terms which will be useful in understanding the concept of 3-d shapes and geometry-

  • Perspective Drawing –

It is a drawing method that shows how things appear to get smaller as they get further away, converging towards a single ‘vanishing point’ on the horizon line. It is a way of drawing objects upon a flat piece of paper (or other drawing surface) so that they look three-dimensional and realistic.

perspective

perspective drawing

  • Isometric Drawing 

It is a method for visually representing three-dimensional objects in two dimensions in technical and engineering drawings. It is an axonometric projection in which the three coordinate axes appear equally foreshortened and the angle between any two of them is 120 degrees.

isometric_paper

isometric drawing

  • Oblique projection

It is a simple type of technical drawing of graphical projection used for producing two-dimensional images of three-dimensional objects. The objects are not in perspective, so they do not correspond to any view of an object that can be obtained in practice, but the technique does yield somewhat convincing and useful images.

In short a  projection made by parallel lines drawn from every point of a figure and meeting the plane of projection obliquely.

Oblique-projection

In the end I hope this article helped you to clear your concepts and gave you  knowledge about 3- dimensional drawings and it’s relation with 2-dimensional surfaces.

Answers- 3(4), 4(4)

 

Material Study – Part 1

 

What Are Some Basic Terminologies In Architecture ?

 

Colour Theory

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