In computer graphics, the art of transforming three-dimensional objects into a two-dimensional representation is essential. This process, known as projection, allows us to portray complex 3D scenes on a flat screen, enabling us to comprehend and interact with the digital environment effectively.

Two popular projection methods, parallel and perspective projection, serve as the backbone of computer graphics. While both techniques aim to bring 3D objects into the realm of 2D, they do so in vastly different ways, each offering distinct advantages and applications.

**The main difference between parallel and perspective projection lies in their visual effects. Perspective projection provides a sense of depth and realism, while parallel projection maintains equal object sizes and does not create the illusion of distance.**

**What is parallel projection?**

Parallel projection is a technique in computer graphics used to project three-dimensional (3D) objects onto a two-dimensional (2D) plane while preserving parallelism and maintaining the same size of objects regardless of their distance from the viewer.

Types of parallel projections commonly used:

**Orthographic Projection (Orthogonal Projection):**In orthographic projection, the projection rays are perpendicular to the projection plane. It is as if the viewer’s eyes are infinitely far away from the scene. This results in no foreshortening or perspective effects, making all objects appear with equal sizes and no sense of depth.**Oblique Projection:**In oblique projection, the projection rays are at an angle to the projection plane. This creates a skewed appearance of the objects, but like orthographic projection, it does not involve perspective effects or depth perception.

**A parallel projection** is a projection of an object in
three-dimensional space onto a fixed plane referred as the projection plane or
image plane, where the rays, known as lines of sight or projection lines are
parallel to each other. The projection is referred to as *orthographic* if the rays are perpendicular to the image
plane and oblique or skew if they are not.

Parallel projections are popular in technical applications, since the parallelism of an object’s lines and faces is preserved, and direct measurements can be taken from the image. Among the parallel projections, orthographic projections are the most realistic and are commonly used by engineers whereas certain types of oblique projections such as cavalier projection, military projection are very simple to implement and are used to create quick and informal pictorials of objects.

In other words, in parallel projection, the projection rays or lines from the 3D points are parallel to each other and perpendicular to the projection plane. This means that the projection does not take into account the perspective effects that occur in natural vision. As a result, all objects appear the same size, and parallel lines in the 3D scene remain parallel in the projection, leading to a more straightforward and schematic representation of the objects.

**What is perspective projection?**

Perspective projection is used in computer graphics and photography to create the illusion of depth and realism in a two-dimensional representation of a three-dimensional scene. It simulates how objects appear smaller as they recede into the distance, just as they do in our natural vision.

In other words**, perspective projection** can be described as the projector lines (lines of sight) that converge at the center of projection, which results in many visual effects of an object. Perspective projection depends on the relative position of the *eye* and the *viewplane*. A perspective projection of an object is often considered more realistic than a parallel projection, since it nearly resembles human vision and photography.

A key concept in perspective projection is the vanishing point. In a perspective projection, all lines that are parallel in 3D space appear to converge and meet at a vanishing point on the horizon line. This creates the visual effect of depth and the sense that objects become smaller as they move away from the viewer. The number of vanishing points depends on the type of perspective projection used.

**Types of Perspective Projections:**

**One-Point Perspective (Single-Point Perspective):**In one-point perspective, all lines parallel to one of the three principal axes (usually the z-axis) converge to a single vanishing point on the horizon. This type of projection is often used when the scene has objects aligned in a straightforward manner, such as looking down a straight road or a corridor.**Two-Point Perspective:**In two-point perspective, lines parallel to two of the principal axes (usually x and y) converge to two vanishing points on the horizon. This type of projection is commonly used in architectural renderings, as it allows for the depiction of buildings and structures with two visible sides.**Three-Point Perspective:**Three-point perspective is an extreme case of perspective projection where lines parallel to all three principal axes (x, y, and z) converge to three vanishing points. This type of projection is rarely used in standard applications and is mainly reserved for highly artistic or dramatic depictions of scenes with extreme foreshortening.

## Perspective Vs. Parallel Projection In Tabular Form

BASIS OF DIFFERENCE | PERSPECTIVE PROJECTION | PARALLEL PROJECTION |

Description | A perspective projection can be described as the projector lines (lines of sight) that converge at the center of projection, which results in many visual effects of an object. | A parallel projection is a projection of an object in three-dimensional space onto a fixed plane referred as the projection plane or image plane, where the rays, known as lines of sight or projection lines are parallel to each other. |

Types | One-point perspective Projection. Two-point perspective projection. Three-point perspective projection. | Orthographic parallel projection Oblique parallel projection. |

Accurate View Of Object | Perspective projection cannot give the accurate view of object. | Parallel projection can give the accurate view of object. |

Object Representation | Perspective projection represents the object in three dimensional way. | Parallel projection represents the object in a different way like telescope. |

Realistic View of Object | Perspective projection forms a realistic picture of object. | Parallel projection does not form realistic view of object. |

Distance Of The Object From The Center Of Projection | The distance of the object from the center of projection is finite. | In parallel projection, the distance of the object from the center of projection is infinite. |

Projector | Projector in perspective projection is not parallel. | Projector in parallel projection is parallel. |

Preservation Of Relative Portion Of An Object | Perspective projection cannot preserve the relative proportion of an object. | Parallel projection can preserve the relative proportion of an object. |

Lines Of Projection | The lines of perspective projection are not parallel. | The lines of parallel projection are parallel. |

**Key Takeaways **

**Basic Principle:**- In parallel projection, all the rays or lines from the 3D scene are projected onto the 2D plane parallel to each other. This means that the vanishing points are at infinity, and there is no convergence of lines in the projection.
- In perspective projection, the rays or lines from the 3D scene converge towards a common point called the “vanishing point.” This creates a sense of depth and realism, simulating how objects appear smaller as they move away from the viewer.

**Realism and Depth Perception:**- Parallel projection does not provide a realistic sense of depth or distance. All objects appear the same size, regardless of their position in the scene. It is often used for technical drawings or diagrams where maintaining accurate proportions is essential.
- Perspective projection mimics human vision more realistically. Objects closer to the viewer appear larger, and objects farther away appear smaller, giving a sense of depth and creating a more immersive visual experience.

**Types of Parallel Projection:**- Orthographic projection is a type of parallel projection where the projection rays are perpendicular to the projection plane. It is commonly used for engineering and architectural drawings.
- Oblique projection is another type of parallel projection where the projection rays are at an angle to the projection plane, resulting in a skewed appearance. It is used less frequently due to its non-realistic nature.

**Types of Perspective Projection:**- In one-point perspective, all lines converge to a single vanishing point on the horizon. This is suitable for scenes where objects are aligned along one primary direction, such as railway tracks disappearing into the distance.
- In two-point perspective, lines converge to two vanishing points on the horizon, typically used when the scene contains objects with edges that are parallel to two principal axes, such as buildings or rooms.
- Three-point perspective is used in extreme cases where objects are viewed from an extreme angle, resulting in three vanishing points. It is more common in artistic and architectural illustrations.

**Mathematical Representation:**- Mathematically, parallel projection involves a straightforward transformation of 3D coordinates onto the 2D plane without any perspective effects. It can be implemented using simple matrix operations.
- Perspective projection requires more complex mathematical calculations involving homogenous coordinates to achieve the converging effect towards the vanishing point.