Math in Visual Art: Learn It 1

  • Explain the concept of perspective and its application in art, design, and architecture
  • Recognize and understand the fundamental concepts of reflection, rotation, and translation symmetry as they relate to two-dimensional shapes and patterns

Perspective in Art, Design, and Architecture

An empty road leading off to the horizon

 

Perspective is a crucial technique used across a range of visual disciplines to suggest depth and volume in two-dimensional spaces. By simulating the way our eyes perceive distance and proportion, perspective makes drawn and designed representations appear more realistic. When we view a scene, objects in the distance appear smaller than objects close to us, and parallel lines recede to a point on the horizon known as the vanishing point.

perspective

Perspective is a drawing technique that portrays depth and volume on a flat surface. It is a visual representation of how we see the world with our eyes. 

It is important when working with perspective to understand viewpoint. Viewpoint, in the realm of visual arts, refers to the position from which the artist observes or envisions their subject.

The chosen viewpoint has a profound impact on how the subject is perceived, influencing the composition, detail, and depth of the resulting artwork, design, or architectural structure. The main types of viewpoint are high viewpoint (bird’s eye view), low viewpoint (worm’s eye view) and eye-level viewpoint.

  • A high viewpoint allows an artist to see and depict the scene from above. This viewpoint often results in a composition where the subject or subjects seem smaller, and more of the surrounding context can be seen.
  • A low viewpoint positions the observer below the subject matter. In this perspective, objects appear larger and more dominant, creating a sense of scale and power.
  • An eye-level viewpoint, as the name suggests, places the observer’s perspective at the same level as the subject. This is the most naturalistic viewpoint, as it corresponds with how we typically perceive the world around us.

The connection between viewpoint and perspective is that the chosen viewpoint directly impacts the perspective in the composition.

types of perspective

There are three different types of perspectives: one-point perspective, two-point perspective, and three-point perspective.

 

  • In one-point perspective, all lines converge to a single point on the horizon. This point is known as the vanishing point. In one-point perspective, vertical lines remain vertical, and horizontal lines remain horizontal.
  • In two-point perspective, the object is viewed at an angle rather than from the front. Hence, there are two vanishing points on the horizon line. This perspective is commonly used in architectural drawings and urban scenes.
  • Three-point perspective is typically used when you want to create a bird’s-eye view (looking down on an object) or a worm’s-eye view (looking up at an object). In addition to the two vanishing points on the horizon line, there’s a third vanishing point either above or below the horizon.

 

Below are some examples of these perspectives:

  • One-point perspective: Imagine standing in the middle of a straight road, looking towards the horizon. The sides of the road meet at a point on the horizon. 
A long tunnel from a one-point perspective
  • Two-point perspective: Visualize yourself at a corner where two walls meet. Each wall extends back into space, converging at separate vanishing points on the horizon line.
a drawing of a shed with the door open from a two-point perspective
  • Three-point perspective: Picture looking up at a tall building from its base. The sides of the building recede towards two vanishing points on the horizon, while the top recedes towards a third point above.
A building from a three-point perspective

As we delve deeper into perspective, two fundamental concepts come to the forefront: the horizon line and vanishing points. The horizon line and vanishing points are crucial elements when creating a perspective drawing. They help an artist establish depth and spatial relationships between objects, allowing for a more realistic depiction.

horizon line

The horizon line is a horizontal line that runs across the paper or canvas to represent the viewer’s eye level and delineate the sky from the ground. 

In other words, the horizon line is the actual height of the viewer’s eyes when looking at an object, scene, or landscape. Whether you’re standing on the ground or looking down from a tall building, the horizon line becomes the point at which the sky appears to meet the ground.

In the context of perspective drawing, the horizon line can be placed anywhere in the scene, not necessarily in the middle of the canvas, and it doesn’t have to represent a visible horizon. The positioning of the horizon line can have a dramatic impact on how the final image is perceived; a low horizon line can make an object appear towering and imposing, while a high horizon line might make the same object seem small and distant.

vanishing points

Vanishing points, on the other hand, are points located on the horizon line where parallel lines appear to converge in a perspective drawing. They give depth to the drawing and are crucial in creating a three-dimensional effect.

In one-point perspective, there is a single vanishing point located directly on the horizon line. This is typically used when objects are viewed front-on, such as a road or railway track stretching into the distance. Two-point perspective uses two vanishing points, which are beneficial when representing an object or scene from a corner or edge view. Three-point perspective uses three vanishing points and is typically used for buildings seen from a bird’s or worm’s eye view.

Depiction of perspective. In the center, there is a dot labeled Vanishing Point. Through it, there is a horizontal line labeled "horizon line." There are two cubes shown as well, with lines coming from the vanishing point outwards lining up with the edges of the cubes.
1-point, 2-point, and 3-point perspective

 

Perspective in Art

Artists use perspective to bring depth to their creations, transforming flat, two-dimensional canvases into portals peering into three-dimensional worlds. As far back as the Renaissance, artists like Leonardo Da Vinci used linear perspective to create an illusion of distance and depth. They employed vanishing points, where parallel lines seem to converge, giving their paintings a realistic depth that mimics the way human eyes perceive the world around us.

Perspective in Design

Design fields, such as graphic design, industrial design, and UI/UX design, use perspective to make their creations more visually compelling and realistic. For instance, in graphic design, perspective can add depth to what would otherwise be flat, static images. Similarly, in industrial design, using perspective when sketching products can help give a more accurate representation of how an object will look and feel in real life. In UI/UX design, perspective is employed to create a sense of depth in screen interfaces, helping users understand the hierarchy and importance of different elements on the screen. Icons and menus may be designed with perspective to show that they’re interactive, or to make 2D screen elements seem almost 3D.

Perspective in Architecture

Perspective is an integral part of architectural drawings and plans. Architects use perspective to represent three-dimensional buildings on two-dimensional paper or digital screens. It helps to provide a realistic view of the building and allows architects to visualize and plan the structure effectively.