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Essential Concepts

• Perspective is a drawing technique that creates a sense of depth and space on a flat surface. It shows how objects appear smaller in the distance and how parallel lines converge at a vanishing point on the horizon. There are three types of perspective:
  • In one-point perspective, all lines converge to a single point on the horizon. This is like standing in the middle of a straight road and seeing the sides meet at a point on the horizon. Vertical lines remain vertical, and horizontal lines remain horizontal.
  • In two-point perspective, the object is viewed at an angle. There are two vanishing points on the horizon line, and this perspective is commonly used in architectural drawings and urban scenes.
  • Three-point perspective is used for bird’s-eye view or worm’s-eye view. In addition to the two vanishing points on the horizon line, there’s a third vanishing point either above or below the horizon.
• Viewpoint is the artist’s position or perspective when observing or imagining a subject.
  • A high viewpoint is like looking down from above. It makes the subject appear smaller and provides a broader view of the surroundings.
  • A low viewpoint is like looking up from below. It makes objects appear larger and more dominant, creating a sense of scale and power.
  • An eye-level viewpoint is at the same height as the subject. It is the most natural perspective and represents how we typically see the world.
• The horizon line is a horizontal line that represents the viewer’s eye level and separates the sky from the ground in a drawing or painting. It shows where the sky meets the ground, regardless of whether it’s visible or not. The placement of the horizon line can affect how objects are perceived, with a low line making them look tall and powerful, and a high line making them appear small and distant.
• Vanishing points are points on the horizon line where parallel lines in a drawing seem to converge. They create depth and a three-dimensional effect in the artwork.
• Perspective adds depth to art, design, and architecture. It creates a three-dimensional illusion on flat surfaces. Artists use it in paintings with vanishing points.
• Designers use perspective for realistic visuals and UI/UX depth.
• Architects use perspective to represent buildings on paper or screens, aiding visualization and planning.
• Reflection symmetry, also called mirror or bilateral symmetry, occurs when one side of an image or design is the mirror image of the other side. It creates balance and harmony.
• Rotation symmetry, or radial symmetry, happens when an object or design can be rotated around a central point and still look the same. The degree of rotational symmetry is the number of distinct orientations in which it appears identical.
• Translation symmetry, also known as slide symmetry, involves repeating an image or design in a straight line without changing its orientation. It creates a pattern that extends infinitely.
• Proportion is about the size and quantity relationship between elements in a composition. It creates balance and harmony in art, design, and architecture. Getting the proportions right is crucial for the overall look and function of the composition. The three types of proportions are:
  • Symmetrical Proportion: Elements mirrored on both sides create balance and stability.
  • Asymmetrical Proportion: Different elements balance without being identical, creating a dynamic composition.
  • Hierarchical Proportion: Elements sized according to importance or rank, emphasizing the most important.
• Proportion in Art: Proportion is the size and arrangement of elements in an artwork, impacting balance and visual interest. It is used to create realistic figures and evoke emotional responses.
• Proportion in Architecture: Proportion affects the aesthetics and functionality of buildings, considering the balance and harmony between elements. Well-proportioned buildings are visually pleasing and comfortable.
• Proportion in Design: Proportion in design involves the relationship between elements to create harmony and balance. It influences aesthetics and functionality in various design fields, such as interior design and graphic design. Principles like the Golden Ratio and Rule of Thirds are commonly used.
• The Golden Ratio is a special number that people think looks nice when used in art and architecture. It’s about [latex]1.618[/latex], and it’s often shown with the Greek letter Phi ([latex]\phi[/latex]). Many artists and architects believe that using the Golden Ratio in their designs makes them more attractive because it’s also seen in nature.
• The Fibonacci sequence is a pattern of numbers where each number is found by adding the two numbers before it. It starts with [latex]0[/latex] and [latex]1[/latex], and then each number after that is the sum of the two preceding numbers. So it goes like this: [latex]0[/latex], [latex]1[/latex], [latex]1[/latex], [latex]2[/latex], [latex]3[/latex], [latex]5[/latex], [latex]8[/latex], [latex]13[/latex], [latex]21[/latex], and so on.
• A golden rectangle is a special rectangle with a length-to-width ratio that equals the golden ratio, which is approximately [latex]1.618[/latex]. If the longer side is “[latex]a[/latex]” and the shorter side is “[latex]b[/latex],” it’s a golden rectangle when the ratio of [latex]a/b[/latex] is the same as [latex](a+b)/a[/latex], which is the golden ratio.
• The Rule of Thirds is a simple principle used in art, photography, and design. It suggests dividing an image into a [latex]3[/latex]x[latex]3[/latex] grid and placing important parts of the picture along the lines or at their intersections. This creates a more interesting and balanced composition, making the viewer look around the picture instead of just focusing on the center.

Glossary

asymmetrical proportion

involves different elements that balance each other out, without being identical

Fibonacci sequence

a series of numbers in which each number is the sum of the two preceding ones

golden rectangle

a rectangle in which the ratio of the length to the width is the golden ratio

hierarchical proportion

involves elements sized according to their importance or rank

horizon line

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

one-point perspective

where all lines converge to a single point on the horizon

perspective

a drawing technique that portrays depth and volume on a flat surface

proportion

refers to the relationship in size, quantity, or degree between different elements within a composition

reflection symmetry

when one half of an image, shape or design is the mirror image of the other half

rotation symmetry

when a design or image can be rotated around a central point and still appear the same

Rule of Thirds

an image can be divided into nine equal parts by two equally spaced horizontal lines and two equally spaced vertical lines

symmetrical proportion

when elements are mirrored on either side of an axis

symmetry

a sense of harmonious and aesthetically pleasing proportionality and balance

three-point perspective

used when you want to create a bird’s-eye view or a worm’s-eye view

translation symmetry

when an image or design is repeated in a straight line

two-point perspective

where the object is viewed at an angle rather than from the front

vanishing points

points located on the horizon line where parallel lines appear to converge in a perspective drawing

viewpoint

the position from which the artist observes or envisions their subject

Key Equations

Golden Ratio

[latex]\phi=\frac{1+\sqrt{5}}{2}[/latex]