Drawing Basics: How To Find Angles and Proportions In Linear Perspective

Drawing Basics: How To Find Angles and Proportions In Linear Perspective

This article is Part Two in a series of tutorial articles explaining linear perspective from a visual, non-technical approach. By visual, I mean drawing from direct observation and the imagination rather than from a measured approach. My goal with this series is to help beginners and more experienced artists, illustrators and designers improve their drawing and observation skills.

The principles of linear perspective describe the way things actually are, how we observe what’s in our visual field. So we’re not concocting a theory and applying it, but instead we’re observing visual principles in action in the world around us.

When constructing perspective drawings, there are 4 relationships you need to begin with: where eye level is, where the objects you’re drawing are in relationship to the picture plane, how those objects are angled, and how far away the objects are from you (the viewer).

Every point on an object (object point) is connected to the viewer’s eye by an understood but invisible line of sight. These lines of sight are straight, implied lines. They are unseen, but necessary for the observer to view the object. These lines of sight pass through the conceptual picture plane from the object to the viewer’s eyes. The conceptual picture plane is your imagined viewfinder as you look at a scene. The actual picture plane is what you draw on your paper in which you place your drawing.

 

Drawing a perspective view from observed reality is simply a matter of depicting the proportions and angles as they actually exist.

 

The image you create or capture should be consistent in angles and proportions with those of the observed objects. So, drawing a perspective view from observed reality is simply a matter of depicting the proportions and angles as they actually exist.

 

Four perspective relationships you need to begin with

The height of eye level

Eye level is the distance from the ground to your eyes. When you stand, your eye level is higher and when you sit, it’s lower. Objects appear differently depending upon the height at which you’re viewing them.

Objects can be above eye level, at eye level, or below it.

 

Line of sight diagram by Alvalyn Lundgren

 

The distance of the object from the picture plane

A close-up view of objects leaves little background in the picture plane, and a distant view may allow background to take up most of the picture plane. When you create an image, or you photograph reality, how are you frame the image makes a difference in how the objects and the space are understood by the viewer.

 

cropping: the distance of the object form the picture plane by Alvalyn Lundgren

 

The distance of the object from the station point

The station point is the position of the viewer in relationship to the picture plane and everything within it. Objects diminish in size as they increase in distance from the station point.

There is a limit to the distance human beings are able to see.

Objects can recede in any direction. That means that each object you observe in a scene will appear to decrease in size until it disappears and vanishes completely from sight. Every object in a scene acts on its own and has its own, independent relationship to the viewer.

The farther away an object is from the viewer, the closer it appears to eye level. This is true whether the object is above eye level or below it.

 

The angle of the object to the picture plane

Every object in a picture plane can be rotated in any direction. For example, in the same scene, there can be three objects stacked in a pile and each one has its own perspective angles unrelated to the other two. One object can be in one-point perspective using a single vanishing point at eye level, while the other two can each use two-point perspective and use two vanishing points at eye level. In that scene as a whole, there will be five different vanishing points.

An object can be in one-point, two-point, or three-point perspective. We’ll cover three-point perspective in a later article in this series.

Angle of the object to the viewer by Alvalyn Lundgren

 

Eyeballing to estimate angles

To find the angles of an object in one-point perspective

  1. Find a vertical edge on the object nearest your center of vision
  2. Find the first angle of the receding plane off the vertical edge. To “find” the angle, imaging a grid that’s horizontal and vertical, and estimate the angle of an edge off horizontal or vertical. When you’re first learning to eyeball, it’s helpful to use an artist’s viewfinder INSERT LINK HERE that you can hold up between your eyes and what you’re drawing. With experience, you’ll no longer need to use the viewing grid.
  3. Find the second angle of the receding plane off the vertical edge.
  4. The point at which these receding lines intersect is the vanishing point. It will be on eye level.
  5. Draw the eye level as a horizontal line parallel to the ground plane or baseline of your drawing.

 

Eyeballing to find angles by Alvalyn Lundgren

 

Finding angles in one-point perspective by Alvalyn Lundgren

 

To find the angles of an object in two-point perspective:

  1. Find a vertical edge on the object nearest your center of vision
  2. Find the first angle of one receding plane off the vertical edge.
  3. Find the second angle of the same receding plane off the vertical edge.
  4. The point at which these lines intersect is the first vanishing point (at eye level)
  5. Draw the eye level as a horizontal line (parallel to the ground plane
  6. Find the first angle of the second receding plane off the vertical edge.
  7. Find the second angle of the second receding plane off the vertical edge.
  8. The point at which these lines intersect is the second vanishing point (at eye level).

 

finding angles in two-point perspective by Alvalyn Lundgren

 

When vanishing points are located beyond the picture plane boundary:

  1. Do steps 1-3 above.
  2. Use a ruler to mark the angles in the margin beyond your drawn picture plane. Use these marks as a reference. Label the marks as you need to.

 

perspective-using-margin-guides-by-Alvalyn-Lundgren

Eyeballing to estimate proportions

  1. Use a straight edge or the butt-end of a drawing pencil. (Drawing pencils have no erasers attached)
  2. Hold the pencil vertically at arm’s length. Do not angle it. Keep it perpendicular to your line of sight and the ground plane.
  3. Position the end of the pencil to correspond with the top edge of the object closest to you.
  4. Mark the “drop” or distance to the bottom of the object with your thumb.
  5. Without moving your thumb, pivot the pencil to the horizontal position, keeping it perpendicular to your line of sight. Compare the horizontal distance observed with the vertical distance observed.

 

Read Part One of this series here.

Related Articles On This Site:

What is Eye Level?

8 Tips for Improving Your Drawing Skills

Alvalyn Lundgren

Alvalyn Lundgren is the founder and design director at Alvalyn Creative, an independent practice near Thousand Oaks, California. She creates visual branding, publications and books for business, entrepreneurs and authors. She is the creator of Freelance Road Trip — a business roadmap program for creative freelancers. Contact her for your visual branding, graphic and digital design needs. Join her on Twitter, Facebook, Instagram, and subscribe to her free monthly newsletter.

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