What Are Orthogonal Lines in Drawing?

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In a linear perspective drawing, orthogonal lines are the diagonal lines that can be drawn along receding parallel lines (or rows of objects) to the vanishing point. These imaginary lines help the artist maintain perspective in their drawings and paintings to ensure a realistic view of the object.

In its most basic form, orthogonal lines are used to create the look of three-dimensional objects in a two-dimensional medium.

Orthogonal Lines

Orthogonal is a term derived from mathematics. It means "at right angles" and is related to orthogonal projection, another method of drawing three-dimensional objects.

The term is applied to the vanishing lines used in perspective drawing as these are:

  • At right angles to the front plane when observing an object in one-point perspective.
  • At right angles to each other in two-point perspective.

To understand these lines, imagine yourself standing in the middle of a road. The lines on each side of the road converge to a vanishing point on the horizon. Along with the center line painted on the road, these are all orthogonal lines—they run parallel to each other and give you a sense of perspective.

Note: The frequently used term "orthagonal" is, in fact, a misspelling of "orthogonal" and is not a word. Think orthodoxy or orthodontist and you'll remember the correct spelling.

Also known as convergence or vanishing lines, orthogonal lines are fundamental to perspective drawing. They may not appear in the drawing but are imaginary or temporary lines to keep your objects in line with the picture's vanishing point. 

To explain this in its simplest form, draw a square that is squared off (parallel) to the page. Add a vanishing point along the horizon line on the right side of the paper. To make this square a cube, we will simply draw a line from each corner of the square to the vanishing point using a ruler.

When doing this, notice how the orthogonal lines do not meet until they touch the vanishing point. They remain parallel to each other even though they converge to a single point. This, in turn, maintains a correct perspective in the picture.

Transversal Lines

Did you notice that we did not actually create a cube in that example? That is because we now need to add transversal lines between the orthogonal lines.

Transversal lines run perpendicular to the orthogonal lines to establish a fixed height or width for the object. 

In our square-to-cube example, you will now draw one line between the two outer orthogonal lines on the vertical and horizontal planes.

  • The new lines should be parallel to the original box as well as the picture itself (because our box is squared up to the paper).
  • These lines should meet one another on the orthogonal line that comes from the top-right corner of the square and they form a right angle to one another.

You should now have the outline of a solid cube on the page.

If you wanted to create a hollow cube, you would simply connect the orthogonal line that runs from the lower-left corner of the box with transversal lines. To maintain the size of the cube, each transversal should connect to the corner created by the first two transversals we drew.

With the orthogonal and transversal lines in place, erase portions of any lines that overlap the solid sides of your cube. Also, erase the portion of the orthogonal lines that extend from the back side of the cube to the vanishing point. You should now have a cube drawn with perfect one-point perspective.

Where Do You Go From Here?

Understanding orthogonal and transversal lines is key to every perspective drawing that you will make in the future. This quick lesson simply gives you a foundation for understanding this concept and how it applies to art. Depending on your drawing, it can become far more complicated with multiple vanishing points and transversal and orthogonal lines running every which way. 

For now, you can use this knowledge to draw a simple house or another building and add doors, windows, and other architectural elements. Simply remember that it is all a series of straight lines and squares worked in the same manner as our example.