Ellipse drawing tutorial: Creating a circle in perspective.
Lesson in how to draw a circular oval ellipse with Adobe Illustrator.
All Tutorial Text & Images - Copyright © 2011 KHI, Inc.
Any technical illustration is only as good as its weakest element. Perhaps the most important (and often overlooked) element of any illustration is the ellipse. When an ellipse is executed correctly it disappears into the overall illustration, but when an ellipse is drawn incorrectly, it is glaringly obvious. Even the uninitiated eye can spot an incorrectly drawn ellipse, although they may not be able to identify or articulate why the illustration is amiss. As you will see in the latter portion of this tutorial, it will not be sufficient to simply "squeeze" to circle into an ellipse, then rotate it onto a vertical or horizontal plane, as this does not properly address the receding aspects of that plane.
In this lesson we are going to learn the principles of drawing a circle as a vector ellipse in a 1 point Perspective and 2 Point Perspective view, using Adobe Illustrator. For this tutorial it is important to use vector drawing software such as Adobe Illustrator or CorelDRAW. In this case, we will be using Illustrator's Free Transform tool to distort the shape and "aspect ratio" or "ellipse ratio" of the circle to make it appear to be in perspective.
Basics of Drawing an Ellipse in Illustrator
We will start out by drawing a perfectly round circle with a 90 degree (1:1) width to height ratio Fig. 1, using Adobe Illustrator's 'Ellipse Tool' (L). Our circle is positioned inside a square box (blue line) with equal height and width, created using Illustrator's 'Rectangle Tool' (M). The major axis of the circle is represented by a magenta vertical line and there are green bullet points at each intersection of the major axis to the outer edge of the circle. Adobe Illustrator Tip: Hold the 'Shift' key while dragging, to constrain the 'Rectangle Tool' and 'Ellipse Tool' to a perfect circle and/or square.
In Fig. 2 the minor axis of the circle is represented by a magenta horizontal line and again there are green bullet points at each intersection of the major axis to the outer edge of the circle. The major axis and the minor of the circle intersect at the center point of the circle and are at a 90 degree angle to each other as shown in Fig. 3.
In Fig. 4, 5, & 6 we have rotated the major axis by 20 degrees (clockwise) and we have changed the ratio between the major and minor axis. The left ellipse (fatter ellipse) now has a 40 degree (1:1.55) width to height ratio and the right ellipse (skinnier ellipse) has a 20 degree (1:2.92) ratio. As in the examples above, we have marked the intersecting points between the outer diameter of the circle and the major and minor axis points.
Drawing a 1-Point Perspective Ellipse
We will now begin to construct an ellipse in 1 point perspective. We will start by drawing diagonal lines that intersect with all four corners of the blue box that surrounds our circle. In Fig. 7 these intersection points are marked with green bullet points. If we were to simply decrease the width of the minor axis in relation to the major axis we would create an isometric image of our circle Fig. 8. A true isometric ellipse is approximately 35 degrees with a ratio of 1:1.75. An isometric image has no perspective and all parallel straight lines are at the same angle. For more information on isometric vs. perspective drawing go to the: 2 Point Perspective Drawing Tutorial.
In Fig. 9 we have created an artificial 3 dimensional environment with a "1 point Perspective Grid." This means that there is only one vanishing point along the horizon line. In this example, our horizon line is also our minor axis. You will notice that the major axis is not aligned to the center point of the ellipse as it was in our isometric ellipse in Fig 8. The new major axis is now aligned to the perspective center point marked with a green bullet point and the left and right side of the circle are very different in size and shape. These are the distinct characteristics of a "Perspective Ellipse".
The next step will be to divide a receding plane into equally divided increments. Starting in the upper left corner (A) of our boxed ellipse (Fig. 10), we will draw a diagonal line (solid blue) until it intersects the mid-point (B) of the boxed ellipse along the horizon and minor axis line. Continue the diagonal (solid blue) line until it intersects with the lower vanishing point line (C). From that point we will draw a vertical line upward until it intersects the upper vanishing point line. This will now define a square that is the same "size" as our first square containing the circle (now an ellipse).
Repeat the process outlined in the preceding paragraph until you have five equally divided square spaces (Fig. 11). Now form a second ellipse in the last (5th) space. You will notice that not only has the vertical size of the ellipse diminished as we recede towards the vanishing point, but the width and ellipse ratio has changed as well. Our first ellipse (foreground left) is 30 degrees with a ratio of 1:2 and our second ellipse (background right) is 20 degrees with a ratio of 1:2.92. This phenomenon is due to the fact that the viewer is at a steeper angle of view when looking an object that is in close proximity as opposed to an object of the same size that is farther away (Fig. 12) and therefor, viewed at a shallower angle. The "picture plane" in Fig 12 represents the observer's perception of perspective.
In the physical world, the "picture plane" in Fig. 12 represents the observer's perception of perspective as interpreted by the lens of the eye. In the world of illustration, the "picture plane" is actually the flat surface of the paper or computer screen, and the perception of 3 dimensional depth or perspective is an illusion.
2 Point Perspective Ellipses
Now we will create a 2 point perspective grid (Fig. 12) using the same principles that were used in Fig. 9 through 11. Start with a horizon line and create both a left and right vanishing point. From the right vanishing point (RVP) we will project our ellipse centerline as well as an upper and lower vanishing point line. Create your equally spaced divisions just as you did in Fig 10.
From the left vanishing point (LVP), project your minor axis line until it intersects the center point of the first (foreground) box and beyond. Now draw your vertical major axis line so that it intersects with the center point of the ellipse box (green bullet point). Keep in mind that even though the major axis line should always be at a 90 degree angle to the minor axis line, we ill place less importance on it when constructing a 2 point perspective ellipse..
Now that our perspective grid is constructed we will start to fill in the foreground and background ellipse. In our foreground ellipse box (Fig. 14) you can see that if we were to simply take a 30 degree ellipse (roughly the correct ratio) generated by the Ellipse Tool (L) in Adobe Illustrator and rotate it so that the major and minor axes line up (green ellipse) it does not look correct. Even if the green ellipse touches all for sides of the ellipse box, it does not touch them in the correct locations (see Fig. 15). As mentioned in the preceding paragraph, this is why we will not rely on the major axis to construct our 2 point perspective ellipse.
In Fig. 15 we see that the points at which our green ellipse intersects the blue box (red arrows) are in the wrong locations. A correct ellipse should intersect with the blue box at the four center points indicated by the green bullet points. Additionally, our green ellipse in Fig 15 does not intersect with the diagonal blue lines in our box template.
The solution for this problem is to use our vanishing points to construct a smaller box of the exact same proportions (equal width-to-height ratio) within our main template box Fig. 16. This smaller box will identify the correct intersecting points that our ellipse must make contact with (Fig. 16). Keep in mind that the Ellipse Tool (L) in Adobe Illustrator is not capable of creating this type of ellipse. But do not despair, there is an easy way of doing this using a quick workaround solution which will be covered in the following sections.
Note: The point of the inner square shown in Fig 16 is to show how an isometric ellipse (using Illustrator's Ellipse Tool) will not meet the requirements of a true perspective ellipse. It is not the "size" of the inner square that matters, but the fact that all four of its corners are capable of touching the ellipse. If this does not, or can not happen (as in Fig 15), you do not have a true perspective ellipse.
Our last example in Fig. 17 shows a comparison between an Adobe Illustrator "Ellipse Tool" generated ellipse (dashed green line) and a modified and corrected ellipse (solid black line).
Now we will remove our constraint grid boxes (blue lines) and evaluate the overall appearance of the corrected ellipse (Fig. 18). This is where things get a bit tricky. As you can see, our ellipse still does not "look" correct. Remember that our goal is to "deceive" the viewer into perceiving a 3 dimensional object while looking at a flat 2 dimensional image. This is where the "fudge factor" comes into play. There are complicated mathematical equations that can solve some of these issues, but in the real world of commercial illustration, deadlines provide insufficient time for using this method to complete the illustration. A quick and easy solution (Fig. 19) is to rotate the "corrected" ellipse enough to split the difference between our corrected ellipse (dashed red line) and the Adobe Illustrator Ellipse Tool isometric ellipse (dashed green line).
Our final example in Fig. 20 (above) shows a compromise between technical accuracy and visual trickery. Once incorporated into the overall illustration, you will find that this technique produces very natural looking ellipses that blend nicely with the perspective of the object they belong to.
All of the principles covered in this ellipse tutorial were utilized to create this line drawing of a linear accelerator shown in the screenshot above. By learning and following this basic set of drawing fundamentals you can create perspective illustrations of any subject, regardless of the level of complexity.
Back to: Illustration Tutorials
Copyright © 1996-2012 KHI, Inc. and AutomotiveIllustrations.com. All rights reserved.