Thursday, March 26, 2015

Circles and Cylinders in Perspective

A circle drawn in perspective looks like an ellipse. An ellipse touches the center of each side of the square in which it fits. Drawing an ellipse mechanically is a little laborious, but it sure looks great in the end. First, find the center of the rectangle. Use this center to draw the following circles: draw a circle with a diameter of the width of the rectangle and a circle with a diameter of the length of the rectangle. Draw several lines from the center of the circles to each circle. Mark the points where these lines intersect the circles. For all the points on the small circle, draw lines parallel to the length line. For all points on the large circle, draw lines parallel to the width line. The points where these lines meet are points on the ellipse, which you can now draw. Norling offers two other ways to draw an ellipse, but I prefer this one. Last thing to note: the two axes of the ellipse meet at a right angle.

Drawing a cylinder in perspective was really frustrating. I spent hours futilely trying to draw a cylinder contained within a rectangular box with two square sides. Finally, I realized that the problem was that I was not actually drawing a  square-shaped side in perspective, which is why, as I elongated my box, the ellipses on the further ends were harder and harder to draw without warping. To draw a cylinder in perspective, imagine that it is contained in a box with two square sides. Draw this box in perspective. Find the center of each square side by drawing intersecting diagonals. Draw a line connecting these centers. Within each square side, draw a line that passes through each center at a perpendicular to the center-connecting line: this line is the long axis of the ellipse. Then, draw the ellipses, remembering that an ellipse must touch the center (in perspective) of each side of the square.

Monday, February 9, 2015

Finding the Centre and Spacing in Perspective

To find the centre of a rectangular object in perspective, you draw diagonals on each side. The point where these diagonals intersect is the centre. After locating the centre, you can then use it as a point of reference for other objects, such as doors or text on a billboard.

I've often wondered how to draw evenly spaced posts in perspective. First, you draw two posts in perspective, using the usual EyeLevel-VanishingPoint technique. Then, you draw a diagonal from the top of the first pole through the centre of the second pole, and keep going until this line intersects the line going to the VP. Now you have the base point of the third pole.

Saturday, January 17, 2015

Placing Furniture in Perspective in a Room

To place furniture in perspective in a room, you first draw a box based on where you are standing in the room. The first image occurs when you are standing at the center of the opposite wall to the door, which means that there is only one vanishing point. The second image occurs when you have moved closer to one of the corners of that wall, such that there are now two vanishing points. To place furniture round a room, first draw in the general rectangular shape of each piece in order to determine its position in perspective. Then, you can fill in the particular details of each object. It seems that once you can draw the basic shapes in perspective, the rest of the drawing becomes much easier and more likely to turn out.

Friday, December 26, 2014

Determining Center of Interest and Roofs in Perspective

Norling asserts that you only include in a drawing what you can see without shifting your eyes. Trying to include objects that you can see out of the corner of your eyes results in warped perspective. Thus, it is very important to establish the picture frame around whatever object you wish to be the center of interest. In the first drawing, the tracks are the center of interest and there is only one vanishing point. The tree is at the corner of vision; therefore, it is largely not within the picture frame. In the second drawing, the tree is the center of interest and there are two vanishing points.

When a group of roofs have the same slope, then the lines of these roofs meet at two points along a line, drawn through one of the vanishing points, that is perpendicular to the horizon. All roofs that slope to the left go through the two points on the line that is extended from VP A. All roofs that slope to the right go through the two points on the line that is extended from VP B. It seems that the two points on these perpendicular lines are equidistant from their respective VP point (A or B). This lesson was confusing at first, but once I began to draw the roofs as demonstrated, it began to make a lot of sense. I'm really enjoying that perspective is so methodical, not some esoteric mystery.

Saturday, November 22, 2014

More on Perspective: Avoiding Warping, Moving the Vanishing Points, and Placing People

I've made my way through several more chapters in Norling's "Perspective Made Easy." I generally learn well by copying, as shown by my investment in Bargue, so I've copied out some of the images from Norling's chapter. I'm beginning to get a feel for how important knowing perspective is and I've been rather ruefully contemplating my early attempts at oil painting, which now look obviously off (and which I haven't yet had the courage to post).

To avoid warped perspective, as shown in the first drawing of the bedroom, the vanishing points must be spaced widely apart. Norling doesn't provide a formula for how far apart exactly to place the points, but the spacing seems to depend on the size of the subject being drawn. If the subject is large, then one of the vanishing points may go off the page. Drawing the first vanishing point seems to depend on your location relative to the subject, as shown in the two drawings where you get a different perspective of the bedroom depending on your position relative to the closest bed.

This drawing traces the movement of the vanishing points relative to each other as an object is spun clockwise. The first VP is A and the second is B. The superscripts indicate each turn of the object. The two vanishing points never converge. When you look at a square object face-on, you can only draw one vanishing point because the other extends to infinity along a line parallel to the eye level line.

The most important step in a perspective drawing is to locate the eye level line. Then, you can build rectangular objects by piling bricks. Below the eye level line, you can see three sides of the brick. Above the eye level line, the parallel edges of the top of the brick converge, so you can only see two sides and the parallel lines of these sides tilt downward to reach the vanishing point. In short, parallel lines below the eye level tilt upward to the VPs and parallel lines above the eye level tilt downward toward the VPs.

It turns out that there is an easy and methodical way to place people in perspective relative to a building. First, locate the average height of a person standing right beside the building. Draw two lines passing through this point to the two vanishing points: this is the height line. Extend the base lines of the building. A person standing on this baseline would be as high as the height line. To find the height of a person not standing on this base line:

1. Mark a point where you wish this person to stand.
2. Draw a line from this point to the VP until this line intersects the base line.
3. Draw a line straight up until it intersects the height line.
4. From this intersection, draw a line towards the VP until this line passes above the original point.
5. Now, as you can see by the arrows, you have the height of this person.

Sunday, August 24, 2014

One-Point and Two-Point Perspective

I'm studying perspective using Ernest R. Norling's 1939 book Perspective Made Easy. He has a calm, firm, yet easy-going tone, and does not make learning perspective seem daunting. I especially enjoy that he states concepts simply, as if he truly wishes his readers to understand and apply them. So far, I've learned these essential points:

1. One must first locate the eye-level of a drawing. The eye-level is both the height of one's eyes and the horizon, which can be represented as a straight line across a drawing. Objects are oriented at, above, or below the eye-level.

2. Parallel lines converge at a point on the horizon called the vanishing point. Parallel lines that are parallel to the picture plane (basically one's drawing sheet held parallel to one's body and perpendicular to the ground) do not converge to a vanishing point, but remain parallel. An example is the height lines of the book in the above drawing.

3. When an object is turned, as in the book above, all parallel lines other than the height lines converge at their respective vanishing points on the same eye-level line. The vanishing points change position on this line, but the line remains unchanged.

As an exercise, I placed a book on a table and turned it to several positions. I elongated the width and length parallel lines and, if the vanishing point was within the bounds of the paper, marked it on the eye-level line. The first position shows one-point perspective: all parallel lines that are not parallel to the picture plane (my sheet) converge at one vanishing point. As I turned the book, there were two sets of parallel lines that were not parallel to my picture plane, so there were two vanishing points, most of which can be imagined as converging on the eye-level line somewhere outside of the sheet. So, what I understand is that before one begins a drawing, one must first locate the eye-level, then adjudicate whether one's object is in proper perspective by imaginatively elongating the converging parallel lines and extrapolating whether their vanishing points are indeed located on the same eye-level line. 

With Bargue, I was copying from flat. Now that I'm venturing into drawing from life, I find that the hardest thing to get used to is knowing that an object is 3D, but visualizing it as 2D, as flat on my picture plane. It seems that I must see the angles not on an X-Y-Z axis, but on an X-Y axis. It's a little disorienting, but exciting.

Friday, July 4, 2014

Bargue Plate 53 Scaled

Life-mask of a young girl. For a more challenging experience, I scaled this plate to twice the size of the original, which landed me with quite a huge amount of work. I think I spent 60 to 70 hours on this plate! I kept on underestimating the time required to complete it, much to the irritation of my partner, who kept asking "is this the last day yet?" after my ever-accumulating 7-hour marathons, before everyone of which I kept saying "this is the last day." I'm very happy with the level of accuracy and am taking a (very) long break from Bargue to study perspective and, later, watercolor. Bargue has been invaluable to improving my drawing skills, but I think I've plateaued in my learning and need to move on. There are more, interesting plates, so I may return sometime in the future. I'll post my progress on perspective and watercolor.

Sunday, May 11, 2014

Bargue Plate 52 With Steps

Lucius Junius Brutus. I've kept a record of the major phases of doing a Bargue drawing. I'm going to do two more Bargue plates before moving on to watercolour and some original drawings, and I'm going to make these plates more challenging by doubling the size of the original.

Phase 1: The Line Drawing

I first draw the contour lines of the plate, carefully rendering each small section. I start under the left ear and work my way around. The part that tends to be off is usually the top of the skull. Once I am reasonably satisfied that the angles and curves are accurate and proportionate, I draw the outlines of the major shadow areas.This phase takes 2 to 4 hours.

Phase 2: The First Shading

Using a lightly-held 2H pencil, I fill in the major shadow areas. It's at this point that I begin to see whether the line drawing was significantly off, so this phase tends to involve erasing and adjusting.This phase takes 3 to 5 hours.

Phase 3: The Second Shading

This phase involves darkening the major shadow areas. I crosshatch the 2H layer with a 2B, then crosshatch the 2B layer with a 4B, making sure that I do not over-darken. The right ear has a blend of values, so I left it at the 2B layer for now. For this plate, the darker shadows emphasized that something was off with the distance between the lower lip and the chin, so I had to move the chin down by one millimeter or so. One must always be ready to erase. This phase takes 3 to 5 hours.

Phase 4: Rendering Value

This phase is the most difficult after the line drawing. I've done the groundwork for the drawing and must now fill in the subtle values. I work all over the drawing, darkening here, lightening there. To achieve the gradation in the dark shadow area that encompasses most of the right side of the face, I crosshatch another 4B layer. Then, I do the right ear, the eyes, and the forehead. Lastly, I do the beard. Once the drawing looks mostly done, I step back and take a close look at the original in comparison with my copy to make sure that the values look appropriate. I tend not to go darker than a 4B (I find going darker than 2 or 3 layers of 4B, or using a 6B, makes the graphite clumpy and shiny), so my plate ends up lighter than the original, but I have to make sure that the relative values are accurate. This phase takes 10 to 15 hours.

Monday, March 17, 2014

Bargue Plate 50

Marcus Brutus. I've been working on and off for two months on this plate, with a large portion of the time spent shading the dark side of the face, which has a surprising amount of subtle variation in it. Thanks to my new and incredible daylight simulation light, I've been able to better judge the values and consider this my best plate yet. There is a slight bulge in my sketchbook that throws the photo a bit off and I'm not quite sure how to deal with it. I'm entering crunch time with marking and preparing for the oral portion of my field exam, so I may not be able to post again until May.

Sunday, December 29, 2013

Bargue Plate 49

Middle-aged Marcus Vipinius Agrippa, a Roman administrator under Augustus, lighted from above. It was nice to work on this plate's simple lines and shadows. I initially made the chin shadows too deep and had to do some careful erasing. I've upgraded from my smartphone camera to a full-fledged camera and really got to learn about its features and to experiment with setting up the drawing so as not to get that slant on the taped-on original. The top of my sketchbook is more lighted than the bottom, which washes out the darks in the top of the photo, especially around Agrippa's eyes, and intensifies the darks in the bottom.