Sunday, January 27, 2013

Discussion: Convex lines and the figure

I have run across the idea that the human form should be drawn only with convex lines because "there are no concave lines in the figure." The argument goes that the outer contours are governed by the bulging masses of the bones and muscles. Even when you cup your hand, your hollow palm is made up of a set of smaller convex shapes. Convexity is synonymous with life, volume, and fullness. Even on a thin person, the planes and lines should gently curve outward. Concave contours can be conceived as a series of overlapping convex forms.

The opposing view is that the figure is made up of a variety of lines and planes, including straight and concave. Some artists emphasize only straight lines, especially in the layin. Regarding concave contours, elastic skin stretched across any acute angle will form a concave shape, such as on the inside of the elbow or the curve of the neck. This would be true even on Mr. Universe or a heavyset person. Concavity is expressive of receptivity and inertness. Variety is the spice of life, and good drawing is a product of contrast.

I haven't made up my mind yet on this issue, and would be interested in your comments. Maybe you can make one case or the other better than I can. What have you been taught, and what thought process produces the best for you? You can also add your vote to the poll at left.

46 comments:

zillipede said...

Many good drawings - perhaps especially cartoony ones - are about simplifying shapes and bringing out the essence in a pose or movement. Simplifying the human body typically creates concave curves as well as convex ones. Dividing a concave curve into two convex ones will disrupt the "flow" of the line and can lessen the feeling of motion that the drawing evokes. I would definitely use concave curves unless I were drawing the Michelin Man.

Yoav de-Shalit said...

+1 vote for Convex
I can't see how the argument for concave forms can be physically possible. I guess maybe in some extreme cases of old skin it can act like drapery and form concave forms because of gravity, still it is barely noticeable.
Another issue regarding convex and concave forms is that cognitively we see convex forms as foreground. I suppose we evolved that way because there are barely any concave forms in nature, not only in the human body. Some character designs for animation use concave forms heavily. personally I think it flattens the image and confuses between the character and the background when they aren't moving.

Christopher Smith said...

This is interesting. I was taught with using convex curves, mainly to focus on the form. I tend to still only use mostly convex curves. In my opinion it helps to bring across the three dimensional form of not just the figure, but most organic objects. It helps me to visualize the complete form on all sides, not just the side I am viewing.

Tom Hart said...

Funny, in all my classes and books I never ran across this rule. I haven't reflected on this to any great extent, but my initial reaction is that although convex shapes would predominate in a drawing of the figure, that concave shapes exist and have their place. Surely it's possible to draw the figure with only convex shapes, and I'd say off the cuff that it's not possible to draw the figure convincingly with only concave shapes. Building on what Zillipede says, drawing is always a simplification, to one degree or another.

I may not be completely following the "convex only" argument, but just looking at my own reflection in the computer screen, I see a concave line defining my nostrils, and the indentation in the upper lip (I forget the name for that anatomical feature).

zillipede said...

As an example, here's a cartoony image with plenty of concave curves:

http://i45.photobucket.com/albums/f86/projectrooftop/Wieringo%20Week/Impulse-by-Jemma-Salume.jpg

I think it's got a beautiful flow to it - I love the way that the curves go in-out-in-out - that would be destroyed (or at least lessened) if the concave curves would be broken up into convex ones. An "S" curve describes a better, clearer, line of action than a "3".

Or why not bring out the Preston Blair page on line of action, while I'm at it: http://www.animationresources.org/pics/pbanimation07.jpg

The most expressive drawings are those that follow a simple, clear curve, and if you want to draw a body that follows a simple curve closely, it will include concave lines. Sure, if I'd draw for a biology/medicine textbook, concave lines would be rare, but if I want to draw something expressive and cartoony, I'd go wild with them.

adam said...

interesting post,
seem's like a 'don't use black' type of semantics rule.

isn't it relative to how you perceive things?

isn't concave and convex used to describe a shape?

how can a line be either or?

Maywyn said...

The question feels like math anxiety shock huh?-ness.

Matt Atherton said...

This.

Allen Garns said...

Good question. My thought is that the more concavity a drawing has, the weaker the form. However, a few concave contours can be a good counterpoint to convexity and make for an interesting drawing. Comments have been made using cartoon figures as examples of concave forms and I think there it can work better than with a more traditional/realistic drawing. One reason I believe it is often given as a rule is because students tend to over use concave contours and their figures start looking like Gumby.

David Still said...

I've had one teacher say this to me, and I agree with it up to a point. (The same teacher also pointed out that whether you follow this rule or not depends on what you're trying to do).

I would say that rather than categorically stating that a figure must only consist of convex lines, it's more useful to say that it's often best (when going for a more classical figure drawing, emphasizing form using line) to use two or more convex lines instead of a concave one.

For example the sweep of the trapezius from the neck to the shoulders, can be drawn quickly and simply as a concave line, but using a series of convex ones will give a stronger feeling of the round form of the muscle.

Try to find a convex line on this drawing. (There's one on the little finger - but that's not a very finished part of the drawing.)

Keith Parker said...

I have a hitch-hiker thumb, you can't draw that accurately without both convex and concave lines...and what about my ears, or spurs on someone's feet, or the bridge of a swooping pug nose in prophile? This rule might be easier to debunk that the silly I after e rule from grade school. At least that's my thoughts.

zishen said...

I think it`s not whether you use only concave or convex lines, but where and how you use them.

I`m an animator and the word "Contrast" is like the word of God[ of animation] for us.

There is no golden rule in drawing. Rules can, and should, be broken for effect.

Erik Bongers said...

Remember the "How to draw an owl."-joke? It states you should draw two circles...and then fill in the details.

The joke works around the obvious fact that it's those in-between steps that are the most difficult.

So if it's the in-between steps that define the final result, does it really matter that much if you start with circles, rectangles, concave or convex lines?

Ayal Pinkus said...

I think it is advice that came from the book "Drawing lessons from the great masters". The book shows many examples from old masters who did this.

I always thought of convex lines as a "trick", a way to suggest fleshiness, a tool in my toolchest for me to apply whenever I want.

According to that book, there were more things the old masters drew in that you wouldn't see on a live model. They'd render lots of muscles you don't really see in life, to brag about their knowledge of anatomy :-)

I found that book incredibly enlightening. Personally, At the moment I prefer to use confident traight lines though...

Great post! :-) By the way, LOVE your blog, envious of your skills!

James Gurney said...

Eric, I think it does matter how a person conceives of lines, shapes and planes, and it matters all the way from the beginning steps to the finishing bits. A painter like Duveneck thinks more of straights and planes compared to, say, Ingres who thinks more in terms curves. Or someone like Rubens is more of a "convex form" guy, and it shows up in his work at any stage.

Tom, this may not be a big issue, but I've encountered the teaching in four or five places.

It's great hearing from the animators! From what I've read, Walt Stanchfield, Preston Blair, Ollie Johnston, and other great animation teachers have discussed this topic, usually as Zishen says, in terms of opposing curves against straights and setting up contrasts, not just in space, but in time to get elasticity, compression, and a sense of gravity and dynamics---isn't that right?

Yoav de-Shalit said...

Obviously there is no absolute rule and artists are not judged by the type of curves they use. And yet, it is one question whether concave forms appear in nature and another if they appeal to the eye. Gestalt psychologists noted that concave regions of an image are perceived as background while convex shapes pop out in the foreground. This makes sense considering most natural forms are convex due to the physical forces holding them together.
Because of the way we perceive these shapes, designs relaying heavily on concave curves may seem flat. It has nothing to do with fluidity or appeal but only with the perception of space. Character designs done for "The Secret of Kells" or "Kung Fu Panda" are top notch and yet use concave curves extensively. In animation as opposed to still images, the motion itself gives a feeling of volume so the priority of silhouette properties is different.
Regarding life drawing, adding a couple of extra bumps to the form is far less noticeable then smoothing out with concave curves.

mdmattin said...

I learned that convexity suggests tension or energy,while concavity or a catenary curve suggests relaxation or repose. Any pose is a dynamic between the two. The contour of an arm would be handled as predominately convex if in action or supporting weight, concave or hanging like a clothesline if externally supported or passive. But both modes would be present.
Convex contours can also imply a saddle shape, like the indentation between the hips and ribs.

mdmattin said...

I meant to say:
Concave contours can also imply a saddle shape, like the indentation between the hips and ribs.

James Gurney said...

MD Mattin, I never thought of it quite that way. If you consider the form three dimensionally, then a given contour can only be concave in only one dimension at a time (say height). In order to be visible, it must be convex in the dimension of the line of sight. So a neck could be concave as it reaches to the shoulders, but the form is also convex seen looking straight down. Therefore, all concave contours describe either forms that are flat shapes bent, like a piece of paper, or a saddle shape. If a form is concave in both dimensions at once (such as the inside of a bowl), it wouldn't be visible as a contour.

Yoav, very eloquently and concisely put, and thanks for those links.

mp said...

The convex lines rule applies to landscape as well, according to John F. Carlson. In his book, Carlson's Guide to Landscape Painting, he says:
"Try to feel that almost all natural, growing forms are convex lines rather than concave. Many a mountain outline has been spoiled by being made concave. All earth-forms bulge up, as it were. The mountain rises, the ground swells, trees tower. Concavity creates a "hanging" line, and unless it is imperatively needed for artistic reasons, beware of its use. Note the heroic forms of Delacroix and Michelangelo, and you will see little concavity present."

I tend to agree with the convex lines rule. Creating the illusion of 3d form on a 2d surface would seem to require bumping the lines more toward convexity, for the most part.

alaric said...

Too many counterexamples spring to mind for me to accept this. Obvious examples are the concave curve of the bridge of the nose to the brow, the concave line to the throat from an upwardly turned chin. More subtle, but equally important examples arise, particularly with dynamic poses--for instance, the concavity formed from iliac crest to ribcage during lateral flexion of the spine. Auguste Rodin's "Danaide" illustrates this beautifully:

http://www.1st-art-gallery.com/Auguste-Rodin/Danaid-%5Bdetail%3A-1%5D.html

I posit that the above cannot be captured with anything but a concave curve. Concavity gives us grace and reach.

If we allow the scope of the discussion to extend beyond physical form to gesture, then concave line becomes indispensable. The work of Mike Mattesi comes to mind. He is all about rhythm in gesture (or "force" as he calls it), a large part of which involves the natural flow from convex to concave, straight to curve, etc.

mp said...

Convex forms sometimes present concave outlines depending upon the viewing plane. It is usually desirable to indicate the convexity of the third dimension in such situations in drawing.

Don Ketchek said...

Generally, I think art rules are a bad thing - because there are almost always exceptions. Maybe I'm not understanding the convex and concave thing, but there seem to be concave lines in the neck and in the waist. And in the line going from calf, through the ankle to the heel.

The biggest problem with rules, however, is that they keep artists from actually observing.

That being said, I think that the biggest problem that I see when looking at beginning artist's paintings and drawings of the figure, is that there are far too many straight lines. When I taught an online figure class a few years ago, I tried to stress that almost all the lines in a figure are curved. I had a few photo references and highlighted the curves in some places - they almost looked wrong they were curved so much! (I'm not talking about the obvious female curves, either!) So, rather than stress convex, I would just stress curves and roundness. Same with the head. In my experience (not that I have ever done a survey), very few people have planes on the head, either. Heads are much more rounded and egg shaped, in my opinion. Creating planes, especially in the forehead, temple, side of the head area might be a good teaching tool to emphasize that these areas are receiving differing amounts of light, but if they retain the harder edges of planes coming together it always looks a bit amateurish to me. That's just my opinion, obviously, but again I would stress curves rather than planes or straight lines when it comes to the human form.

Jeff Fennel said...

I notice many, many concave edges or contours - mainly in areas of transition. Larger masses tend to be convex but connected by short concave "bridges". Forearm to hand transition and the hand itself is full of concave contour. Holding up my right hand I notice the outer edge of my thumb is dominated by three long concave contours, as is its gesture. I've also noticed over the years that exterior concave contour tends to overlap into interior concave transition - much the way cast shadow transitions to form shadow.

Andy said...

You gotta love these hard and fast rules. It's like the one about how no highlight value in a painting should also appear in the shadow set of values - oh, except in snowscapes, or seascapes or various other situations including shadows on pale very objects with highlights on very dark objects.

Nice guideline but no need to be fundamentalist about it. (I use the straight line method, these days, by the way)

Adam Worrall said...
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David Still said...

While I agree with the general consensus of this discussion, i.e. that the use of convex or concave curves depends on artistic intent, and that rules in art can be nothing more than guidelines, my pedantic nature compels me to illustrate the core of this rule, since I think a few people here might have misunderstood it.

The sentence "the only right way to draw a figure is using only convex lines" is obviously false. A better thing to say would be "the human figure is generally made up of convex forms" and then leave the representation of those forms in line up to the individual artist.
Let me illustrate.

Adam Worrall said...
This comment has been removed by the author.
Craig Banholzer said...

An example of what happens when you follow the "convex rule" to its limit is the kind of drawing you saw in Italy in the late 16th Century, which gave us the famous "sack of walnuts" look. Although these drawings are beautiful and distinctive, they are not as lifelike as drawings that account for the real variety of human form, which definitely does, sometimes, include concave lines.

zishen said...

James -
Absolutely. On a drawing level, I definitely agree that most shapes we see on the body are convex. But that doesn`t mean that we should totally discount concave[and definitely straight] lines as well.

Certain areas can best be abbreviated with concave lines, and sometimes by using concave lines, we inadvertantly emphasis the convex nature of other lines!

Chris James said...
This comment has been removed by the author.
James Gurney said...

Chris, great point, to which I would add: Bill Tytla.

Everybody, I just want you to know how much I'm appreciating ALL your comments, and they're coming from some awesome talents and great teachers. Excuse me for not responding to each point. I realize I sort of manufactured the argument for the sake of discussion, but I'm coming away with a lot of fresh thoughts that hadn't occurred to me before. Also, I appreciate all the links, which have led me to some new artists and new understandings.

Chris James said...

I find concave and straight contours on the figure unsightly and don't well represent organic, three dimensional form. There is no contour -even the examples cited in these comments- on the body that can't be represented with a degree of convexity or series of convexities, with the added benefit of fullness and supple strength.

Even in animation, I associate the superior work of folks like Bob Clampett, Chuck Jones, John Kricfalusi, early Disney, with convex, organic forms, although straight and concave lines were used liberally. I would go as far to say that the quality of draftsmanship at Disney, and animation in general, suffered a drop off when the balance shifted towards straight and concave contour lines. How many times since have seen features that sit flat on the face, instead of wrapping around the larger form of the head, in films like Treasure Planet and Pocahontas.

Nick Woolridge said...

From the point of view of information theory, this idea is directly contradicted: concavity conveys more information about underlying structure than convexity:

Feldman J, Singh M. Information Along Contours and Object Boundaries. Psychological Review, Vol 112(1), Jan 2005, 243-252. doi: 10.1037/0033-295X.112.1.243

(this is a math and information-theory heavy proof of the notion that for arbitrary enclosed forms, concavity carries more information about the enclosed shape than convexity.)

More practically: on the face of it, its seems absurd to argue about it, since both are clearly necessary; apart from a perfect circle, convexity requires adjoining concavity to even be distinguished.

Shaun Stipick said...
This comment has been removed by the author.
New Kid said...

I just started taking life-drawing classes last week and in my first class my teacher instructed me to draw only convex lines. I believe he also said there are no concave lines in the human form and concave forms are created only by the joining of two convex lines. I thought about this for about a half a second and immediately incorporated it into my drawing. First, it simplified my thinking and in my first life drawing class simplification was a blessing. Second, it made me think about the forms underneath the skin, the bones and muscles, pushing themselves out to define the form. For now I’ll be using this idea as I draw; in six months things could be different.

Shaun Stipick said...

Sorry about that. Didn't mean to delete. Here's my post again...

Tony Ryder discussed this in his figure drawing book and I have also heard this as well from others. In the end I believe that it is a great tool\rule for perception but not maybe the best tool for interpretation (although helpful). When I think of concavities on the human form I think of death and sickness, for example bedsores. It is ultimately this effect that we should want to avoid, unless of course this is our intention. If the artist\viewer is aware that a concavity consists of multiple convexities at a junction point (e.g. thinking of the depression over the top of the greater trochanter or the jugular notch) then the decision to interpret it as a concavity versus a series of convexities becomes an issue of beauty and intention. One would assume that a knowledgeable and trained artist would choose the best mark to indicate the turning of the form, regardless of rules.

All in all I like the rule if only to help train our perception of form across the surface of the human body. But like all rules in art it should be held to a far greater rule and that is "if it looks wrong or ugly then another better and\or more beautiful solution should be found."

Edit...
Raphael's ink drawing of David is (I believe) a fun example of this rule at work. the exterior consists mostly convexities with a lovely sweeping concavity on the lower leg. And what about those interior marks indicating both form and value? Are they convexities or concavities? I could make an argument either way.

Shaun Stipick said...

I hope I am not being out of line by posting a link to an image on another blog. If so please let me know.

Here is another example by the great Cornwell. Mostly convexities, but where thrust and action are needed (stretched side of the abdomen or foreshortened forearm holding the handle) a concavity is used.

links below

http://4.bp.blogspot.com/-M0OdHLEQPTM/Tf0I26ANlpI/AAAAAAAAAtY/S43EfgwRrkQ/s1600/Cornwall+drawings+002.jpg

http://www.artvalue.com/photos/auction/0/47/47894/cornwell-dean-1892-1960-usa-boy-with-a-jug-mural-study-2568314.jpg

Nathan Fowkes said...

Yes, it would be really bad to have a rule that it should be either way but I find that beginning students frequently use 1 concave line for a form that is really made up of overlapping convex shapes. The result badly hurts the sense of form.


Sometimes the convex forms need a little extra emphasis to create the illusion of three dimensional form on a 2-D page.

Shaun Stipick said...

Mr Fowkes,

1) Huge admirer.

2) I couldn't agree more.

Chris James said...

Information theory is not aesthetics, or anatomy, and I would argue that Rubens or Pontormo's contours convey more information than Cornwell's

"Sometimes the convex forms need a little extra emphasis to create the illusion of three dimensional form on a 2-D page."

Couldn't agree more.

etc, etc said...

It's largely a psychologically conditioned aesthetic response (of course a great deal of aesthetics is in fact conditioned). If you accept it on authority and internalize it, then concavities will seem wrong when you encounter examples. Just like the compositional rule, "a line should never lead into the corner of a canvas", of which there are thousands of examples by the old masters that "break" the "rule".

herczfeld said...

Seems to me that what you are discussing is the figure as a positive form, in islolation.The figure (or anything else) will not exist entirely on its own, it will be part of a context. I'm thinking that the convex curve of the negative space definitely has its reason for existing. What is convex one one side is concave on the other side of the (implied) line. The rhythm or flow of curves is part of what makes the 'music' of the visual arts.

The inside of the cupped hand made with convex curves definitely works, but then thogether they are a series of shorter curves which together form sort of a 'meta curve' which is concave. Vexing thought. ;-)

Diana Moses Botkin said...

What an interesting discussion here! I loved reading all the points, pro and con.

However, the idea that the figure should be represented with only convex forms seems absurd to me.

Some of the loveliest curves on the human body are concave. To use only convex forms, one would need to draw the small of the back, those little valleys on either side of the nose next to the eyes, the palm of the hand, a slender waist, the neckline running to the shoulders, the curve of the armpit (and many other valleys of the human form too numerous to mention) as straight lines.

Craig Banholzer mentions the "sack of walnuts", which made me chuckle. Marvelous description.

Tom Hart, BTW, that little indentation on the upper lip you mentioned is the philtrum. http://en.wikipedia.org/wiki/Philtrum

Carlson is obviously a great teacher more knowledgeable than I, but I see concave forms in the landscape too, although convex shapes and flat planes are much more abundant. For example, there are a number of mountains in our area with natural bowl features. And our pond sits in a small valley and fills up only part of that natural concave form.

mdmattin said...

I just got back from a life drawing session in which I tried to keep the convex outline idea in mind. It did allow me to see certain situations in which a line, at first glance concave, turned out to be composed of little convexities riding on it like signals on a carrier wave. By the same token, I saw ostensibly bulgy contours whose underlying armature was clearly concave. It seemed to me that my job as an artist was to emphasize one or the other in service of expressing the spirit of the overall pose.

Vyrmis said...

In my hobbies of tabletop wargaming, and miniature figure sculpting for the same, I often see new hobby sculptors pick up the wax carvers and epoxy putty and sculpt figures of almost all convex contours. They Do Not Look Good.