Thoughts and Exercises about Geometric Drawing from a Noob

[~Faust~]

Well, I guess this would be just another of those threads about how to draw and perspective and all these things. Please note, that the ideas here are not to be taken without critical thinking. My skills are not even close to a professional level and this thing here is just another effort of mine to ultimately achieve that goal and I'll refrain from beginning every sentence with "I think" "in my opinion" and so on. This should be implied.

TBH the stuff I am doing here is in a way very sloppy looking, mainly because I try to train myself using as little tools as possible. For example, I am refraining from using tools like rulers and other such things other than my eyes for my studies because I want to train my brain to make lines as straight as possible, to draw within perspective without having to measure every single line. Becuase eventually, in the end, as the images get more complicated, these crooks will begin to hinder the progress. Besides, I do not see anything against using a ruler or the shift-key to speed up a process while making an illustration, but I think it would be a sad picture to have to rely on those things.

Saying that, I will begin with some exercises I began sporadically in the past and am doing every day now with pen and pencil, and it seemed to have helped me using those mediums a great deal, trying to more deeply understand the geometry of objects is crucial when you want to construct them on paper I think. Also, I would like to encourage everyone to help out by telling me what he or she has to say on that subject (I think there are as many opinions as there are artists), and if anyone wants to give it a try, too, then please be my guest! The more, the better I say.

This is going to be digital, however. I have even less expertise when it comes to drawing with the tablet but I hope this will help me a lot mastering the digital drawing and consequently the painting-process at last-

Saying that, I already began somewhat more extensively the past days collecting some first basic exercises. BTW, prior to that, one should try to make lines somewhat straight and precise, for that, there is a great thread going on here: http://www.conceptart.org/forums/showthread.php?t=117915

[~Faust~]

Exercise 1

Saying that, the first exercise is what everybody does all the time, try to master focal points. Focal points are vital to basic eucledian geometry. eucledian geometry meaning considering the basic paradigms like the 180 degrees in a tiangle and so forth. I am not a mathematician so I'll not go to deep into that, only that I find it possible to go up to 3-point-perspective using that form of geometry, the often citated 4-point 5-point, even 6-point (!!!) perspective I find in a lot of tutorials are violating the paradigms of euklidian geometry and are therefore not intuitively applicable anymore (I will try to explore that later when it come to non-euklidian geometry, when we have to abandon the principle of focal points in the classical way, but I am not even close to be there yet , just taking one little step at a time)

So the first little step is actually a huge and very difficult one. Draw cuboids (Haha, I actually looked that up, cubes are too hard to draw yet. all they have to posess are 90degree-edges.) in 1 2 and 3-point perspective. do it WITHOUT drawing a dot somewhere. the guessing is the whole purpose of it. Afterwards, control your efforts and weep! I guess, did have a small learning curve on this, but I have not done faaaaaaar enough of those. I will stock this up later with new trials. Please note how the errors seem to shrink with the distance to the focal point. This is surely not the case, since one premise is that hand-drawn lines are NEVER perfect, but with increasing distance, the angle gets easier to approach the optimum.

[~Faust~]

Exercise 2

This is about retangles. In modern simulation software, like for example all 3D-engines, the principles of finite elements is used. Saying that every object can be displayed with the help of a very small amount of different types. For examples, triangles and retangles are used often to describe a more distinctive object. So what I'll do is getting the hang of retangles to describe things going on. Now there 's the problem of drawing an optimal retangle. In 2D-space, it is relatively simple. We now take the concept of angles. Draw a line and another one going 90 degrees away from it. Then draw another one with the angle of 45 degrees. Following that, you can draw a simple retangle and the accuracy is quite astonishing doing it freehand, even for me. Of course, there's always something to optimize.

Doing that, transforming the retangle into 3D-space should be simple, right? Well, we have focal points and can say where the edges go but making an optimal retangle begins to be QUITE difficult. Because now we need a concept of how much 45 degrees is in 3-Dimensional space. taking simply the half of the angle displayed does indeed NOT suffice, since the part facing us should have a bigger angle. But for simplification one might do that at first.

Also, in order to give a feel of form, the retangles do not have to be optimal. They can be used as individual polygons with different measures. Indeed, later we can vary the measures of the retangles in order to simplify and speed up the process.

Because in 3D the agles are getting more and more quenched, tilted and so forth, drawing a perfet cube becomes more and more impossible. The reason I see for that is that one must be familiar with circles and how they are affected by perspective to make angles according to the prespective. That will be the next exercise.

[~Faust~]

Exercise 3

As seen in the previos exercise, one can try to build up a curved surface and even a sphere out of retangles. In order to draw a circle one can use this principle when drawing.

The difficulty of drawing circles in perspective can not be overestimated. It is extremely difficult to tilt those things right and they I sure need a lot more practice of those.

[John]

Really like this stuff, would like to see it developed further. I checked your sketchbook as well, good stuff! What've you been up to? Shoot me a pm, last i heard you were in Duisburg (i think?). Did you check out the Scott Robertson dvd's?

[Farvus]

Very interesting ideas. Personally I would practice this type of stuff with traditional media on big paper. I think it's essential if you want work on straight lines beacause doing big strokes with whole arm trains your muscle memory better :).
When it comes to exercises.
Exercise 1 - I have doubt about that method and I think it would work the opposite way. You draw a lot with perspective point marked on paper and slowly start to remember the whole concetric arrangement of lines. But continue the way you like. It has to be fun :).
Exercise 2 - This one sounds complicated. Maybe just construct a perfect cube out of cardboard and draw it under different angles and distances. You'll see what looks natural just by looking at life.
Exercise 3 - You reminded me I should practice drawing ellipses. Maybe I'll join you in this quest.

Keep it up. If I find some useful info about this, I'll post it here.

[bakatron]

i love this. its like youre literally prototyping a 3d engine in its early stages of development.

[reidaj]

Interesting stuff- my comments I guess would be that when we draw on a 2D surface, we are applying a perspective transformation, and this transformation is non-linear. A linear projection of 3D space into 2D space has more in common with isometric projection.

In order to create convincing perspective, you must adopt a system that operates in 2D space, as a perspective drawing is a product of not only geometry, but also viewpoint (camera). The drawing of a cube is removed from the underlying geometry it is derived from as it is a "projection" of 3D space into 2D space- an optical illusion. Vanishing points and perspective guide lines are part of a time tested system for producing the optical illusion of depth- a solution engineered from the flat surface of the page.

As for computer graphics, the problem of perspective is solved with brute force.. usually a variant of a simple idea: given a 3D point (x,y,z), we can find the 2D point (x',y') as x' = x/z, y' = y/z.

[Moftah]

:D.
i like were ur heading here,keep going.


Moftah's Sketchbook