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Fantasy Art Tutorials in the FARP Section

By :-) William Li, Gallery 6.

 Understanding and Refining


© 1998 William Li, except where stated otherwise.
Newtek LightWave3D was used for creating 3D CGI.


As it became clear in the previous chapter, the level of realism when rendering highly reflective metal objects depends on the amount of detail in the reflection. Look at the drawing below. The ball on the right is clearly the more realistic one.

0. Which one looks more real to you?

In this chapter I will discuss the making of reflections and other factors that influence reflections.
First you need some insight on what you see in reflections. This will be shown in Reflection construction which serves a load of information. This is necessary in order to understand the drawing method that follows for creating complex looking reflections (like the drawing above).
After that other factors will be discussed such as dull metal and textures.
Now prepare for a long tutorial...


Reflection construction

The basis of reflections lies in mathematics and can be quite complicated. First a basic principle of reflection:

1. normal of a surface

Here you see a reflection of the red arrow (or ray if you will). This blue dotted line is called the normal of the surface. A normal of a surface indicates the surface's direction (so it's always at 90 degrees with its surface). In this example the surface direction is upwards.
The red ray is reflected according to the normal. The incoming angle a between the ray and the normal equals the exiting angle b between ray and the normal.

2. normals on a curved surface

This image above shows a number of normals of a curved surface. On the right you see that different normals result in different reflections.



Before we continue, please note that the point of view I will be using here is the same as the ray tracing method in 3D software. Basically this means that I try to determine what I see starting from my eye. So all the "viewing rays" start from my eye, represented by arrows.
In the real world the opposite is true of course: objects reflect light and some of it reach my eye. This however exceeds the purpose of constructing reflections.
If this doesn't make any sense to you, don't mind it and continue!


In the image below you see the reflection of a green ball constructed on a flat mirror. If you look in a mirror, it's like the space extends into it.

3. reflection construction on flat mirror

So, in this scene it's like seeing the green ball behind the mirror (dotted line ball). The blue lines are normals of the mirror, where the "vision rays" hit it. The ball is reflected between the two blue lines.

A curved surface is more difficult. Because of the varying normals the reflection shows a distorted image. We call a curvature rounded towards us a  convex surface.

4. reflection construction on convex mirror

Now look at the following: a concave surface. Note that the reflection shows an upside down image!

5. reflection construction on concave mirror

I've included the centre of this circular convex mirror to show the origin of the normals. You should also keep in mind that the origin of normals of curved surfaces is not always 1 point (see figure 2).


In the picture below you see one of the simplest forms of a reflection scene: a flat surface mirroring a perpendicular plane (the red line is drawn on it).

6. 3D reflection construction on perpendicular surface

On the white horizontal plane is a red line which we will mirror.
The mirroring plane is coloured yellow. The normal of the yellow reflecting surface is coloured fuchsia. The green line is the mirroring line; in this case it's also the intersection of the two planes. The blue lines are the constructed reflections of the red lines.
Notice that the black arrow lines indicate equal lengths. This example is without perspective. In using perspective you would of course take into account any shortening due to distance.

7. height doesn't change the reflection
Here you see the same situation, but the yellow mirror has been elevated (h) from the white plane. 
You will notice that the reflection is exactly the same as above when not elevated. It shows that the height or distance does not matter
Only angle and curvature matter, which will be discussed next. 
I have shown you just a very simple reflection scene. Real life scenes are much more complex. Think of curves and angles: these reflections are extremely hard to construct as the following will show.

Take a good look

Because it is very important that you see and understand reflections on objects I will show you a basic reflection of a grid on a variety of standard geometries. Considering the complexity, I will use 3D rendered images.
Use these images for reference. They're quite useful for that!
Ref1. The standard ball on a grid
Characteristic is of course the curved reflection. 
Also note the reflections recursing between ball and plate. On the grid you see the ball reflected ever smaller. This would go on infinitely, because they're two mirrors facing each other. 
That's reality, but it is quite rare that you should encounter the need to do this.
Ref2. A box
You'll notice that each face is a plain flat mirror. Also, the reflection of the horizon is at the same height as the real horizon. 
These reflections are relatively easy to reconstruct.
Ref3. A cylinder
You see a curvature in the reflection. 
And just like the rectangular object: any surface that is perpendicular to the ground surface reflects the horizon at the same height.
Ref4. A cone, upside down
A curved reflection. Because the cone is pointed downwards, it only reflects the ground.
Ref5. A classic setup of ball and cone
This demonstrates the warped reflections between rounded objects. You will also notice the elongated highlight on the cone. 
Ref6. A cylinder on its side, aligned
Basically it's the same as a flat standing mirror, but in this case the image is squashed and curved along the cylinder's axis. 
Please note that the reflected horizon is at the axis of the cylinder.
Ref7. A cylinder on its side
This demonstrates again some similarity with a flat mirror. compare it with Ref2.
Ref8. A cone on its side
This is like the cylinder, with the reflection following the geometry of the cone. So the reflection is pinched on the cone top. 
As with the cylinder, the reflected horizon is at the axis of the cone.
Ref9. Box at an odd angle
Here no faces of the box are perpendicular to the ground. This shows in the reflection of the horizon: it doesn't align with the real one. 
Look the complex recursive reflections on the surface facing down. Drawing this may be an awesome feat, but serves no purpose: the result is just confusing and your effort will not show. 
Makes you want to give up on drawing and take up 3D imaging? The images above demonstrate that we "hand artists" can indeed only go so far. But don't get discouraged. If you keep the reflections above in mind, you can achieve much. The trick is to apply them efficiently.

Pursuing a high level of realism demands a good eye for reflections on all sorts of curved surfaces. Partly you can reconstruct these reflections. For other reflections you have to rely on your experience in analysing real world reflective objects. Being a trained observer will help you greatly in creating credible reflections.
Great illustrators like Sorayama Hajime (world famous for his female chrome robots) collect metal mugs, tubes and other assorted reflective objects as reference for their work: very simple and very effective.
Free your mind for the creative tasks!


A way for the artist

Still, you can approximate all this: the artist's way! Of course the result depends on your approximation. It requires you to think three-dimensionally and "trace rays" (like its Computer Generated Imaging counterpart ray tracing ;-)).
How to do this?
Basically, you imagine rays starting from your eye. A ray bounces off the reflective surface you've drawn and finally hits something in its environment. This something will be reflected on that surface. As you can imagine, this requires some skilled 3D thinking. As always: practise makes the master.
Note: this is not a method that gives accurate results. It gives an approximation only. It is a way to derive reflections from logic without the accuracy of calculations. Purists will shriek in rage, I'm sure ;-)

An object with flat surfaces

8. rays from your eyes: what you see reflected

This is the easiest type of reflection. Again: different normals have really different reflections. The green arc shows the reflected surroundings that you see.

A curved object

8. rays from your eyes: what you see reflected 2

This is more complex. As you might have expected, a totally curved object reflects everything of its environment. You see everything reflected within the green arc. Because of its roundness the reflections will be deformed (warped, distorted etc.).

A demonstration

With this in mind, let's construct some reflections.
I will demonstrate how you can approximate reflections with just your eyes and your perception of space. No calculations or computer generated solutions are used.

Consider the scene in the image below: a shield resting on a rectangle and some other objects around it.
The shield will be our reflecting object our "reflector". I've drawn some lines across it, so you can understand the flow of its surfaces. The blue cross hair represents the centre of the image: this is our viewing point, our eye (this is not a 100% correct, but one has to start with something).

9. demonstration: setup

Please note the shadows I've put in. I've used a distant light shining vertically down so that the shadows really mark their objects' positions. You need to know where you're objects are in space in order to make the reflections. Of course you can have your lights anywhere you want, as long as you know the relative positions of the objects in your drawing.
In the next image you see the approximated reflection of the ball. You can sketch these arrow lines on your drawing to help you "see the rays", but make sure you can erase them.
Draw straight lines from the centre to where you think the ball would reflect. To do this search for a spot on the reflector with normals pointing more or less in the direction of the ball.
You see a construction of green lines: these show the relative positions of ball and shield. If you make this first it will help you a lot it determining where the ball is reflected.
Another tip: start with the ray that would hit the centre of the ball. The reflection is coloured red.

10. demonstration: reflected ball

The rod's reflection is done in the same way.
Remember the curvature of the shield? Look at the first image of this series.
I decided that the rod is reflected on the centrepiece and on the rim of the shield. The rim is connected to the centrepiece, so the reflection is seen on both surfaces, but will look "broken", because they are not a continuous surface.
The broad rim will reflect the rod as well. However, in this case I think it will only reflect a part of the rod. As I said: it is an approximation in my mind, no calculations so I'm not sure. But that doesn't matter too much.

11. demonstration: reflected rod

But I could also have decided otherwise, like this:

12. demonstration: alternatively reflected rod

Basic point is: I don't know for sure. Both reflections are possible.

At the start of this chapter, I showed this image:

The reflections on the right ball are drawn using the approximation method I described above.
Whenever possible use a grid (that you use temporarily and erase later). Try to reflect that grid. All other objects standing on that grid are now pinpointed on the reflection!
Having said that, look closely at the reflection: see if you can discover the error in the reflected grid! Faded or distant lines that aren't seen in the reflection do not count!


Reflective properties

Two factors define how you see the reflection on an object: specularity and texture.

A reflection is the result of reflected light. In other words, a reflection is an image. The way and the amount that is reflected depends on the specularity (of the material). Specularity can be judged on the contrast of a reflection. It is defined by the material itself (due to molecular, atomic matrix or crystalline properties). It is a material-specific property.
Consider these polished balls (I'm showing polished versions so you're not distracted by other factors).

Low specularity
High specularity 
13. specularity comparison

Reflective materials are typically considered highly specular.

Texture is the structural quality of the surface (grooves, scratches, polish, bumps). It defines the glossiness or the diffuse look of a surface. Usually texture is a property of the object, not of the material. It is caused by man, weather or other forces.
In short, e.g. a material has just one level of specularity, but it can have many textures.
Note: the word texture is also used for a type of material (e.g. wood, granite), especially in 3D software in which natural/organic materials are simulated using image textures. We are using the word texture here in a real, physical sense.

14. one texture with different specularities
15. one specularity with different textures


Dull metal

Dull metal can be recognized still because of its specularity, although you don't see much reflected. The level of specularity is evident in visibly reflected colours and the contrast between light and dark. The image below shows how.
16. Which one looks more like metal?

The ball on the left can be considered plastic, but what if it's a spray painted metal ball? It would look just like that!  The two on the right are closer to metal, the main reason being the reflections on the surface.

Metal is dull because it is not polished. It is brushed or chipped, or it has scratches and dents.  These aged, weather-beaten or worn metal textures are among the hardest to render. Because of its reduced reflectivity it is difficult to identify them as metal.

The only way is using the object to tell the viewer that the material is metal. That's why it is easy to understand that a sword is made of metal, even if it's all smeared with blood.
There is a heavy reliance on context, so there is no standard sure method to render them. If you draw a battered steel shield it is recognizable as metal, because you know a shield like that can only be made of steel, not plastic. But if you show just a zoomed in part, it will be hard to recognize it as metal.
Some examples of metal context:

  • Use of nut and bolts. We all know that these are (usually) made of steel and usually they are only used on steel. It's quite funny, but if you draw a steel beam with nuts and bolts, it doesn't matter what colour, specularity of texture you give to it: you'll always see a steel beam!
  • Armoured tanks are another example: they're green or brown coloured, but still we assume they're from steel!

The main guidelines to use are still the standard ones:

  1. Use high contrasts.
  2. When possible show reflections, as blurred as they might be.
Oh, and use context...



You have reached the end of Chapter 2. The information presented here should give you a clear understanding of the behaviour of reflected light. You've also seen that it is hard to draw realistic reflections.
Drawing dull or worn metals is also difficult. Using context helps more than the shading of the metal itself.
A solid advice would therefore be: avoid constructing reflections if you don't have to. If you must, try suggesting the reflections. And naturally there is no recourse when you actually must see the reflection.

Finally, here's an example why so many people still draw or paint and are not using 3D software to render their visions for them: it's not only metal we (want to) see...

17 not just metal...
Helmet and armour have many facets, so each of these surfaces need attention for increased realism. Only the sky-earth method is used here, because:
  1. the scene is outside
  2. there was no need to see any real reflection. 
If you would make this using 3D software you would be busy for many years or you'd not be reading this tutorial. You'd be an extremely well paid 3D-CGI artist in Hollywood! ;-)

To chapters:
  1. Introduction
  2. Fast metal
  3. Understanding and refining reflection
  4. Transparency

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