By  William Li, Gallery 6.

 Understanding and Refining

Reflections

Overview

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

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.

Construction

2D

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).
 

3D

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.

Take a good look

	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.

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

An object with flat surfaces

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

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

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

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

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.
 

Dull 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.

Context
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.

Conclusion

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: the scene is outside there was no need to see any real reflection.

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

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