By William Li, Gallery 6.
Understanding and Refining
© 1998 William Li, except where
Newtek LightWave3D was used for creating
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...
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
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
The red ray is reflected according to the normal. The incoming angle
between the ray and the normal equals the exiting angle
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
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
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.
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.
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
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!
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.
||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
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.).
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
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
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
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!
Two factors define how you see the reflection on an object: specularity
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).
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.
14. — one texture with different specularities
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.
15. — one specularity with different textures
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
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
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:
Oh, and use context...
Use high contrasts.
When possible show reflections, as blurred as they might be.
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...
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! ;-)
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.
Understanding and refining reflection
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