Real Glass

Written by Tels

Abstract

In this article you will learn how to make good-looking, realistic glass objects/effects, which can be applied to images giving them a nice 3D touch. You will also learn how to speed things up, so that they work in real-time.

Preface

I once asked the authors of a very good demo coder book here in Germany if I could do some work for them. They said yes, and I wrote a small demo, containing glass spheres. I never heard back from them, but the second edition of the book contains my effect. So, if you want to steal these things, go on - but I will hunt you down.

The glass effect was conceived by me a year ago, or even longer. But as you know, I bet there are people who have thought of these things, too. Alas, I never saw a description of it - everybody goes 3D these days. To preserve the idea, I wrote this article, and while I was there, expanded the stuff a little bit. So, HAVE FUN!

And remember: This stuff isn't new, I only combined it to get something new, unique out of it.

The Things Glass is About

When you look at a raytraced image of a glass sphere, you will notice a couple of things:

When you render the image with 3D-Studio, you get instead:

You see the difference? The raytraced image shows us the refraction, whereas the rendered image has only light effects.

So, to make real glass, we need:

• refraction (!)
• reflection (maybe)
• light effects (maybe)

The first thing is the most important thing, as you can see on the images above.

How to make refraction

When light rays travel through a glass object into your eye, you see the things behind the object. But you see them distorted. This is a law of nature, and caused by the difference of the speed of light in glass and air.

When we simulate this in the computer, we send the rays from the eye to the world and measure where they hit the objects. This works, since the rays of light are reversible.

To simulate the distortion, we use the following equation:

sin a1   c1
------ = --
sin a2   c2

a1 and a2 are the two different angles of the light ray, and c1 and c2 are the different light speeds in the two different materials.

Here is a small picture:

You can find some values for different materials in any physics book.

Let's Make a Sphere

To make a sphere, we take only a quarter (since a sphere is highly symmetric) and calculate the things for it. Then we copy it to the other 3 quarters.

A sphere has a surface which is formed like this:

To simulate the light rays, we need the angle with the surface and the light. We assume that we look from directly above the sphere, and all light rays come straight down. (Camera view would distort (and complicate) this, we project just from top.)

As you can see from the picture above, the surface of the sphere drops down to the outside by the function cos(x). This is true for every point for the direction from the center of the sphere to the outside.

So, for every point in the quarter, we loop through the following pseudo-code:

   for Y=0 to Radius/2 do
    for X=0 to Radius/2 do
     // only for points inside the sphere
     if (x*x+y*y) < (radius*radius) then begin
       // the point we see is not the point , but
       // a point on a different radius
       newRadius = function (x*x+y*y);
     end

function calculates a new radius.

Well, this doesn't help us much, since we got the new radius, but not the new coordinates.

To make a quick hack, we can modify the code above to the following:

   for Y=0 to Radius/2 do
     for X=0 to Radius/2 do
       // only for points inside the sphere
       if (x*x+y*y) < (radius*radius) then begin
         // the point we see is not the point , but
         // a point on a different location
          ixo = function ( (x*x+y*y) / (Radius*Radius*dB) )*dB*x;
          iyo = function ( (x*x+y*y) / (Radius*Radius*dB) )*dB*y;
       end

function takes an argument from 0.0 to 1.0 and is defined as (for example):

return sin ( 0.5 * PI * argument);

The value of dB should be between 1.0 and 4.0, but 2.0 looks best.

What do we now with the new coordinates? Remember our friend, the look-up table? Ok, let's create such one:

   for Y=0 to Radius/2 do
     for X=0 to Radius/2 do
       // only for points inside the sphere
       if (x*x+y*y) < (radius*radius) then begin
         // the point we see is not the point , but
         // a point on a different location
          ixo = function ( (x*x+y*y) / (Radius*Radius*dB) )*dB*x;
          iyo = function ( (x*x+y*y) / (Radius*Radius*dB) )*dB*y;
         //Since the sphere is symmetric, we store it four times
          iXDiff[ioa+x+ioy] = ixo;  iYDiff[ioa+x+ioy] = iyo;
          iXDiff[ioa+x-ioy] = ixo;  iYDiff[ioa+x-ioy] = -iyo;
          iXDiff[ioa-x+ioy] = -ixo; iYDiff[ioa-x+ioy] = iyo;
          iXDiff[ioa-x-ioy] = -ixo; iYDiff[ioa-x-ioy] = -iyo;
       end

Well, now we got two different fields, one with X-Offsets and one with Y-Offsets. When drawn, they look like:

Red means negative value, green positive, white is zero. Black parts mean both X and Y offset are zero. The left picture shows the X Offsets, the right Y.

So, how do we apply this?

For every point to draw, take its location, and add the X and Y offsets to it. then draw that point instead:

   for x=0 to width do
     for y=0 to height do
       //background[x,y] would be the original
       newx = x + iXDiff[x,y]
       newy = y + iYDiff[x,y]
       screen[x,y] = background[newx,newy]

The result will look like:

You'll notice couple of things that are slightly wrong. First the refraction is not mirrored. We can fix this by swapping the four parts of the sphere. Next, the refraction function doesn't look like the real one. We can fix this by popping in a better refraction function. To fix the refraction you need to:

• calculate the angle between the surface of the sphere and the incomming light ray
• calculate with that the angle of the light ray inside the sphere
• use this angle then to calculate the point where the light leaves the sphere
• with this point, calculate the angle between the sphere's lower surface and the outgoing ray
• then calculate the exact angle that the light leaves the sphere
• take an (arbitrary) height of the sphere over the background surface and calculate the point where the light hits it

This is left as an exercise for the reader ;-) Remember that you have to do this for X and Y! Vector math would be real handy for this task.

So, what can we do to make the image look even better? How about shading? The raytraced image shows us that the glass sphere absorbs some amount of light, thus the background appears darker inside the circle.

This is a tricky thing, but you could pull a trick with the palette. For every point inside the sphere decrease the color by a constant factor, or use a light map with concentric circles. For speed reasons use a look-up table!

   for x=0 to width do
     for y=0 to height do begin
       //background[x,y] would be the original
       newx = x + iXDiff[x,y]
       newy = y + iYDiff[x,y]
       screen[x,y] = shadedcolor[ background[ newx, newy ] ]
     end

The result (without swapping this time again) is:

The Shadows Fled

Well, now we need a light source. To simulate this, we add a shadow under the sphere, and then add a highlight above it. The normal but slow way to do this is as follows:

1. draw the empty background
2. shade a circle where you want the shadow to be
3. apply the glass effect (this will shade the shadow darker if they overlap)
4. draw a light effect on top of the glass effect

In the last section you will learn how to do this very quickly.

Scrolling

For scrolling, just double the background image in height, and modify the start pointer to the background for every frame you draw by one line. This doesn't cost you extra time, since you only have to increase a pointer (and make sure it does wrap around!) for every frame.

The Need for Speed

Well done, girls & guys. We have a glass effect.

Hey, where are you going? Didn't I tell you we will do these things in real-time? So, fasten your seatbelts again!

The code above needs many array look-ups to build the effect. Since this needs a considerable amount of time per pixel, we do something different.

Let's eliminate the shading look-up table:

We add the background image twice, once normal, and once shaded a little bit darker (for scrolling this means we need the background four times). For every Y-Offset inside the sphere add the height of the background pic divided by 2 (since the background is twice, for scrolling divide by 4), and instead of seeing the normal background, you get a slightly darker sphere. And this, of course, at no extra speed charge. :) This is because we combined the refraction table with the shading table.

With this method we can add only a darker shade with the same amount for every pixel. When we would use scrolling and different shades, the shades would scroll, too! To avoid this, make the second image is shaded by the same amount on every place, and overlay a small shaded highlight-effect after drawing.

Next thing we want to eliminate are the two different array for X and Y. Since our glass effect arrays have a fixed width, we can calculate a combined array and eliminate the multiplication by:

  for y=0 to height do
    for x=0 to width do begin
      iDiff[x,y] = iDiffX + (iDiffY + HeightOfBackgrounPic / 2) * Width;

Optimized pseudo code after this:

   bpl = pointer2Background;
   spl = pointer2Screen;
   opl = pointer2Offsetarray;   // combined X & Y: iDiff
   for y=0 to screenheight do begin
     for x=0 to screenwidth do begin
       //background[x,y] would be the original
       // add the current offset to the background pointer,
       // fetch the color and store it onto the screen
       *spl = *(bpl + *opl);
       spl++; bpl++; opl++;
     end
     // adjust pointer here ifbackground and shadetable
     // have different sizes than screen
   end
   overlayhighlight();

I bet someone can line this up in assembler with two or less clocks/pixel. :-)

Another nice idea is to have the background sixfold, with two different shades. Before applying the sphere, add a circle of twice the background height to create a shadow. Here is a picture of the final result:

A further speed enhancement can be made by applying the glass effect only on these parts really needing it. For this you could maintain a list of starting/ending point into the glass effect buffer.

Ok, that's all. There is the source code available for this example. It is not perfect but should give you some ideas. I created it with the Visual Builder and the VisualAge C++ of IBM and used the DIVE-based FastCanvas by Dave B.

Hope you had fun!