What is a shadow, even?

Well, let me start off by saying that I love shadows more than light, and I have chosen the one room in the house where every being of the room occludes light. Occludes light… Hmm… How do we know what’s behind the light frustum, and what’s in front of the light frustum, or frusta?

 

Let us scrutinize shadows first. What are shadows? When you shine a light on an object with a wall behind it, what happens?

Look at this picture:

 

Umbra: Full, hard-edged shadow.

Penumbra: Half, soft-edged shadow.

What happens if we take the light source furher and further away, until the light frustum become so wide that umbra does not seem feasible anymore? Then, umbra turns into antumbra, where different penumbras meet.

Shadow Mapping

The concept was popularized by Lance Williams in 1978. Lance Williams is also the person behind mip-mapping, which we’ll discuss in another post, moon-god-willingly. So what is Shadow Mapping? It’s by far the only feasible real-time shadowing solution, as raytracing is rather resource-intensive and volume shadows are not suiable for real-time rendering.

 

Such a happy man!

Native API support is also another reason to choose shadow mapping. GLSL, for example, has a native texture type for receiving the shadow map as a Sampler2D Uniform, which we’ll see. 

But what is shadow mapping?

 Imagine angle of the light is less than 180 degrees. If we choose camera position as the light position, camera direction as the direction of the light, and shine the light frustum on the scene then the resulting depth buffer is our shadow map.

 

Left: Light Frustum Shone on the Scene | Right: The Resulting Framebuffer becomes out shadow map
Depth as seen from a ligh

The moment of truth

We said all those things, and we showed you the result, but how exactly do we know that an object occludes light at a certain position? Let’s see what happens when it doesn’t and then we’ll see what happens when it does so.

Imagine this spot on our Utah Teapot:

 

Imagine if Z_{sm} is the depth value point on the teapot. And imagine Z_{ls} is the depth value of the length of the light source to the lit point.

 

There will not be a shadow in this case, because Z_{ls} = Z_{ms}. However, imagine if Z_{ms} was behind the teapot:

 

In this case, when Z_{ls} < Z_{ms} there this point is definitely in the shadow, and since each point is a fragment, this fragment should be shaded In an Octopus’ Garden in the Shade!

Again, I’m burying the lede, and I’m sorry for that. Octopus’ Garden in the Shade has nothing to do with shaders! Anyways, we must factor in a bias when we do compare the depths. Because if we don’t, as you see in the photo, there will be surface acne.

In a scene with dueling frasta, i.e. more than one light source and shadow map, the size of the shadow map shan’t be different from each other, otherwise, as a result, the shadow will be pixelated.

 

Shadow Map: Pros vs. Cons

Shadow Map Pros are:

  1. No matter how heavy they may look, they are still better for real-time rendering than the alternatives (e.g. RayTracing).
  2. You can adjust the size of the texture which holds the depth data, ultimately, add it as an option to your game, or demo.

 And the Cons are:

  1. Aliasing occurs in low-res textures.
  2. Textures are heavy and occupy a lot of memory.
  3. Effects of self-occlusion may be visible in the output as sparkling. This can be fixed by polygon offset.

 Finally, let’s implement it in the code using OpenGL.

OpenGL Implementation

With all that said, how exactly is this implemented in OpenGL? Here’s how. The following code is taken from OpenGL Superbible 7th Edition.

Listing 1: First, we create the shadow depth buffer.

 

GLuint shadow_buffer;
GLuint shadow_tex;

glGenFramebuffers(1, &amp;shadow_buffer);
glBindFramebuffer(GL_FRAMEBUFFER, shadow_buffer);

glGenTextures(1, &amp;shadow_tex);
glBindTexture(GL_TEXTURE_2D, shadow_tex);
glTexStorage2D(GL_TEXTURE_2D, 1, GL_DEPTH_COMPONENT32,
               DEPTH_TEX_WIDTH, DEPTH_TEX_HEIGHT);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_LINEAR);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_MODE,
                GL_COMPARE_REF_TO_TEXTURE);
glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_COMPARE_FUNC, GL_LEQUAL);
glFramebufferTexture(GL_FRAMEBUFFER, GL_DEPTH_ATTACHMENT,
                     shadow_tex, 0);

glBindFramebuffer(GL_FRAMEBUFFER, 0);

Listing 2: Then, we create model-view-projection matrices, but this time, instead of the camera, we use the light!

 

vmath::mat4 model_matrix = vmath::rotate(currentTime, 0.0f, 1.0f, 0.0f);
vmath::mat4 light_view_matrix =
    vmath::lookat(light_pos,
                  vmath::vec3(0.0f),
                  vmath::vec3(0.0f, 1.0f, 0.0f);
vmath::mat4 light_proj_matrix =
   vmath::frustum(-1.0f, 1.0f, -1.0f, 1.0f,
                  1.0f, 1000.0f);
vmath::mat4 light_mvp_matrix = light_projection_matrix *
                               light_view_matrix * model_matrix;

Listing 3: Thusly, we generate a shadow matrix.

const vmath::mat4 scale_bias_matrix =
     vmath::mat4(vmath::vec4(0.5f, 0.0f, 0.0f, 0.0f),
                 vmath::vec4(0.0f, 0.5f, 0.0f, 0.0f),
                 vmath::vec4(0.0f, 0.0f, 0.5f, 0.0f),
                 vmath::vec4(0.5f, 0.5f, 0.5f, 1.0f));
vmath::mat4 shadow_matrix = scale_bias_matrix *
                            light_proj_matrix *
                            light_view_matrix *
                            model_matrix;

List 4: Nothing can be done without shaders, so we implement the vertex shader for this shadw. Not much different than any other vertex shaders.

#version 420 core

uniform mat4 mv_matrix;
uniform mat4 proj_matrix;
uniform mat4 shadow_matrix;
layout (location = 0) in vec4 position;

out VS_OUT
{
    vec4 shadow_coord;
} vs_out;

void main(void)
{
    gl_Position = proj_matrix * mv_matrix * position;
    vs_out.shadow_coord = shadow_matrix * position;
}

As you can see, we’ve got two model-view-projection matrices, one we use for ourselves, and one (the shadwo matrix) we pass to the fragment shader to see if each fragment is in the shadow, or in the light.

Listing 5: the fragment shader of it all.

#version 420 core

layout (location = 0) out vec4 color;

layout (binding = 0) uniform sampler2DShadow shadow_tex;

in VS_OUT
{
    vec4 shadow_coord;
} fs_in;

void main(void)
{
    color = textureProj(shadow_tex, fs_in.shadow_coord) * vec4(1.0);
}

That’s it! Notice something that we’ve never before seen in this blog, sampler2DShadow. It’s something recent, and not found in 3.3. This is why I say Superbible is better than LearnopenGl.com. It’s up to you, do you want something outdated written by a fan, or something up-to-date written by ARB? You choice!

 

Well, that is it for today! I might make another post, but it would be for the Europeans, because by the time I post my second entry of today, Americans will be asleep. A lot of people have visited my blog, this blog is not far from generating profit. So thank you! Don’t forget to leave a comment. I love each and everyone of you, if that’s not creepy. Really. I love everyone who reads the drivel I write. This gives me a feeling of self-importance. Anyways, before we have engaged in coitus, goodbye for now!

Let me christen this blog through a Processing tutorial.

I hereby promise to fill this blog with game assets that I myself have created, graphics-related tutorials such as After Effects, Cinema 4D and Blender plugin development tutorials, Processing tutorials and scripts, and of course, game development tutorials! I don’t know much, but I’ll share what I know. And that’s how you get into heaven.

Chubak Bidpaa


And now, break the champagne bottle!

Anyways, in this tutorial, I want to teach you how to find out how a color matches the theme of your game wonderfully by using scripting language of Processing. Processing is a Java library that helps with aides artists and programmers in creating artwork. You can download it from here.


The Raw Power of Processing

Processign is a very powerful language, and it’s very useful. Processing is a Java library, so it’s very similar to  its container language. It has OOP support, and each code has a setup() and draw() method which cater to initiation and the main loop, respectively.

Let’s say your level has a red theme, and by red theme I mean the overall feel of the level. And out want to know what colors beset our main color. So let’s start by setting up a window with a red background:


void setup() {
  size(400, 400);
  color c = color(255, 0, 0);
  background(c);
  noLoop();
}

This will create a 400*400 window with a red background. noLoop() later comes into play, when we write a draw() function, it’ll make it so that the draw() does not loop.


Processing renders a 400*400 window with a red backgroun

Now, to write the draw function. It’ll be much more complicated, by a small margin.


void draw(){
  
  float red = random(255);
  float green = random(255);
  float blue = random(255);
  color random_color = color(red, green, blue);
  
  textSize(16);
  text(red, 10, 350);
  text(green, 10, 370);
  text(blue, 10, 390);
  
  fill(random_color);
  rect(100, 100, 200, 200);  
  
}

First, we create three floating point integers that hold a random number between 0 and 255. Then we create a color object with it. Then, we print those numbers for later reference, as there must be a way to assess what RGB values makes up our new color. We then change the color to the new color and draw a rectangle in the middle of the screen (origin point is top-left).


It has generated a green rectangle…

As we see, the green rectangle does not elate the red color. So we discard it and generate a new color.


It has generated a purple color

As we can clearly see, purple does not go with red either. We’re not lucky today, are we?

Well, there’s no need to beat around the bush. Let’s make a hundred million colors!

In order to do so, add this line:


saveFrame("color_swatch########.png") //org jpg

At the end of the draw() function. Also, remove the noLoop() line from the setup() function. But before running the code, save the file in a separate folder. Once you run the code, it’ll save images in a folder where you’ve saved the file. Peruse through them, and maybe you’ll find your swatch!


In Part 2…

In Part 2 of this tutorial, I’ll teach you a bit about color theory and how to generate opposing colors.

For now, Semper Fi!