it-ebooks - Graduate Computer Graphics (NYU CSCI-GA.2270-001)

From: Graduate Computer Graphics

3D Coordinate system

WebGL exists in a 3D world:

• x goes to the right
• y goes up
• z goes forward (out of the screen)

This is called a right hand coordinate system.

For now we are going to be doing allof our work starting with the x,y plane.Specifically we will be working with a squarethat extends from -1 +1 in both x and y.

Square as a triangle strip

Our geometry will be a square.

In WebGL everything is made of triangles, so we will need two triangles.

We define these as a triangle strip.

In a triangle strip,every three successive vertices makes a new triangle,so we will need to specify a total of four vertices,as in the figure to the right.

Z-buffer algorithm

The GPU (Graphics Processing Unit) renders using a "Z-buffer algorithm"

For each animation frame,this algorithm consists of two successive steps:

1. For each vertex:The GPU runs a vertex shader to:
   • Find which pixel of the image contains this vertex;
   • Set up "varying" values to be interpolated.
2. For each triangle:The GPU interpolates from vertices to pixels.
   For each pixel:The GPU runs a fragment shader to:
   1. Compute color;
   2. If this is the nearest fragment at the pixel, replace color and depth at this pixel in the image.

Vector3 object

One data structure that will be very useful is a vector of length 3,which we can use to represent x,y,z coordinates, as seen in thefigure to the right.

In Javascript we can define this object via a constructor,which contains all of its properties that can change per instance,as well as a prototype, which contains properties that do notchange from one instance to another (such as functions todo such operations as setting values).

The Vector3 objectwill grow in capability as the semester progresses, butto the right is a starter version.

Note that the x,y and z properties, which changefrom instance to intance, are defined in theconstructor itself.

The set property, which will be the same functionfor all instances, is defined in the prototype.

function Vector3() { this.x = 0; this.y = 0; this.z = 0;}Vector3.prototype = { set : function(x,y,z) { this.x = x; this.y = y; this.z = z; },}

Uniform variables

GLSL (for "GL Shading Language") is the C-like language that is used forshaders on the GPU.One of its key constructsis a uniform variable.

Uniform variables on the GPU have the same value at every pixel.They can (and often do) change over time.

By convention, a uniform variable name starts with the letter 'u'.

For your assignment, I have create some useful uniform variables:

float uTime; // time elapsed, in seconds vec3 uCursor; // mouse position and state // uCursor.x goes from -1 to +1 // uCursor.y goes from -1 to +1 // uCursor.z is 1 when mouse down, 0 when mouse up.

Vertex shaders

A vertex shader is a program that you (the application programmer/artist)writes which gets run on the GPU at every vertex.It is written in the special purpose language GLSL.

To the right is a very simple vertex shader program.An "attribute" is a constant value that is passed in fromthe CPU. In this case, it is aPosition, the x,y,z position ofeach vertex in the scene.wIt is of type vec3,which means that it consists of three GLSL floating point numbers.

attribute vec3 aPosition; varying vec3 vPosition; void main() { gl_Position = vec4(aPosition, 1.0); vPosition = aPosition; }One of the most powerful things that a vertex shader can dois set "varying" variables.These values are then interpolated by the GPU across thepixels ofany triangles that use this vertex.That interpolated value will then be availableto fragment shaders at each pixel.

For example, "varying" variable vPositionis set by this vertex shader.By convention, the names of varying variables start with the letter 'v'.

This vertex shader does two things:

• By setting gl_Position,it determines at which pixel of the image this vertex will appear.
• It sets varying variable vPositionto equal the attribute position aPosition for this vertex.

Fragment shaders

A fragment shader is a program that you(the application programmer) writes which isrun at every pixel.

Because pieces of different triangles can bevisible at each pixel (eg: when triangles are very small,or pixels where an edge of onetriangle partly obscures another triangle),in general we are really defining the colors offragments of pixels, which is why these are calledfragment shaders.

Since our vertex shader has set a value for vPosition,any fragment shader we write will be able to make use of thisvariable, whose values will now have beeninterpolated down to the pixel level.

Guides to WebGL

There are many guides on-line to WebGL.I find this Tutorial on WebGL Fundamentals to be particularly clear and easy to followfor people who are new to WebGL.

I also find this Quick Reference Cardto be very useful when writing WebGL shaders.I think you will find the list of built-in functions on the last page to be particularly useful.

Assignment 1

Your assignment for this week is to start with,which we went over in class, and replace the fragment shaderin index.html with your own fascinating and wonderfuland original fragment shader.

Important: Create something of your own.Don't just make a minor variation of what I did in class.Have fun with it.

Your homework is due before the start of next week's class.

WebGL Cheat Sheet

As I mentioned last week, there is a convenientcompact guide to WebGL.

The last page in particular is useful for writing shaders in OpenGL ES.

Note that OpenGL ES fragment shaders do not allow recursion.

Gamma correction

Displays are adjusted for human perception using a "gamma curve",since people can perceive a vary large range of brightness.

For example, the image to the right shows the values 0...255 on the horizontalaxis, the resulting actual displayed brightness on the virtual axis.

Various displays differ, but this adjustment is generally approximately x2

Since all of our calculations are really summing actual photons of light,we need to do all our math in linear brightness, and then do a gamma correctionwhen we are all finished:

Roughly: c sqrt(c)Output brightness

Ray tracing: Forming a ray

At each pixel, a ray from the origin V = (0,0,0) shoots into the scene, hitting a virtual screen which is on the z = -f plane.