Finally! We have been building skill for this moment! You learn most of the GLSL foundations. You know about types and functions. You practice your shaping equations over and over. Now is time to put all that together. You are up for this challenge. In this chapter we are going to finally learn how to draw simple shapes in a parallel procedural way.
Imagine we have a grid paper, like the one we used on math classes, and the homework is to draw a square. The paper size is 10x10 and the square suppose to be 8x8. What you will do?
You paint everything except the last and first rows and last and first column. Right? But now you are probably asking your self what this have to do with shaders? Each little scare of our grid paper is a thread. Each little scare knows their position, like the coordinates of a chess board. In previous chapters he have mapped *x* and *y* to the *red* and *green* color channels, we learn that’s our field and space. A narrow two dimensional territory between 0.0 and 1.0. How we can use it to draw a centered square in the middle of our billboard?
* Sketch a peace of code that use ```if``` statements over our spacial field.
Well done! This is a great step and accomplish. And speaking about steps, how we can simplify this code that use ```if``` statements with ```step()``` functions? Take a look to the following code.
If we look close, on the previous code we repeat the structure for each side axis for left and bottom. We can save some lines of code by passing directly two values and treating them in the same way with the same function. Check the following code.
But this rectangle is not centered, is in the top right corner. We need to “take out” equal peaces on both extremes on left-bottom and tight-top to obtain a centered square.
So, to repeat this on the top-right side we can invert the ```st``` gradient and repeat the same ```step()``` function. That way the ```vec2(0.0,0.0)``` will be on the top right corner. This is the digital equivalent of flipping the page.
Interesting right? Because we only know the coordinate position per pixel, our drawing methods are based on it. Drawing shapes is all about flipping and stretching this coordinate system.
* Experiment with the same code but using ```smoothstep()``` instead of ```step()```. Note that by changing values, you can go from blurred edges to elegant antialiased borders.
* Make another function that just draw the outline of a rectangle.
* How do you think we can move and place different rectangles in a same billboard? If you figurate out how, show of your skills making a composition of rectangles and colors that resemble a [Mark Rothko](http://en.wikipedia.org/wiki/Mark_Rothko) painting.
In the same way is easy to draw squares on grid paper, is relatively easy to draw rectangles with cartesians coordinates. But circles requires another approach. Some how we need to *treat* the spacial coordinates in a way that at the end we can draw circles with just a ```step()``` functions.
Going back to the grid paper and the math class, we were hable to draw perfect circles by opening a compass by the desired radius, pressing one of the endings on the desired center of the circles and spinning the other end around.
If we do this over a grid paper, thinking that each square on the grid is a pixel, we can draw a circle by *asking* each pixel (or thread) if they are inside the area of the circle. Right? We can know that area by computing the distance to the center of the center of the circle.
There are several ways to calculate that. The easiest one is just using the ```distance()``` functions, which internally computes the ```length()``` of the difference between two points (in our case the fragment coordinate and the center of the canvas). The ```length()``` function is nothing but a shortcut of the [hypotenuse equation](http://en.wikipedia.org/wiki/Hypotenuse) that use square root (```sqrt()```) internally.
So far I just describe three functions (```distance()```, ```length()``` and ```sqrt()```) you can use. The following code contain this three functions and how to get the exactly same result with each one. Note that on it we are mapping the distance to the center of the billboard to the color brightness of the pixel.
The resultan *mapping* values between distance and brightness can be a really helpful technique. Note that, the closer the pixel is to the center the lower (darker) values it have. Values don't get to high because from the center ( ```vec2(0.5, 0.5)``` ) the maximum distance barely goes over 0.5. Contemplate this map and think:
Imagine the above example as an inverse altitude map. The darker the taller. The gradient show us the pattern of something shape similar to a cone view from above. Imagine your self on the top of that cone, under your foot you hold the tip of a ruled tape while the rest of it goes than the hill. Because you are in the center of the canvas, the ruler will mark "0.5" in the extreme. This will be constant in all your directions. Buy choosing where to cut horizontally the top of cone you will get a bigger or smaller circular surface.
Interesting right? We can combine this re-interpretation of space to make shapes based on the distance to 0. This technique is known as “distant field” and is use in different ways from font outlines to 3D graphics.
In terms of computational power ```sqrt()``` function (and all the once that depend on it) can be expensive. Here is another way to create a circular distance field by using ```dot()``` product.
Distance fields can be use to draw almost everything. Obviously the complex the shape is, the more complicated the equation will be, but it pays off; a convenient feature of this technique is the ability to smooth edges. Because the “topological” nature of them, sharp edges get blended together producing softer edges the more away you are from the center you sample. This is particularly useful on fonts rendering.
Take a look to the following code and note how the space is mapped. Like concentric rings on a Zen garde the distance field values on edges get smooth and rounder the further away they get from the center.
If you play with the code you will discover that inside the triangle there is a negative area. Which in position makes shapes extremely sharp to the extreme. Because the values are under zero we can not see the difference but by changing ```fract()``` by ```sin()``` in line 43 you can see the triangle go shrink until disappear. This signed properties particular of **Signed Distance Fields**.
In the chapter about color we map the cartesian coordinates to polar coordinates by calculating the *radius* and *angles* of each pixel with the following formula:
In the previous examples we have use the radius (from the center) to draw a circles. Now, if we compute the angle from the pixel (threat) to the center, we can modulate the radius to achieve different shapes. How? Yes! Shaping functions!
Below you will find the same functions in the cartesian graph and in a polar coordinates shader example (between lines 21 and 26). Uncomment one by one the functions paying attention the relationship between one coordinate system and the other
Congratulations! You have made it through the rough part! Take a break and let this concepts sediment, drawing simple shapes on Processing is really easy but not here. In shader-land everything the way to thing on shapes is twisted and can be exhausting to adapt to this new paradigm of coding.
Now that you know how to draw shapes I'm sure new ideas will pop to your mind. In the following chapter we will learn more about how to move, rotate and scale them moving. This will allow you to compose them!
