Graffiti: Graffiti Tutorial
Even though you might not think of Graffiti art as "math," many Graffiti artists do make use of it. For example, when you see a shadow effect used, the artist is dealing with different angles to give it that look. Also, keeping objects (such as a building) in correct proportion ensures that when you look at the art, you will be able to indentify what exactly you are looking at. Perspective can also be used as in the image below.Cartesian Coordinates
Graffiti artists often work on a piece in sketchbooks before they actually begin painting it. The sketchbooks sometimes use a grid to help plan out the design. Sometimes they go beyond planning, and create visual effects that look as if they were stretching or folding the grid. In the picture on the right, you can see someone who actually shows the folded grid, although this is rare. More commonly, you might see graffiti writers use the actual brickwork as a grid itself, as we can see in this picture below.
Whether it's a grid in a sketchbook, or a grid of bricks on a wall, these grids are much like the Cartesian coordinate system in mathematics. Let's see how we can map the Graffiti artist's grid onto the Cartesian coordinate system.
Cartesian Coordinates and Lines
In the Graffiti Grapher software we will use Cartesian coordinates to locate the start and finish of each line. Each coordinate is a pair of numbers. The X coordinate tells you how far left or right. The Y coordinate tells you how far up or down. Cartesian coordinates use both negative and positive numbers, so don't forget to use the "-" sign.
The most important lines in graffiti are the boarders of letters. Lets look at the boarder line that starts and ends in the red circles below.
Practicing Shapes with Lines
You can create a shape like the one you just saw with two connected lines as we show below.
When you click on the shape below you will be able to edit the parameters for one of the lines on the right.
Notice that one of the endpoints is colored blue and the other is collored yellow. This is to help you tell which parameters describe which point. The x1, y1 parameters describe the blue point; the x2, y2 parameters describe the yellow point. Together they describe one line. There are two lines that create the shape.
Now that you've seen how to indicate location based on a pair of values (Cartesian Coordinates), it's time to look at a different way to express location on a grid - Polar Coordinates. Polar Coordinates use an angle and a distance from a center point (known as the origin) to determine location. With an origin consisting of x and y coordinates, a distance r, and an angle a, you describe a polar coordinate.
Practicing Polar Coordinates
Like the square cartesian coordinate grid that you are probably used to seeing there is also another general kind of grid called the polar coordinate grid, which is a circular grid. It is shown on top of the square grid below. Like the square grid, it gives you an idea where points would go when you plot them with different parameters.
Change the parameters below and see if you can predict where the point will go. See if you can get the blue point inside the 4 red targets.Arcs and Polar Coordinates
Using polar coordinates, we can draw the curved shape of an arc. The arc below, which is drawn in blue, is described by two polar coordinate points. For the first point, the origin is at x=0, y=0, the distance from the origin is 70 and the angle is 15. For the second point, the origin is at x=0, y=0, the distance from the origin is 70 and the angle is 45.
Arcs and Spirals
Most of the graffiti that you see uses pretty complex arcs, where the radius of the arc changes as the arc moves from one endpoint to another. Mathmaticians call this a "delta" or a "unit of change". By comparing the blue arcs below you can see how changing the delta from 0, where it has no effect on the arc, to .5 changes the way the arc looks.
With an origin, a starting distance r, a starting angle SA, an ending angle EA and adding some ammount d to the radius after each degree that the arc travels from its starting angle to it's ending angle, you can get spiral arcs like the one below.
With a value of d=0, you get what amounts to a circular arc, with a d that is greater than zero you get an arc that rapidly spirals out. As graffiti artists draw arcs the distance between their shoulder and the surface changes similarly, frequently creating these kinds of complex arcs.
Practicing Shapes with Spirals
You can also create shapes with complex arcs and spirals. There are two complex arcs that create the shape.
Author: Saber Photo: Birch