We all know that it's no fun to be caught in an actual tornado, but scientists need to study them to learn how to keep people safer. But how can scientists study tornadoes without putting themselves in danger? The trick is that scientists use computers to build virtual tornadoes based on what they know about real tornadoes. This visualization shows off some of the key features of a digitized tornado. But how do you take all the complexity of something in the physical world like a tornado or even just a human hand with all of its curves and corners and make a virtual replica of it that you can explore for science or make computer graphics images from. On a geographical map, a 2D grid is laid over the region to help you find points of interest. If you're looking for the Grand Canyon, this map tells you to look at cell 9I. Let's see if we can use the same concept to digitize a hand, I need to find a way to turn the position and shape of the hand into numbers that the computer can interpret. So to digitize the hand, I'm going to slap it on a 2D grid, and then we can then consider every curve and corner of the hands to be like a point of interest on the map. In order to put some real numbers to this hand that I can use in the computer, I need to have a starting point. I'm going to choose this point right here. In computer graphics, that's what we refer to as the origin. The map use letters and numbers to identify the horizontal and vertical components of the cell location. In computer graphics, generally we refer to the horizontal and vertical as the x-axis and the y-axis respectively. We also need to know the scale of the grid. If we measure a hand in miles or angstroms we're going to get really big or really small numbers, and those don't really makes sense. We're going to use centimeters on this grid. This combination of an origin, axis and spacing, is what we refer to as a coordinate system. So now I'm going to place the hand onto the 2D grid and mark out a bunch of points of interest and then I'm going to give them numerical values. Each one of these dots is a vertex, which is a special point that belongs to a geometric shape. The only thing left to do is connect the dots. A line connecting two vertices is called an edge. Edges show the connectivity of points for geometric shapes. Now let's draw the rest of the edges. Oops. It looks like we forgot what order the points need to be connected in. When digitizing data, it's important to know what order the points are meant to be connected in. For this hand data, we'll use a numerical order. So now we should be able to connect the dots in the correct order. As a proof of concept, I will now load these numbers into the actual computer graphics software, I use called Houdini. First, I enter each of these values. The point number, the x-axis coordinate, and the y-axis coordinate, and I put them into a basic text file with a program like Notepad or TextEdit. Then I will load my TextFile as data, into my computer graphics software. I create a small network and now you can see a digitized version of our hand. It's worth mentioning that a square x-y coordinate system, called the Cartesian coordinate system, is not always the best choice of a coordinate system. Another common coordinate system is measured by angle and radius, it's called the Polar coordinate system. Now the vertices of the hand are measured in a different way. Instead of measuring the horizontal and vertical components of the position, we measure the angle from the vertical and how far away it is from the origin. So these angles are measured at 0 degrees, 30 degrees, 60 degrees and 90 degrees, and the radii are 5, 10, 15, 20, 25, 30. So now if I want to give a point a position in this polar coordinate system, I'll see that it's at an angle of about 50 degrees and at a radius of about 29. Full disclosure, polar coordinates aren't really ideal for hand data, they are not very intuitive and they don't describe the shape all that well. The polar coordinates are pretty intuitive for something round like this plate. You can see that round objects are easy to describe in polar coordinates, because all of the radii have the same value. Coordinate systems can get pretty weird for some types of data. For instance, let's say we want to efficiently capture the shape of a hand and a forearm. So the forearm is a pretty basic shape, but the hand is really complex with corners and edges. In this situation, scientists might use something called a stretched grid. A stretched grid is a nonuniform coordinate system that puts more detail where the more interesting features are. Scientists usually try to use the most efficient coordinate system to capture the details of the data they're creating. Sometimes scientists will even invent new coordinate systems to get as much detail as they can out of their data. For instance, the data that created this video of a coronal mass ejection, was recorded in a stretched polar coordinate system. It was stretched so the data could be more complex near the surface of the sun and it was polar so the curvature of the sun would be maintained. Any physical objects can be captured into a coordinate system. The positions of it's important features just need to be described by numbers to a computer. While there's a big jump between digitizing the outline of a hand and a tornado or a coronal mass ejection, the way the computer understands objects and their positions is the same basic concept. Fun fact, 3D computer graphics imagery was first used in a feature film for the 1976 movie called Futureworld. The computer graphics featured a rotating 3D model of a hand created by the eventual founder of Pixar Animation Studios, named Ed Catmull. To create the hand, he made a plaster mold of his own hand, then drew more than 100 vertices on that mold.
