All images from The Magic of Houdini by Will Cunningham. Reprinted with permission.

This is the next in a series of excerpts from the Thomson Course Technology book The Magic of Houdini by Will Cunningham. In the next few months, VFXWorld readers will learn the basics of the dominant tool that has been used in the creation of some of the most awe-inspiring animation and cinematic effects ever made.

Where is 3D?
So you are determined and excited now, right? That is good, because before you can jump into the glory of creating an alien world or a terrestrial apocalypse, you must first ensure that you have a solid understanding of the 3D concepts that comprise your new environment. Most of you have, at one time or another, had the experience of measuring a mattress. After all, how else can you ensure that every square foot of your room is covered in springy good times? After taking these measurements, you usually describe them in terms of a width, height and depth. Now imagine you are floating above and looking down on one mattress. From this perspective, the left to right measurement indicates width, the top to bottom measurement indicates height, and the measurement from the top side to the back side of the mattress indicates depth.

This sort of visualization is easily understood in terms of 3D coordinate systems as well. Houdini uses a rectangular coordinate system that is basically the same as the one René Descartes created way back in the 1600s. In fact, the story goes that René was lying in bed while watching a fly. At some pivotal moment, he realized that he could exactly describe the fly’s position by using just three numbers. He devised a system wherein each of the axes described above was designated with a letter: x for width, y for height and z for depth. The point at which each of these axes intersects is called the world origin. This point divides each axis into a positive and a negative side. Houdini uses a right-hand coordinate system, which means that x values become larger to the right of the origin and smaller to the left, y values become larger above the origin and smaller below it and z values become larger the nearer the viewer and smaller as they are farther away from the viewer. Figure 1 shows this type of system.

[Figure 1] Slightly above and to the right of the default view in a right-hand coordinate system.

Using this system, you can give any point (or fly) a position in 3D space using the world coordinates x, y and z (x,y,z). For example, (0,1,0) indicates a point one unit above the origin. (-4, 3, -2) indicates a point that is four units to the left of the origin, three above it and two units forward, or “into” the monitor.

When using the terms left, above and into, it is important to remember that these are somewhat loose terms. They describe the default state of the coordinate system in relation to the viewer. However, if the view is changed in some way, those terms might no longer be accurate. The new view might be showing positive Y going down, to the left or some other direction. So, it is important to remember that the generic terms only apply when the axes are being viewed in the default, home position.

Another important point to consider is that the units in Houdini are arbitrary real-world distances. One unit to the right doesn’t necessarily mean 1 meter, 12 inches or 1 mile to the right. The units are adjusted to whatever seems most useful for the particular project at hand.

The Building Blocks of 3D Space
Now that you have an expansive playground before you, how do you begin to create sandboxes and swings to populate it? Every complex 3D model is comprised of smaller and smaller building blocks, just as we humans have bodies comprised of organs, which are comprised of cells, which are in turn comprised of atoms, which are then comprised of quarks, which are likely comprised of ever smaller phenomenon we have yet to discover. Fortunately, the aspiring 3D artist can treat the point as the smallest measurable unit.

So, place a single point out there in the void and suddenly your universe is populated! Place another point out there in a different location and you begin to play. Connect these two points and you have now created what Houdini calls an edge, which is a polygon face or curve. Experience the grandeur of evolution! Place yet another point off to the side somewhere and connect it to one of the points. Check out Figure 2 to see where this is going. Houdini calls this an open polygon.