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Music 9. News Round Table of Knowledge "metaphor" Music Horse race The entire process of calculating the appearanceof the 3D model—converting it to an entity that can be drawn on a two-dimensional 2D screen and then actually displaying the resulting image—is called rendering. Coordinate SystemsWhen we refer to the dimensional measurement of an object, we use number groupscalled coordinates to mark each vertex corner of the object.
We commonly use the vari-able names X, Y, and Z to represent each of the three dimensions in each coordinategroup, or triplet. There are different ways to organize the meaning of the coordinates,known as coordinate systems.
We have to decide which of our variables will represent which dimension—height, width,or depth—and in what order we intend to reference them. Then we need to decide wherethe zero point is for these dimensions and what it means in relation to our object. Oncewe have done all that, we will have defined our coordinate system. When we think about 3D objects, each of the directions is represented by an axis, the infi-nitely long line of a dimension that passes through the zero point.
Width or left-right isusually the X-axis, height or up-down is usually the Y-axis, and depth or near-far is usu-ally the Z-axis. Using these constructs, we have ourselves a nice tidy little XYZ-axis system,as shown in Figure 3. Now, when we consider a singleobject in isolation, the 3D spaceit occupies is called object space. The point in object space whereX, Y, and Z are all 0 is normallythe geometric center of anobject.
The geometric center ofan object is usually inside theobject. If positive X values areto the right, positive Y valuesare up, and positive Z values areaway from you, then as you cansee in Figure 3. The Torque Game Engine uses a slightly different coordinate system, a right-handed one. In this system, with Y and Z oriented the same as we saw in the left-handed system, X ispositive in the opposite direction.
In what some people call Computer Graphics Aerobics,we can use the thumb, index finger, and middle finger of our hands to easily figure out thehandedness of the system we are using see Figure 3. With Torque, we also orient the system in aslightly different way: The Z-axis is up-down, the X-axis is somewhat left-right,and the Y-axis is somewhat near-far seeFigure 3. Actually, somewhat means thatwe specify left and right in terms of lookingdown on a map from above, with north atthe top of the map.
Right and left positiveand negative X are east and west, respec-tively, and it follows that positive Y refers tonorth and negative Y to south. Don't forgetthat positive Z would be up, and negative Zwould be down. This is a right-handed sys-tem that orients the axes to align with theway we would look at the world using amap from above. By specifying that the zeropoint for all three axes is a specific locationon the map, and by using the coordinatesystem with the orientation just described,we have defined our world space.
A 3D triplet is always specified inXYZ format. Take another peek at Figure 3. Notice anything? That's right—the Y-axis is verticalwith the positive values above the 0, and the Z-axis positive side is toward us. It is stilla right-handed coordinate system. The right-handed system with Y-up orientation isoften used for modeling objects in isolation, and of course we call it object space,asdescribed earlier.
We are going to be working with this orientation and coordinate sys-tem for the next little while. Figure 3. Let's take a closer look, by start-ing with a simple 3D shape,or primitive—the cube—asdepicted in Figure 3.
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