Coordinate Systems

Coordinate Systems


Ted Boardman tedb@tbmax.com         http://www.tbmax.com

Where in the world…

Have you ever wanted to place an object on top of an inclined surface of another object and ended up spending much too much time moving and rotating in all four viewports and still only getting the object approximately in place? Or have you tried the Align command only to abandon it in frustration?

One issue in 3D Studio Max and VIZ that I see as a fundamental hindrance to production for many users, both new and experienced, is a lack of understanding of the coordinate system. To use several important commands in both VIZ and Max users must understand the various coordinate systems in the software. The Align and transform type-in commands being the most notable. In both Align and transform type-in you are asked to enter numeric data to align or array objects along the X-, Y-, or Z-axis. However, the direction of X, Y, or Z depends on the active coordinate system and the active viewport.

All users are familiar with the Absolute World coordinate system in VIZ or Max because it is defined by the default Grid planes that show in the viewports when you start VIZ and Max. However, the World Coordinate System is just the starting point for the possibilities for maneuvering and manipulating objects in space.

Reference Coordinate System In the Toolbar menu, you will see a field with View in it by default. This is the Reference Coordinate System that is currently active. Click on the View field and you will see a pop-up menu of the different Reference Coordinate Systems available. See Figure 1.

Fig 1. Menu showing available Reference Coordinate Systems for VIZ 3 and 4 and max 4.

Note: max 5 has an additional Reference Coordinate System called Gimbal

I will talk you through a simple exercise that will illustrate some of the differences between the various Reference Coordinate Systems. You can either try the exercise on your computer or, better yet, just read along to get the idea, then go to the computer and do the exercise. In any case, at some point you should sit down and just play with very simple objects to get a feel for how the system works. As with many VIZ and Max tools, don’t try to learn this during the deadline crunch on a large project. With a little practice the Reference Coordinate Systems will become second nature and your productivity will increase accordingly. At the end of the article I will summarize the attributes of each system.

Getting the Lay of the Land

Start with a new session of either VIZ or Max. The display should be set to four viewports -Top, Front, Left, and Perspective. In the Top viewport, create a Cylinder in the middle of the display and click the Zoom Extents All button. See Figure 2.

Fig. 2 Cylinder zoomed to the extents in four viewports

I’ll talk you through a description and some exercises that will highlight the individual Reference Coordinate Systems that appear in Figure 1.

View Reference Coordinate System

Notice that the Axis Tripod shows positive X to the right, positive Y up, and positive Z out toward the viewer and that the current active Reference Coordinate System is set to View. Right-click in the Front viewport to activate that viewport without deselecting the cylinder and notice that the Axis Tripod adjusts to make the positive axis’s point in the same relative directions as in the Top viewport. Right-click in the Left viewport to see a similar change. The Axis Tripod adapts itself to the orthographic viewports while in View Reference Coordinate System so that positive X is always to the right, positive Y is always up, and positive Z is always out toward the viewer.

Now, right-click in the Perspective viewport and notice that the Axis Tripod corresponds to the World coordinate system by aligning with the Home grid. You can check it against the small tri-color tripod in the lower left corner of each viewport that always indicates the World Coordinate System. This is true for all non-orthographic viewports while in View Reference Coordinate System - Perspective, User, Camera, and Light viewports.

Tip: You can activate a Light viewport by selecting a light and pressing Shift + $. This allows you to look down a light from the light source to see exactly what the beam covers. The navigation buttons at the bottom right of max or VIZ will switch to light controls, also. Omni and Point lights cannot use this feature, of course.

Screen Reference Coordinate System

Right-click in the Top viewport, then click View in the Toolbar and choose Screen Reference Coordinate System in the list. Right-click in the other viewports and notice that the Axis Tripod. Screen Reference Coordinate System is exactly the same as View for orthographic viewports – X to the right, Y up, and Z out. However, for non-orthographic viewports the positive Z-axis points out of the screen toward the viewer. Arc-Rotate in the Perspective viewport and watch the Axis Tripod move in the other viewports. Screen Reference Coordinate System allows you to move objects in space based on your line of site in non-orthographic viewports and is useful for moving logos across the scene, for example.

World Reference Coordinate System

Right-click in the Top viewport and switch to World Reference Coordinate System. Right-click in the other viewports and you will see that World coordinate system is always active for all viewport types.

Parent Reference Coordinate System

The next Reference Coordinate System in the list is Parent, which requires an object to be hierarchically linked to another object in the parent/child relationship. In Parent Reference Coordinate System, the child always uses the parents’ Local coordinate system, which will be explained next.

Local Reference Coordinate System

Right-click in the Top viewport and choose Local in the Reference Coordinate System list. Right-click in the other viewports and the Axis Tripod is the same as it was for World Reference Coordinate System. This is a coincidence because you created the cylinder in the Top viewport. Right-click in the Perspective viewport and rotate the cylinder roughly 45 degrees in both the X and Y View Reference Coordinate System. See Figure 3.

Fig. 3 Rotate a cylinder at some random angles in at least two axis.

At this point you will notice that even though you had the Reference Coordinate System set to Local, it switched automatically to View when you picked the Rotate button. The current Reference Coordinate System is sticky for each Transform; Move, Rotate, and Scale. Once you set the Reference Coordinate System it will be retained for that Transform until you change it again. The Axis Tripod also changes to the Transform Gizmo when the Transform buttons are picked.

Right-click in the Top viewport, click the Move Transform button, and set the Reference Coordinate System to Local. Right-click in the other viewports and you will see that the Axis Tripod stays oriented to object as it was created. This is an especially powerful tool for production that you will want to familiarize yourself with.

Grid Reference Coordinate System

The Grid Reference Coordinate System requires that you create a new Grid Helper object as the active work plane. Right-click in the Top viewport to activate it. In the Status bar of VIZ, toggle the Autogrid feature on. In max you will find the Autogrid checkbox at the top of the objects in the Create panel, Object Type rollout, that you can check after you select the one of the buttons.

Click the Box button, check Autogrid if you are using max, and as you move your cursor over the cylinder you will notice a tri-color cursor track the Face Normal of the face under the cursor. Hold the Alt key, and pick and drag a Box primitive on the end cap of the cylinder. See Figure 4.

Fig. 4 You can create objects directly on any surface with the Autogrid feature. Holding Alt while you do this creates a permanent grid object in that plane.

Holding the Alt key while creating an object in Autogrid mode concurrently makes the new grid in the scene and makes it the active grid. Switch to Grid Reference Coordinate System and the X, Y, Z axis of the Grid are used for the current Transform.

Click the Select button, pick the new Grid object in the active viewport, right-click on the Grid and, in the pop-up menu, choose Activate Grid, then Home Grid to return to the default grid system. You can have as many Grid helpers as you want, but only one can be active at any time. You can reactivate the new Grid at any time. Grid Helpers are similar to UCS grids in AutoCAD.

Pick Reference Coordinate System

In the Pick Reference Coordinate System you can use the coordinate system of another object in the scene as the current system. Right-click in the Top viewport to activate it and create a small Sphere to one side of the cylinder. Change the Reference Coordinate System to Pick and pick on the cylinder in the Top viewport. The sphere is now using the cylinders’ Local Reference Coordinate System as its own. Also, Cylinder01 is added to the list of available Reference Coordinate Systems.

Pivot Point Options Another aid to production that goes hand in hand with the Reference Coordinate Systems is the active Pivot point type Just to the right of the Reference Coordinate System window is a flyout menu with three choices of Pivot Point types. Understanding the different options makes Transforming objects with Reference Coordinate Systems a more flexible and powerful tool. See Figure 5.

Fig 5. Flyout menu of Pivot Point options

Pivot Point Center

In the Top viewport, select all the objects in the scene. With the Pivot Point Center option set you will notice that each selected object will be Transformed based on its current active Reference Coordinate System around its own individual pivot point. This is especially interesting when you are in Rotate or Scale Transform. (Caution: never Scale objects in either VIZ or Max. Always apply an Xform modifier and scale the Xform Gizmo.)

Selection Center

Choose Use Selection Center in the flyouts and you will see that the entire selection set of objects uses a single Pivot Point in the geometric center of the bounding box of the selected objects. This is most appropriate for rotations.

Transform Coordinate Center

The Transform Coordinate Center uses the 0,0,0 Absolute World Coordinate point except when Pick Reference Coordinate System is active. The selected object then uses the Pick objects Pivot Point as its own.

Summary

The attributes of the various Reference Coordinate Systems is:

• View – the Axis Tripod adapts itself to each orthographic viewport so that positive X-axis is to the right, positive Y-axis is up, and positive Z-axis is perpendicular out of the display. Non-orthographic viewports resort to using World Reference Coordinate System.
• Screen – same as View in orthographic viewports. In non-orthographic viewports the positive Z-axis always points at the viewer.
• World – coordinate system always corresponds to the Absolute World Coordinates.
• Parent – the child object uses the parent’s Local coordinate system in a hierarchically linked parent/child relationship.
• Local – the coordinates always remains with the object as it was created, regardless of rotation angle of the object.
• Grid – uses the active Grid systems coordinate system.
• Pick – uses the Local coordinate system of another object that is picked in the scene.

For the Align, Array and Mirror commands in VIZ and Max, always check the current active Reference Coordinate System to see which X, Y, and Z-axis is being used by the command. The mode is noted in the Align or Array dialog. See Figure 6.

Fig. 6Active Reference Coordinate System shown in parentheses in the Align dialog

(Hint: View Reference Coordinate System is never listed in Array, Align, or Mirror commands. You will always see Screen, which is the same)

As I mentioned at the outset of this column, these are incredibly powerful tools and options that are simple to learn. You are doing yourself a great disservice if you aren’t using these effectively in production every day. Start with simple examples to get the feel of the options and it will come naturally as you work.

Good luck and have fun.