Local Coordinates
(Tea Party)
by Aaron F. Ross
In this tutorial, you'll learn the basics of working with Local coordinates. World coordinates are the XYZ axes of the world, also known as the Home Grid or the Construction Grid. Local coordinates are the XYZ axes of each object.
The local coordinate system is necessary for convincing animation. This is especially true for rotating objects such as character joints. Without it, the character's arms and legs would twist and break in impossible ways.
Local coordinates are directly related to the object's Pivot Point. An object turns around its Pivot Point. The Pivot Point is the center of object transforms, and the origin of the object's local coordinates. In this tutorial, you'll learn how to move the Pivot Point, so that an object can turn more realistically.
1. Open 3ds Max, or if it is already open, select File > Reset.
2. In the Top viewport, create a Tube primitive. Make the Tube approximately 10 units in radius and 40 units in height. These dimensions can be altered in the Parameters rollout of the Modify panel.
3. On the Main Toolbar, click the Select and Move tool, or press the W hotkey. Move the selected Tube object to the coordinate values (60, -60, 0) by entering values in the Transform Type-In area at the bottom of the 3ds Max window.
Create a Tube and move it to (60, -60, 0)
4. In the Top viewport, create a Teapot primitive near the center (origin) of the world. Make the teapot about 45 units in radius.
5. On the Main Toolbar, click Select and Rotate, or press the E key on the keyboard. The Select and Rotate icon lights up to show that the transform is active. Use the Rotate Gizmo to turn the teapot around its Z axis, until its spout is pointing at the Cylinder object. If the teapot rotates in an unexpected direction, Undo the rotation and make sure the current Reference Coordinate System is View.
6. Click Select and Move in the Main Toolbar, or press W. Select the Y axis of the teapot's Transform Gizmo. Use the Move Gizmo to move the teapot about 50 units up, so the teapot is hovering in the air near the cylinder.
7. Click an empty area in a viewport, or press CTRL + D, to deselect all objects. Press the Z key on the keyboard. This is the Hotkey for Zoom Extents All Selected.
Move the teapot up and press the Z key
8. Click Select and Rotate on the Main Toolbar, or press E. Select the Rotate Gizmo of the teapot in the Perspective viewport. Attempt to rotate the teapot to pour tea into the Tube. It's impossible to rotate the teapot to get the desired effect using the default View coordinate system. This is because the View coordinate system uses World coordinates in the Perspective view.
You're only able to rotate the teapot around the X, Y, and Z axes of the World coordinate system, or Home Grid. The teapot's spout always misses the target. You might be able to get it into a static position by making several rotations in various axes, but you can't simulate a pouring motion. This means that you will have problems trying to animate a pouring movement by rotating the teapot in the world axes.
Undo the rotations to restore the teapot to the upright position seen in step 7. To undo, you can use CTRL + Z, or you can right-click the Undo button on the Main Toolbar, which gives you a pop-up window showing the history of commands.
9. With the teapot still selected, choose Local from the Reference Coordinate System drop-down list in the Main Toolbar. Observe how the Rotate Gizmo changes. It is now oriented with the teapot's Local axes. Rotate the teapot around its Local Y axis. Pouring into the cylinder is easily accomplished.
Rotate the teapot in its Local Y axis
10. As you interactively rotate the teapot, notice how unnatural the movement seems. This is because the Pivot Point is at the bottom of the teapot. In the real world, the point of rotation might be near the object's center of gravity, or at a joint or connection. For the teapot, the handle is an appropriate point of rotation.
11. With the teapot still selected, and hovering in the pouring position, click Select and Move, or press the W key. Go to the Hierarchy panel. Select Affect Pivot Only. It lights up to indicate that it is active. The Pivot Point tripod appears at the same location as the Move Gizmo.
Note: The Pivot Point and the Gizmo are not the same. The Gizmo is a manipulator that allows you to move things in the views. The Pivot Point is one of the things that you can move. Right now, the Move Gizmo is oriented with the world coordinates. The Pivot Point is always oriented with the selected object.
In the View coordinate system, the Pivot Point is in the same location as the Transform Gizmo, but they are oriented differently
12. With the Move tool active, choose the Local coordinate system from the drop-down list in the Main Toolbar. The Move Gizmo is now oriented with the Local axes of the teapot, making it easy to move the Pivot Point relative to the object rather than the world.
In the Perspective viewport, select the ZX plane of the Move Gizmo by hovering your cursor over the blue and red corner icon. The Z and X axes of the Gizmo turn yellow. Click on the corner icon and drag the Move Gizmo until it is positioned in the loop of the teapot's handle. Observe the movement of the Gizmo and Pivot Point in the other viewports. Double-check all viewports to make sure the Pivot Point is where you want it.
Move the Pivot Point in the Local coordinate system
13. In the Hierarchy panel, click Affect Pivot Only again to turn it off. The Pivot Point icon disappears, leaving only the Move Gizmo. Click Select and Rotate, select the local Y axis of the teapot once more, and rotate. With the Pivot Point in its new position, the teapot now spins around its handle for a more convincing tea party.
14. Experiment with coordinate systems and Pivot Points. Try moving the Pivot Point of the teapot outside the object. Find out what happens when you rotate an object's Pivot Point, then move and rotate the object in its local axes.
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