Editing Curves

When an object is moving through the scene, estimating the exact point where its position changes direction can sometimes be difficult. Function curves provide this information by presenting a controller's value as a function of time. Each key is a vertex in the curve. Function curves are visible only in the Curve Editor and the Track Bar layout.

Function curves mode lets you edit and work with these curves for complete control over the animation parameters. Figure 33.9 shows the Position curves for a sphere that moves about the scene.

Figure 33.9: Function curves display keys as square markers along the curve.

Inserting new keys and moving keys

Function curves with only two keys have slow in and out tangents, making the animation start slow, speed up, and then slow down. You can add more curvature to the line with the addition of another key. To add another key, click the Add Keys button, and then click the curve where you want to place the key.

If the curve contains multiple curves, such as a curve for the Position or RGB color values, then a point is added to each curve. The Move Keys button enables you to move individual keys by dragging them. It also includes flyouts for constraining the key movement to a horizontal or vertical direction.

Click the Scale Keys button to move the selected keys toward or away from the current time. The keys move only horizontally. Click the Scale Values button to move the selected keys toward or away from the zero value. The keys move only vertically.

Tutorial: Animating a monorail

As an example of working with function curves, you animate a monorail that moves around its track, changing speeds, and stopping for passengers.

To animate the monorail using function curves, follow these steps:

1. Open the  Monorail.max file from the Chap 33 directory on the DVD. This file contains a simple monorail setup made from primitives.

2. Click the Play button, and watch the train move around the track.

   As a default, the Path Constraint's Percent track has a Linear controller that causes the train to move at a constant speed. To refine the animation, you need to change it.

3. Open the Track View-Curve Editor, and locate the train group's Percent track. (You can find this track under the Objects Train Transform Path Constraint Percent menu command.) Click the Assign Controller button to open the Assign Float Controller dialog box. Select the Bézier Float controller, and click OK.

   Note 

   If the Objects track isn't visible, open the Filter Tracks dialog box and make sure the Objects option is enabled.

4. Click the Play button. The train starts slowly (represented by the flattish part of the curve), accelerates (the steeper part of the curve), and slows down again (another flattish part).

   Tip 

   When "reading" function curves, remember that a steep curve produces fast animation, shallow curves produce slow animation, horizontal produces no movement or value change, and a straight curve produces a constant animation.

5. We need the train to stop for passengers at the station, so click the Add Keys button (or right-click and choose Add Keys) and add a key somewhere around frame 115 when the train is near the dock.

6. Select the newly created key, and choose the Move Keys Horizontal button from the Move Keys flyout. Hold down the Shift key, and drag right to copy the key to frame 135.

   The curve is flat, so the train stops at the station.

7. To adjust the actual position where the train stops, choose the Move Keys Vertical button from the Move Keys flyout, select both keys, and move them up or down until the train's position at the station is correct.

   Because the default in and out tangent types cause the curve to flatten out at the keys, the train slows as it reaches the station and then starts out slow and picks up speed as it leaves the station. Anyone who has ever ridden on a train knows that stopping and starting are not always smooth operations. Next, you add a few more keys to make the train shudder to a stop and lurch as it starts out again.

8. Click the Add Keys button (or right-click and choose Add Keys), and add keys somewhere around frames 105, 109, 113, 142, and 150. Use Zoom Region to zoom in on the keys where the train pulls into the station to stop.

9. Change the Move Keys Vertical button back to Move Keys by selecting it from the flyout, and move the keys slightly up or down to send the train backward and forward along the path.

10. As you can see, a little movement goes a long way, so the keys need only to be offset a very small amount. Use the Zoom Values button from the Zoom flyout and the Pan button to help in making the small changes to the animation. Figure 33.10 shows the zoomed in view of this section of the curve.

    
    Figure 33.10: Using Zoom Values to see the stopping position keys

11. Repeat for the keys where the train leaves the station.

    The train also needs to slow down to look at one of the famous buildings in "Primitive Town," the Tubular "building" on the far side of the track.

12. Add a couple more keys somewhere around frames 18 and 50. Lower the second of the new keys until the curve is shallower but not horizontal. Again, adjust the train's position on the track (Percent along the path) by raising or lowering the two new keys.

13. Adjust the Out tangent handle of the very first key and the In tangent handle of the very last key to produce a smooth looping animation.

Figure 33.11 shows the final curve after you've completed the editing, and Figure 33.12 shows the monorail along its path.

Figure 33.11: The finished Percent curve for the train's position along the path

Figure 33.12: The monorail and "Primitive Town"

Drawing curves

If you know what the curve you want is supposed to look like, you can actually draw the curve in the Key pane with the Draw Curves button enabled. This mode adds a key for every change in the curve. You may want to use the Reduce Keys optimization after drawing a curve.

Tip 

If you make a mistake, you can just draw over the top of the existing curve to make corrections.

Figure 33.13 shows a curve that was created with the Draw Curves feature.

Figure 33.13: Drawing curves results in numerous keys.

Reducing keys

The Reduce Keys button enables you to optimize the number of keys used in an animation. Certain IK methods and the Dynamics utility calculate keys for every frame in the scene, which can increase your file size greatly. By optimizing with the Reduce Keys button, you can reduce the file size and complexity of your animations.

Clicking the Reduce Keys button opens the Reduce Keys dialog box. The threshold value determines how close to the actual position the solution must be to eliminate the key. Figure 33.14 shows the same curve created with the Draw Curves feature after it has been optimized with a Threshold value of 0.5 using the Reduce Keys button.

Figure 33.14: The Reduce Keys button optimizes the curve by reducing keys.

Working with tangents

Function curves for the Bézier controller have tangents associated with every key. To view and edit these tangents, click the Show All Tangents button. These tangents are lines that extend from the key point with a handle on each end. By moving these handles, you can alter the curvature of the curve around the key.

You can select the type of tangent from the Key Tangents toolbar. These can be different for the In and Out portion of the curve. You can also select them using the Key dialog box. The default tangent type for all new keys is set using the button to the left of the Key Filters button at the bottom of the Max interface. Using this button, you can quickly select from any of the available tangent types.

You open the Key dialog box, shown in Figure 33.15, by selecting a key and clicking the Properties button or by right-clicking the key. It lets you specify two different types of tangent points: Continuous and Discontinuous. Continuous tangents are points with two handles that are on the same line. The curvature for continuous tangents is always smooth. Discontinuous tangents have any angle between the two handle lines. These tangents form a sharp point.

Figure 33.15: The Key dialog box lets you change the key's Time, Value, or In and Out tangent curves.

Tip 

Holding down the Shift key while dragging a handle lets you drag the handle independently of the other handle.

The Lock Tangents button lets you change the handles of several keys at the same time. If this button is disabled, adjusting a tangent handle affects only the key of that handle.

Tutorial: Animating a flowing river

The default auto-tangent types create a function curve that has ease-in and ease-out built into the curve. This causes the animation to start slowly, speed up, and then slow to a stop. While this may be a good starting point for many animations, it won't work for those that should have a constant speed. This example shows how to create a river with a material animated to a constant speed.

To create a flowing river, follow these steps:

1. Open the  River.max file from the Chap 33 directory on the DVD.

   This file contains a river surface made from a loft. The V Offset for the River Water material's diffuse channel has been animated to simulate flowing water (yes, this river has a checkered past…).

2. Click the Play button.

   The river flow starts out slow, speeds up, and then slows to a stop.

3. Open the Track View-Curve Editor, and locate and select the V Offset track for the river's material. (You can find this track under the Objects Checkered River River Water Maps Diffuse Color: Map #2 (Checker) Coordinates V Offset menu command.)

4. You have two easy options for creating an animation with a constant speed. The first changes the entire controller type; the second changes the individual key's tangent types.

   Option 1: Right-click over the V Offset track, and choose Assign Controller or choose Assign from Controller on the menu bar to open the Assign Float Controller dialog box. Select Linear Float, and click OK.

   or

   Option 2: Select both keys by clicking one key, holding down the Ctrl button, and clicking the other, or by dragging an outline around both keys. Click the Set Tangents to Linear button.

   Whichever method you use, the line between the two keys is now straight.

5. Click the Play button.

   The river now flows at a constant speed.

6. To increase the speed of the flow, select Move Keys Vertical from the Move Keys button flyout, and select and move the end key higher in the graph.

   The river flows faster.

Figure 33.16 shows the river as it flows along.

Figure 33.16: The Checkered River flows evenly.

Applying out-of-range, ease, and multiplier curves

Out-of-range curves define what the curve should do when it is beyond the range of specified keys. For example, you could tell the curve to loop or repeat its previous range of keys. To apply these curves, select a track and click the Parameter Curve Out-of-Range Types button on the Curves toolbar (or select the Out-of-Range menu command from the Controller menu). This opens a dialog box, shown in Figure 33.17, where you can select from the available curve types.

Figure 33.17: The Param Curve Out-of-Range Types dialog box lets you select the type of out-of-range curve to use.

Note 

You can also apply an out-of-range curve to a select range of frames using the Create Out-of-Range Keys utility. This utility is available via the Track View Utilities button.

By clicking the buttons below the types, you can specify a curve for the beginning and end. This Out-of-Range dialog box includes six options:

• Constant: Holds the value constant for all out-of-range frames

• Cycle: Repeats the track values as soon as the range ends

• Loop: Repeats the range values, like the Cycle option, except that the beginning and end points are interpolated to provide a smooth transition

• Ping Pong: Repeats the range values in reverse order after the range end is reached

• Linear: Projects the range values in a linear manner when out of range

• Relative Repeat: Repeats the range values offset by the distance between the start and end values

You can apply ease curves (choose Curves Apply Ease Curve, or press Ctrl+E) to smooth the timing of a function curve. You can apply multiplier curves (Curves Apply Multiplier Curve, Ctrl+M) to alter the scaling of a function curve. You can use ease and multiplier curves to automatically smooth or scale an animation's motion. Each of these buttons adds a new track and function curve to the selected controller track.

Note 

Not all controllers can have an ease or multiplier curve applied.

You can delete these tracks and curves using the Delete Ease/Multiplier Curve button. You can also enable or disable these curves with the Enable Ease/Multiplier Curve Toggle button.

After you apply an ease or multiplier curve, you can assign the type of curve to use with the Ease Curve Out-of-Range Types button. This button opens the Ease Curve Out-of-Range Types dialog box, which includes the same curve types as the Out-of-Range curves, except for the addition of an Identity curve type.

Note 

In the Ease Curve Out-of-Range Types dialog box is an Identity option that isn't present in the Parameter Curve Out-of-Range Types dialog box. The Identity option begins or ends the curve with a linear slope that produces a gradual, constant rate increase.

When editing ranges, you can make the range of a selected track smaller than the range of the whole animation. These tracks then go out of range at some point during the animation. The Ease/Multiplier Curve Out-of-Range Types buttons are used to tell the track how to handle its out-of-range time.

Tutorial: Animating a wind-up teapot

As an example of working with multiplier curves, we create a wind-up teapot that vibrates its way across a surface.

To animate the vibrations in the Track View, follow these steps:

1. Open the  Wind-up teapot.max file from the Chap 33 directory on the DVD. This file contains a teapot with legs.

2. Click the Play button.

   The teapot's key winds up to about frame 40 and then runs down again as the teapot moves around a bit. To add the random movement and rotation to make the vibrations, you use Noise controllers and Multiplier curves to limit the noise.

3. Open the Track View-Curve Editor, and navigate down to the Wind-up Key's X Rotation track. Take a moment to observe the shape of the curve, shown in Figure 33.18.

   
   Figure 33.18: The rotation of the Wind-up Key object

   The key is "wound up" in short spurts and then runs down, slowing until it stops. The vibration, then, should start midway and then taper off as the key runs down.

4. Click the teapot in the viewport to have the curves for its transforms selected and centered in the Track View.

   When adding the Noise controller, you should assign a List controller first to retain the ability to transform the object independently of the Noise.

   Note 

   Assigning controllers through the Animation menu automatically creates a List controller first.

5. Select the Position track, and click the C key to access the Assign Controller dialog box. Choose Position List. Under the Position track are now the X, Y, and Z Position tracks and an Available track. Select the Available track, access the Assign Controller dialog box again, and choose Noise Position. The default controller should remain the Position XYZ controller, so close the List Controller dialog box. Click Play.

   The teapot vibrates the entire animation. You add a multiplier curve to correct the situation.

6. Select the Noise Position track, and choose Curves Apply-Multiplier Curve. Select the Multiplier curve track. Assign the first key a value of 0. Change its Out tangent to Stepped so it holds its value until the next key. Click the Add Keys button, and add a key at frame 50 with a value of 1. Move the last key to frame 120, and set a value of 0. The Multiplier curve should now look like the curve in Figure 33.19. Select the Noise Position track.

   
   Figure 33.19: The Multiplier curve keeps the Noise track in check.

   The noise curve now conforms to the multiplier track.

7. With the Noise Position track still selected, right-click and choose Properties. In the Noise Position dialog box, set the X and Y Strength to 30, set the Z strength to 20, and check the >0 check box to keep the teapot from going through the floor. Close the dialog box, and click Play.

   The animation is much better. Next, you add some noise to the Rotation track.

8. Select the Rotation track, right-click, and choose Assign controller or click the C key to bring up the Assign Controller dialog box. Select Rotation List, and click OK. Select the Available track, access the Assign Controller dialog box again, and choose Noise Rotation.

   Click Play. Again, the noise is out of control.

9. This time, select the Noise Strength track and add a multiplier curve.

   You already have a perfectly good multiplier curve, so you can instance it into the new track.

10. Select the position multiplier track, right-click, and choose Copy. Now select the rotation Noise Strength multiplier track, right-click, and choose Paste. Choose Instance, and close the dialog box.

11. Click the Play button, and watch the Teapot wind up and then vibrate itself along until it winds down.

Figure 33.20 shows the teapot as it dances about, compliments of a controlled noise controller.

Figure 33.20: The wind-up teapot moves about the scene.