Working with Curves

This chapter describes how to work with data in curve channels. Curve channels contain dynamic data that is used to execute operations with which the curve channel is associated.

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Curves

There are any number of ways for you to modify the data in a curve channel: by specifying a value explicitly, defining the curve type used for the action, or even what kind of "treatment" is used on the curve.

A curve generally exists inside an action; that is, it's a subchannel to the action:

Figure 4.1 A sample action, showing associated curve data

The type of curve assigned to the action appears in parentheses after the name of the curve if the curve channel is closed:

Figure 4.2 A closed curve has its name and type in the channel's label

Curves may also contain cues. A cue is a marker that contains a value (either a simple value like a number, or a complex value like a pose or camera view). Values between cues are interpreted differently depending on the curve type specified for the curve. Cues appear as vertical bars across the curve channel:

Figure 4.3 Cues represent a value and time

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Working with Curves

There are a number of ways to work with curves:

• (CLICK-L) on the curve channel opens the channel (if it's closed)
• (CLICK-M) on the curve channel to open the Edit Curve Properties dialog box
• (CLICK-R) anywhere in the channel to bring up the Curve Operations menu

Editing Curve Properties

Figure 4.4 Edit Curve Properties dialog box

Note that the Edit Curve Properties dialog box is actually divided into two sections:

• the properties of the curve channel
• the properties of the curve itself

The parameters you specify for the curve channel are the same for any type of curve; the actual curve properties vary slightly depending on the type of curve you are editing.

Curve Channel Properties

• Name lets you specify the label name for the channel-this is the name that appears on the channel in the script editor. You may want to give a curve channel a descriptive name like "bell" or "big_noise" so you can find it quickly when looking at a script.
• Channel Variable lets you specify a name for the value of the curve over the length of the channel. You might, for instance, name the variable for an
  X Rotate operation X-Rot. As the script executed, the value in X-Rot would change to reflect the value of the curve at that point in time. That variable could be referenced by other channels that could trigger actions when the value in X-Rot was of a certain value.
• Subchannel ID indicates the dynamic value contained in the channel. For example, if you are working with an XYZ Rotate operation, each subchannel is assigned a subchannel ID-the X Rotate, Y Rotate, and Z Rotate curves are each assigned a unique subchannel ID.
• Trace Channel? lets you display the value for the curve (at some point in the script) in the LISP listener window. If you turn this on, you can display the value of a curve over time, for example, as the script animates, or for a single frame by using (CLICK-L) on the frame range area.

The curve properties dialog box also lets you select the type of curve you want to use to animate the operation.

(CLICK-L) in the Curve type field to specify the type of curve you want to use:

Figure 4.5 Curve types

• Linear produces a simple ramp (constant velocity, no acceleration).
• Hold curves can be used to specify a constant value for the duration of the curve, or between cues.
• Conic Spline produces a series of local spline curves that approximates a path through cues but undershoots actual cue values; tension and end treatment can be controlled.
• Kochanek Spline produces an interpolated spline that passes directly through cue values but overshoots these values in the legs of the spline.
• Sketched Curve lets you hand-draw a curve of arbitrary shape, or generate curves with known characteristics (like a sine-wave curve) using a series of pre-defined operations.
• Filtered produces a smoothed series of linear ramps through cues; the degree of smoothing can be controlled by filter width.
• Slow In gradually increases the value before a cue.
• Slow Out gradually decrease values after a cue.
• Slow In/Out curves have values that gradually increase before a cue, and decrease after a cue.
• Spherical Linear is another type of linear curve; this option is sometimes used with certain operations in the Skeletal Animation System to avoid gimbal lock.

The parameters for each type of curve are described in the section "Curve Types," on page 4-6.

There are three buttons at the bottom of the dialog box:

• Do It applies the specified properties to the curve
• Edit Curve applies the specified properties to the curve and displays the curve in the curve editor (as described in "The Curve Editor," on page 4-22.
• Abort exits from the dialog box without applying any changes.

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Curve Types

Figure 4.6 Linear curve parameters

• Start Value is the value of the cue at the beginning of the channel.
• End Value is the value of the cue at the end of the channel.
• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

A sample linear curve (one with cues only at the beginning and end of the channel), looks like this:

Figure 4.7 A sample linear curve

If you add additional cues to the curve, the value changes from cue to cue in a linear fashion:

Figure 4.8 A linear curve containing several cues

Hold Curves

Figure 4.9 Hold curve parameters

• Start Value is the value of the cue at the beginning of the channel.
• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

A sample hold curve (one with cues only at the beginning and end of the channel), looks like this:

Figure 4.10 A sample hold curve

If you add additional cues to a hold curve channel, the value remains constant until a new cue is reached:

Figure 4.11 A sample hold curve with several cues

Conic Spline Curves

Conic splines can be manipulated by cue location as well as tension and end treatment.

Figure 4.12 Conic spline curve parameters

• Bias controls the ramping of the curve before and after cues; a value over .5 weights the curve to the right of the cues; values under .5 weigh the curve to the left of the cues.
• Tension controls how linear the curve appears between cues. Increasing the tension of a spline curve makes the curve more linear. The default value for the tension parameter is 0%, which yields a smooth curve. As you increase tension, the shape of the curve moves toward a series of ramps.
• End Treatment changes a pair of "imaginary" cues before and after the ends of the channel. These cues control the acceleration or deceleration of the animated object as it enters and leaves the sequence. Four cues affect the curve at any point: the cues at the beginning and end of the sequence, and the cues before the start and after the end. There are several types of end treatment available:

Figure 4.13 End treatments for conic spline curves

• Relaxed is the default. The object has no acceleration at the beginning or end of the sequence-the motion before and after the channel is at a constant velocity.

  
  

• Clamped is the opposite of Relaxed. Clamped end treatment maintains the same acceleration as the rest of the curve. At the end of the frame, the object is still accelerating (as opposed to relaxed end treatment, where the object appears to be coasting).

  
  

• Cyclic matches up the ends of the curve. Cyclic end treatment can be useful for animating repetitive action, by copying a cyclic sequence several times, to animate an action such as a pendulum or a walk cycle. The values of the cues at the beginning and end of the channel are averaged when this end treatment is chosen.

  This can be useful if you have two similar (but not exact) keyposes at the start and end of a script; choosing a cyclic end treatment averages the two keyposes into a single in-between keypose, so that looped sequences are seamless.

  
  
• Slow in/out gives zero slope at the ends of the sequence. Using slow in-out gives the appearance that the object accelerates at the beginning of the channel, then slows down near the end.

  
  

• Held curves use the value of the cues at the start and end cues for the two "ghost" cues beyond the start and end channel.

  

• Start Value is the value of the cue at the beginning of the channel.
• End Value is the value of the cue at the end of the channel.
• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

A sample spline curve (one with cues only at the beginning and end of the channel), looks like this:

Figure 4.15 A sample conic spline curve, with bias and tension set to zero

By changing the bias and tension of individual cues on the curve, you can change its shape:

Figure 4.16 The same conic spline curve with modified bias and tension values

Kochanek Spline Curves

The two curve types offer a trade-off: better control at the cue points (Kochanek splines) or between them (conic splines). Kochanek spline curves have the additional property of "continuity," described below.

Figure 4.17 Kochanek spline curve parameters

• Bias is the same as described for conic spline curves, above.
• Continuity determines the "pointiness" of each cue.
• Tension is the same as described for conic spline curves, above.
• End Treatment is the same as described for conic spline curves, above.
• Start Value is the value of the cue at the beginning of the channel.
• End Value is the value of the cue at the end of the channel.
• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

A sample Kochanek spline curve (one with two cues, but default bias, tension, and continuity), looks like this:

Figure 4.18 A sample kochanek spline curve

The cues on a Kochanek spline curve can be manipulated directly in the curve editor. Each cue has a pair of handles associated with it; you can set the bias, tension, and continuity for each cue by dragging the red handle on either side of the cue itself.

Figure 4.19 A sample kochanek spline curve; bias and continuity have been modified on both cues

Sketched Curves

Sketched curves have the following parameters:

Figure 4.20 Sketched curve parameters

• LUT Directory is the directory in which you want to save or load a curve from.
• LUT Name is the name of the file containing (or to contain) the curve data.
• Interpolate specifies whether the curve should be smoothed; when you use a low number of samples, interpolating between the values produces a smoother appearance.
• LUT Size specifies the number of samples (elements in the curve's lookup-table) in the sketched curve. The default value is 128; a higher number of samples produces smoother motion; a lower number of samples produces "jerkier" motion.

Changing the number of samples is useful for very long sequences to avoid motion artifacts due to an inadequate number of samples. If a sequence was 1000 frames long, the interpolation between each pair of samples in a 128-sample sketched curve might produce discontinuous or "jerky" motion. (Of course, reducing the number of samples can also be used to deliberately obtain a jerky motion effect.)

• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

A sample sketched curve looks like this:

Figure 4.21 A sample sketched curve

If you smooth the curve several times, its jagged edges are reduced and transitions over the course of the channel are smoother:

Figure 4.22 The same sketched curve, smoothed several times

Filtered Curves

When you set a cue value, you are specifying the point on the vertical axis where you want the object's motion to take it at that time. When you adjust the filter width, you specify the degree of smoothing that occurs over the curve. The filter width is expressed as a percentage of the parent sequence width and is shown as both the percentage and the time that it represents.

In filtered curves, the smoothing is over a specific duration of time (hence a specific width on the diagram regardless of sequence length). A filter width of 0% gives linear ramps between cues. As the filter width increases, the curve becomes smoother.

While the cues of the curve specify the same values at the same place for both the 25% and 100% filter widths, the curves will be quite different-the 25% filter produces a longer straight section between shorter curves, while the 100% filter width produces continual curves with no noticeable linear sections.

As filter width increases, so does deviation from the cue value. A filter width of zero gives a curve that consists of a series of linear ramps between cues, while a filter width of 100% gives a smooth curve that deviates strongly from the exact cue values.

Figure 4.23 Filtered curve parameters

• Filter width specifies the smoothness of the curve around cues in the channel (see the description above).
• Start Value is the value of the cue at the beginning of the channel.
• End Value is the value of the cue at the end of the channel.
• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

Figure 4.24 A sample filtered curve, with a filter width of .25

Reducing the value of the filter width produces a more linear appearance at each defined cue, since less of the curve is "smoothed:"

Figure 4.25 The same filtered curve, with a filter width of .1

Slow In Curves

The default exponent is 2.5. Adjusting this value determines just how slow the Slow-In is. An exponent of 1 gives a linear ramp. Larger values correspond to proportionately higher rates of acceleration.

Figure 4.26 Slow In curve parameters

• Exponent determines the shape of the curve. Higher values produce a more accelerated effect.
• Start Value is the value of the cue at the beginning of the channel.
• End Value is the value of the cue at the end of the channel.
• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

Figure 4.27 A sample Slow In curve

Slow Out Curves

The default exponent is 2.5. Adjusting this value determines just how slow the Slow-Out is. An exponent of 1 gives a linear ramp. Larger values correspond to proportionately higher rates of acceleration.

Figure 4.28 Slow Out curve parameters

• Exponent determines the shape of the curve. Higher values produce a more accelerated effect.
• Start Value is the value of the cue at the beginning of the channel.
• End Value is the value of the cue at the end of the channel.
• Min Plot Value is the minimum value that can be plotted in the channel.
• Max Plot Value is the maximum value that can be plotted in the channel.

Figure 4.29 A sample Slow Out curve

Spherical Linear Curves

Figure 4.30 Spherical Linear curve parameters

Parameters for this curve are identical to those for the Linear curve type, described in the section "Linear Curves," on page 4-6.

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The Curve Editor

Before using the curve editor, you should select the basic curve type for the channel using the Edit Curve Properties dialog box described in the section "Curve Types," on page 4-6.

Next, enter the basic parameters for the selected curve type, as described in the section "Curve Types," on page 4-6.

Once you've done the basic setup for the curve channel, you're ready to use the Curve Editor. To open the curve editor:

1. (CLICK-M) on the curve.

2. (CLICK-L) on the Edit Curve button at the bottom of the Edit Curve Properties dialog box.

The channel containing the curve expands to fill the entire window; the type of data shown in the channel depends on the curve type selected. Suppose you had created a linear curve in a 30 frame channel with cues at frames 10 and 20. The curve might look something like this in the Script Editor:

If you were to view the same curve in the Curve Editor, it would look something like this:

Figure 4.32 A simple linear curve with two cues

Note that the cues are represented by points along the curve in the Curve Editor. This lets you move the cues either left or right (to change their position in time) or up and down (to change their value).

The various commands in the Curve Editor are described below:

Exit

Reset

If you want to escape from the Curve Editor without saving your changes, choose Reset, then Exit.

Fit

1. Enter those values as your minimum and maximum in the Graph Min/Max text edit boxes.

2. (CLICK-L) or (CLICK-M) on Fit.

The display is adjusted so that the highest and lowest points in the curve are visible in the channel. ((CLICK-M) adds a little padding above and below the highest and lowest points.)

Shifting or Scaling the Entire Curve

• (DRAG-M) interactively slides the curve in value (moves it up or down).
• (SHIFT-DRAG-M) interactively factors the values in the curve (moves it up or down exponentially).
• (DRAG-R) slides the curve left or right in time (for sketched curves only).

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Working with Cues in Curve Channels

Cues in the curve channels can be modified as follows:

Adding a Cue

1. Move the mouse over the curve channel.

2. (CLICK-R) on the channel at the point you want to add the cue.

3. (CLICK-L) on Add Cue.

Note. You can also use the hot key "s" to add a cue.

Moving a Cue

To move a cue:

1. Move the mouse over the cue.

2. (DRAG-L) to move the cue left and right in time.

If you are in the curve editor, you can also move the cue up or down (changing its value)-the new value is displayed in the label at the top of the curve editor.

Cue Type #1: The Cue contains a Simple Value

1. (CLICK-M) on the cue.

The following dialog box appears:

• (DRAG-L) on the slider to change the value for the cue, then display the object's new state.
• (CLICK-M) and drag to interactively update the object in the N-Geometry window.

Each of the elements on the Adjust Parameter Value dialog box are described below:

• Value shows the currently set value. Drag the vertical bar on the slider left or right to change the value.
• Min and Max show the range of values that can be set using the current slider.
• Shrink reduces the range (the min and max values for the curve channel).
• Expand increases the range (the min and max values for the curve channel).
• Recenter recenters the slider, but does not change its value (useful if you've changed the range for the curve).

Cue Type #2: The Cue contains a Complex Value

1. (CLICK-M) on the cue.

A dialog box or list prompting you to select a displacement, pose, or view from a known list of such variables is displayed:

Note that you also have the choice of copying the current state of the camera, skeleton, or model into the cue, so that you can interactively set up your animation.

The method described above is useful if you want to edit a single cue. If you want to edit several cues that occur at the same time in the script, you can use the following method:

1. Open the parent channel that contains the curves whose cues you want to modify.

2. (SHIFT-M) on the one of the concurrent cue you want to modify.

You can (SHIFT-M) on either a cue or, if you have a marker track, on the marker with which the cue is associated. When you (SHIFT-M) on the cue, it and any other cues at that position are temporarily highlighted in red. (This is a toggle-use (SHIFT-M) again to deselect the marker.)

For example, if you were working with the curves in an XYZ Rotate cube action, (SHIFT-M) on the marker would highlight any other cues at that position:

Sliders appear in each channel with a selected cue. There are two ways to update the value of the selected cue; both methods display the updated object in the N-Geometry window:

• (CLICK-L) and drag side to side to update the object after changing the cue value.
• (CLICK-M) and drag side to side to update the object interactively.

Cues are selected based on their position in time, not whether they are linked; this means cues in other open curve channels that exist at the same time as the selected marker can be highlighted (and can be updated) as well.

Figure 4.36 (SHIFT-M) edits cues at the same time, regardless of whether they're linked or not. Note that the first channel contains a view, while the others contain values; you can edit all at the same time using this technique.

Deleting a Cue

1. Move the mouse over the cue you want to delete.

2. (SHIFT-R) on the cue.

3. (CLICK-L) on Delete.

Note. You can also use the "Shift-D" hot key to add a cue.

Editing Sketched Curves

Figure 4.37 Editing a sketched curve

To edit the shape of a curve manually:

1. Move the mouse over the curve channel.

2. (CLICK-L) and drag to change the shape of the curve.

As you draw, a series of black dots show the new shape of the curve; when you let up on the mouse button, the shape of the curve is updated.

Exit

Reset

Smooth

Figure 4.38 Smooth options

• Wrap Around smoothes the curve so that its start and end values move closer to one another.
• No Wrap smoothes the curve without any special end treatment.

You can repeatedly smooth the curve by holding down the appropriate mouse button:

• (HOLD-M) repeatedly smoothes the curve with wrap around.
• (HOLD-R) repeatedly smoothes the curve with no wrap around.

Operations

Figure 4.39 Sketched curve operations

Each of these operations is described below:

Change Phase

• Positive values shift the curve from right to left
• Negative values shift the curve from left to right

A value of 1 returns the curve to its original position.

Figure 4.40 Top, original curve; middle, same curve with phase change of .75; bottom, with phase change of .5

Change Value

• Positive values are added uniformly to the curve.
• Negative values are subtracted uniformly from the curve.

If you add or subtract too much to the curve, you may want to use the Reset command to return the curve to its original state, or expand the displayable range of value using the Graph Min/Max boxes (described below).

Figure 4.41 Top, original curve; bottom, same curve with reduced value

Decircularize

Look at the following curve:

Figure 4.42 Curve showing jump in data

The data starts in a fairly straight line, then makes a large jump and continues along in a straight line.

To decircularize the data in the curve:

1. (CLICK-M) on the curve in the script editor.

2. (CLICK-L) on Edit Curve.

3. (CLICK-L) on the Operations button in the curve editor.

4. (CLICK-L) on Decircularize.

The following dialog box is displayed:

• Threshold specifies how big the jump between adjacent samples must be for the decircularization filter to be applied.
• Cycle Size is the point at which data is considered to be "cyclic." For rotation, for example, this would probably be set to 360; if 106% looked had the same effect as 6%, the cycle size would be 100.

When the curve decircularized, it is automatically made to fit the channel, so the variations along the surface of the curve are more pronounced. If you set the Graph Min/Max range to match the original curve, you can see the effect more clearly:

Figure 4.44 Top, original curve; bottom, same curve after decircularize operation

Invert Curve in Time

Figure 4.45 Top, original curve; bottom, same curve inverted in time (flipped left to right)

Invert Curve in Value

Figure 4.46 Top, original curve; bottom, same curve with inverted value (flipped up/down)

Noise Curve

The current minimum and maximum values are displayed in the upper and lower left corner of the curve channel respectively. When you add noise you can specify the following parameters:

• Min Value and Max Value are context specific depending on the combination specified:


• Add changes the shape of the curve by adding or subtracting randomly to each sample in the curve.

  Min Value specifies the maximum amount that can be subtracted from the curve at any point; Max Value specifies the maximum amount that can be added.

  Specify a negative Min Value if you want to create noise below the current line of the curve.

  
  
• Mult changes the shape of the curve by multiplying each sample in the curve by a random amount.

  Min Value specifies the lowest value by which any sample can be multiplied; Max Value specifies the maximum amount by which any sample can be multiplied.

  Specify a negative Min Value if you want to create noise below the current line of the curve.

  
  
• Set ignores the previous values in the curve; each sample in the curve channel is set to a random value between the specified Min Value and Max Value.

  

Figure 4.47 Top, original curve; bottom, same curve with noise added

Sawtooth Curve

A sawtooth curve looks something like this:

Figure 4.48 Top, sawtooth curve with five cycles; middle, same curve with modified value exponent; bottom, with modified time exponent

The effect is most obvious if you use the Set combination (described below), which will create regular "teeth" on the new curve. Making an existing curve into a sawtooth curve creates the sawtooth effect along the existing shape of the curve.

• Phase Start specifies the initial value for the curve, which determines the position of the "teeth" in the curve.
• Cycles specifies how many teeth there should be in the sawtooth effect.
• Min Value and Max Value have different effects depending on the combination chosen (described below).
• Value Exponent describes how quickly each tooth reaches the maximum value.
• Time Exponent specifies lets you control the length of the phase
• Combination lets you specify whether you want to create a sawtooth effect for an existing curve or create a new (more regular) sawtooth curve. Add, multiply, and set operate as described above for the Noise curve: Add adds or subtracts values to each sample, Mult multiplies each value, and Set creates samples between the specified range.

Sine Wave Curve

Figure 4.49 Top, sine wave curve with five cycles; bottom, with modified time exponent

For a description of the various sine wave parameters, see the description of the sawtooth curve above.

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Curve Operations Menu

(CLICK-R) on a curve channel to see the curve operations menu:

Figure 4.50 The curve operations menu

Each of these commands is described in the sections below.

Cut

Figure 4.51 Cutting a curve

The cue at which the two sequential curves meet shares a single value with both:

Figure 4.52 Sequential curves share a cue

Delete

Insert Parent

Figure 4.53 Top, channel with curve; bottom, parent inserted around curve

Replace with Action

To replace a curve with an action:

1. (CLICK-R) on the curve you want to replace.

2. (CLICK-L) on Replace with Action.

The curve is converted into an action:

Replace with Copy

Replace with Variable

This command is described in more detail in the section "Replace with Variable," on page 3-44.

Replace with Sequential Curves

This command is described in more detail in the section "Replace with Sequential Curves," on page 3-46.

Extend

Freeze Cues/Unfreeze Cues

Frozen cues are described in more detail in the section "Freeze/Unfreeze," on page 3-27.

Respace Cues

1. Move the cursor over the curve.

2. (CLICK-R) on the curve.

3. (CLICK-L) on Respace Cues Evenly.

Figure 4.55 Top, curve with random cue positions; bottom, cues respaced evenly

Set Timeline

Slide this Curve

Add Cue

1. (CLICK-R) on the curve channel where you want to insert the cue.

2. Choose the Add New Cue command.

Note. You can also add cues to the curve using the "s" hot key.

Add Multiple Cues

Figure 4.56 Curve Channel With Five Cues Added, Using Add Multiple Cues

Edit all Cues

Cue Type #1: Cues in the Channel Represent Simple Values

1. (CLICK-R) on the curve whose cue values you want to edit.

2. (CLICK-L) on Edit all Cue Values.

A menu similar to the one in Figure 4.57 appears:

3. Modify any or all of the values by clicking in the appropriate text box.

• (CLICK-L) to modify the existing value.

  
  

• (CLICK-M) to clear the box and enter a new value.

  
  

• (CLICK-R) to update the slider dialog box described in the section "Editing a Cue's Value," on page 4-25.

Cue Type #2: Cues in the Channel Represent Complex Values

Empty of Cues

Deactivate

In the Script Editor, the text label of a deactivated channel is black; the text for active channels is white.

Note. You can also use the "a" hot key to deactivate the channel currently under the mouse.

Remember

Copyright © 1996, Nichimen Graphics Corporation. All rights reserved.