CAP 201a - Computer Animation I

Lesson 3 - Chapter 5, Animating a Ball
and Chapter 6, Animating a Thrown Knife

Objectives:

Chapter 5 introduces the use of the time slider, keyframes, and the curve editor. Objectives important to this lesson:

1. Frames, key frames, and in-betweens
2. Animation: bouncing ball
3. Track editor-Curve editor
4. Tangent types
5. Squash and stretch
6. Layering animation
7. X-form modifier

Chapter 6 continues the lesson on using the curve editor. Objectives important to this lesson:

1. Trajectories
2. Anticipation
3. Momentum

Concepts:

Modeling is a vital skill in computer animation, but so is animation itself. In our previous texts from these authors, animation was introduced in earlier chapters with simple projects. These have been eliminated in this text. We will continue at this point with Chapter 5 to introduce the basic animation tools and to actually animate some objects.

It has been a while since you should have been exposed to some basic terms, so let's review them:

frames, key frames, and in-betweens - Computer animation is based on movie animation. Movies are composed of a series of still photos, frames, that are shown to the viewer rapidly. In the image on the right, photos taken by Eadweard Muybridge are shown somewhat rapidly, one after another. Each frame (an individual image is a frame) in this series is numbered (see the lower left corner). These frames are of historical significance. In 1877, Muybridge took a series of photos of a running horse using a series of cameras placed on a closed training track. According to the legend, he did this to settle a bet about whether all four feet of a running horse are ever off the ground at the same time. Another version of the legend is that the question was whether all four feet of a trotting horse leave the ground at once. This is the version documented in the link above. Muybridge became one of the inventors of movies first by developing a method to capture a series of such pictures in rapid succession, and later by developing a way to display his images in rapid succession, a form of animation. In computer animation, we don't usually take photos, but we do compose frames. We create frames that show objects at significantly different stages of motion, like the frames in Muybridge's sequence. Each of them becomes a key frame. We place each key frame on a timeline, indicating the amount of time that should pass between successive frames. In-betweens are frames that our software creates to fill in the gaps between the key frames. (In the days of hand drawn animation, a lead artist would draw the key frames, and assistant animators would have to to draw the in-betweens.) If the running horse sequence had in-betweens, then the animation would look smoother. It might be argued that we would have to create an infinite number of in-betweens, since motion is often continuous, and each frame is a still. As you can see by viewing this loop of 16 frames, an infinite number of frames are not necessary to create the illusion of motion. The viewer's mind participates in the illusion, creating many in-betweens to smooth out the perceived motion.

As they have done before, the authors ask you to copy the project folder for this chapter to your working area, and to set 3DS Max to use that as the root folder for this project.

For the exercises in these projects, you will want to have Auto Key turned on before you make changes to objects in the scene. The Auto Key feature automatically captures key frame information for common changes to objects, but only when it is turned on.

Project: the Bouncing Ball

This project includes a series of exercises to animate a bouncing ball in several ways. Begin as indicated on page 111, by

1. copying the project file from your download or from the class resource drive to your working area,
   
2. and setting 3DS Max to use that as the root folder for this project.

Project Exercise 1: Animating the Ball 

The exercise starts by telling you to open a scene file. Find it and open it in 3DS Max. The text says that you will be working on the gross animation for the scene first. Setting the gross animation is also called blocking the scene, which may be more familiar to you if you have been an actor. If neither term is familiar to you, you will be working on the major movement of objects (and characters, if the scene had characters). Sometimes programs refer to both objects and characters as actors, since both can be animated in a scene.

1. The scene contains a ball object. In step 1, you adjust its pivot point. Select the ball, then open the Hierarchy panel, choose Pivot, and click the Affect Pivot Only button. Move the pivot point to the bottom of the ball, then turn off the Affect Pivot Only button.
   Pivot points can be located outside the objects they affect, so be careful not to place the pivot point outside the ball in this step.
2. The time slider is used to move forward and backward in time for an animation. It should be at frame 0 by default. Don't move the time slider yet.
3. Turn on the Auto Key feature (by clicking the button that says Auto Key) and now drag the time slider to frame 10. (The currently selected frame number is displayed on the slider.)
4. Click the Select and Move tool, and select the ball. Move the ball to 0 on the z-axis with the mouse or with the transform type-in box at the bottom of the interface. This should result in a keyframe at time 0 and at time 10. I had you turn on Auto Key before moving the time slider to capture the initial position of the ball, not just the second position. In this version of the program, this precaution may not be necessary. In previous editions, it was a good idea.
5. The text starts its numbering over again. I will not do so here. You should turn off the Auto Key function now.
   In frame 20, you want the ball to go back to the same position it was in originally at frame 0. The text sensibly recommends that you copy the keyframe in frame 0 by selecting that keyframe (click it on the timeline), holding down a shift key, and dragging the keyframe to time marker 20. Note that this does not result in a dialog box about making a copy or an instance or a reference. Copies of keyframes are just copies.
6. You should scrub the time slider to check the movement so far. (That means you drag it left and right to see the animation.)
   

The text turns to the idea of turning a few frames into a repeating cycle by using a tool called the Track View Curve Editor. (The Track View tool has another editor, the Dope Sheet, which is not used in this chapter.)

Project Exercise 2: Introducing the Curve Editor 

The exercise starts on page 114.

1. Make sure the ball is selected. Use this menu sequence: Graph Editor, Track View, Curve Editor. You should see a screen something like the one on the bottom of page 114.
2. Look at the illustrations on page 115, regarding step 2. Find the Controller menu, open it, and click the Out-of-Range Types button. (And pause to wonder what kind of person named it that. If someone suggested that name to me, I would have asked them to call it the Extrapolate Curve button. That's what it does.) As the exercise notes, the Out-of-Range part of the name refers to extending the curve beyond the range of the first and last keyframes.
3. Once you have clicked the button with the awful name, you will see a dialog box with a worse name (Parameter Curve Out-of-Range Types) that lets you choose one of the six ways the program knows how to extend the existing curve.
   Question 1: What are names of the six types of curve extensions?
   For this exercise, click Loop, then click OK.
4. Note the dashed line in the curve editor that stands for the extrapolated curve. (To extrapolate means to predict what would happen if something were to continue. Anger at the program is not the only reason to increase your vocabulary.)

The features of the Parameter Curves are discussed on pages 116 and 117. Two more related concepts are introduced: ease-in and ease-out. These features can be applied to any keyframe. They mean that the transition into or out of the keyframe can be made more gradual and less abrupt.

Page 118 brings up the concept of gravity, as it applies to a bouncing ball. The animation does not look realistic yet, because a real bouncing ball moves faster as it approaches the bottom of a bounce, and moves slower as it approaches the top of a bounce: down is working with gravity, up is fighting gravity.

Our ball is moving at the same rate at the top and the bottom of the bounce. The text introduces a new technique to handle this problem, using the Curve Editor again. (This time it uses the Mini Curve Editor. Don't be confused by that. It is just smaller version of the Curve Editor that leaves more of the viewports visible than the larger Curve Editor.) The text refers to the thing you will edit next as a tangency. A tangent is a line that touches a curve at one point. In a sense, the keyframes touch the curve of change for an object at one point on that curve. What you are editing is the way the keyframe is attached to the curve. The default kind of tangent for a keyframe is Smooth, which moves into and out of the keyframe at the same rate.

Project Exercise 3: Changing Tangency Type

In the procedure on page 119, you change the tangency of the keyframe at the bottom of the bounce to Fast. This makes the ball speed up near that keyframe. You leave the tangencies at the top of the curve Smooth. The effect of this is to make the ball "less fast" when it is near a Smooth tangency, and "more fast" when it is near a Fast tangency. Make the changes indicated in the text.

The text changes topics again on page 120, explaining that the ball should also be compressed a bit at the bottom of a bounce, and it should extend (elongate) a bit at the top of a bounce. The two concepts are called squash and stretch.

Project Exercise 4: Squash and Stretch

1. In step 1, select the ball and turn on the Auto Key feature. You are told to turn on the Mini Curve Editor and drag the Track Bar Time slider to frame 10. Before you do this, take note of something. Turn the Mini Curve Editor off, and move the Time Slider on the scene timeline to Frame 10. Now turn on the Mini Curve Editor and check the position of the Track Bar Time slider. It looks like it is on Frame 9, not 10. The scene timeline and the Mini Curve Editor do not appear to use the same numbering scheme. Take this into account as you use the Track Bar Time slider.
   
   After you move the slider, you are told to access the flyout for the Scale tool and choose the Select and Squash mode for the tool. (A tiny picture appears on page 120.) The instruction after that picture is poorly worded. What you should do is place your mouse pointer over the blue handle (z-axis handle) of the transform gizmo that appears on the ball. Watch the values change in the type-in transform boxes at the bottom of the interface as you drag that handle down. You want the value for the z-axis to be about 80. (It is practically impossible to be exactly 80 unless you enter that number manually.)
   
   Note that the other values go up as the z-axis value decreases. The Select and Squash tool maintains a constant volume for the object, so as z is decreased, x and y increase. Get a balloon, blow it up about half way, then play squash and stretch with it. You should get the idea quickly.
2. Step 2 tells you to move to Frame 0. Drag the z-axis handle again, this time to increase the z value to about 120.
3. The text tells you that you could shift-drag keys to copy them from one position to another on the timeline. Since the Mini Curve Editor is blocking your view of the timeline, it is good that you can copy the keys in the Mini Curve Editor (or the Curve Editor) as well.
   1. First, select the Scale track in the Controller window.
   2. Second, find the Move Keys tool in the Mini Curve Editor's toolbar.
   3. Access the flyout for the Move Keys tool as indicated in the text, and change it to the Move Keys Horizontal tool. You will use this tool in a minute.
4. Drag a selection marquee around the indicated keyframes located at frame 0. (You do not need a special tool for this. Just drag a rectangle around them with your mouse.) You can now shift-drag any one of those keyframes to copy it to frame 20, and the others will be copied there as well.
5. Use the Mini Curve Editor's menu bar to select Controller, Out-of-Range Types. Click Loop, and click OK. Test and save incrementally.

The next problem is with the timing of the squash and stretch events. 3DS Max has automatically calculated in-betweens that assume a constant transition from one state to another. This is not realistic: the ball should not squash before it meets the floor, and it should recover immediately upon bouncing. (You should realize that the squash and stretch effects used in this scene are exaggerated, but we still want some realism.)

Project Exercise 5: Setting squash and stretch timing

(From page 122: "...follow these steps as if they were law." I beg your pardon? I know comedy is difficult, but come on.)

1. Close the Mini Curve Editor. On the scene's timeline, put the time slider at frame 8. Make sure Auto Key is on. Use the Curve Editor (not the Mini Curve Editor) for the next steps. Locate and select the ball's Scale track. (The ball has to be selected first.) Find and click the Insert Keys button on the Curve Editor's toolbar. Click a Scale curve at the marked frame. A new keyframe appears on all the Scale curves. The book notes that only two curves appear because x and y are the same values.
2. Examine the picture on page 122. Find the two type-in boxes indicated in that picture. The left box is for the frame number, and the right one is for the value to use at that frame. You should be on frame 8 at this time. Enter 100 in the right box to set all the selected Scale curves to 100% at frame 8.
3. In step 3, you are instructed to move the time slider to frame 12, add new keyframes, and to set the curve values to 100 at that keyframe as well. The effect should be to make the ball squash only for a few frames in each cycle.
4. Turn off Auto Key and test. Change if necessary, and save when it is right.

On page 123, the text discusses adding a forward motion to the ball. It refers to adding this motion at this stage as layering animation. This does not mean that you are using layers as you might in a Photoshop image. It just means that if often makes sense to get one kind of animation right (like a vertical bounce) before you add another kind (like a horizontal movement). This method requires that you think about animation like an animator (or a physicist) instead of like an audience member. You need to plan the different kinds of motion that will be needed for the scene, and assign values to each part of it across time. Of course, this would be easier to do if someone had provided a story board of the planned animated scene to us.

You have already made the ball bounce up and down. Adding a forward motion in the same time sequence will make both motions happen at the same time. You could make the two motions sequential by having them happen at different times. That is not what we want. We want the ball to bounce as it moves along a path. It is useful that you can add the up and down motion, then add the left to right motion, and you will get the resulting arcing bounce motion without having to calculate the arcs. (You will, however, need to fine tune it. Animation is not totally automatic, else you wouldn't be needed as an animator.)

Project Exercise 6: Moving the ball forward

1. This one starts on page 123. In the scene, move the time slider to frame 0. Click the Select and Move tool, then click the ball. Right-click the Perspective (Camera) viewport to select it. Move the ball to the left as noted in the text, which will be a change of about -30 on the x-axis.
2. Move the time slider to frame 100. Turn on Auto Key. Move the ball to the right, to about +30 on the x-axis.
3. Open the Curve Editor. Find and select the x-Position track.
4. The text informs us that keyframes were automatically created on the x and y Position tracks when you created the up and down motion. Those keyframes were placeholders. Find the keyframes on the x-Position track at frame 10 and frame 20. Select them (click them) and delete them (press your Delete key).
5. Click our now-familiar friend, the Out-of-Range Types button. (The text calls it the Parameter Curves Out-of-Range Types button. It used to be called that, now its name is two words shorter. Aren't you thrilled?)
   Choose Constant and click OK. Turn off Auto Key. Note the shortcut key for playing the current animation: /. (This is the slash key, not the backslash key. If you call it by the wrong name, it will become angry.)
6. Note the shape of the curve in the Curve Editor at this point. Its ends (at frames 0 and 100) indicate an ease out and ease in at those points. This is the default tangency at work. You want to change this. Select both keys in the Curve Editor (with a marquee?) and click the Linear Tangent button. Or would an ease out make sense for the first one? Objects do not typically accelerate from 0 to x instantly, do they? The answer depends on the scene. Did someone toss the ball? Ease out of the frame. Did a ball suddenly appear from a rift in space/time? Is it already at full speed, having travelled some distance before we saw it? Use a linear tangent.

This is a good place to pause and save again. Remember to save your file with a new, incremental name, so you have more than one place to go when you need to go back in time.

On page 124, the text addresses a problem it created back at the beginning of the chapter. The ball should also roll as it bounces. This is another natural movement for a thrown ball. The problem in this case is that it can't roll on its pivot point, because we moved the pivot point to the bottom of the ball for squash and stretch. We can't move the pivot point back to the center, because we needed it where we put it. We can't add another pivot point, because it can only have one. (Really? Any more helpful roadblocks?) So what do we do? We can use a modifier that will act like a pivot point: the XForm modifier.

Project Exercise 7: Adding a roll with the XForm modifier

1. Make sure that Auto Key is turned off. Select the ball. Add an XForm modifier to the ball with the menu sequence in the text, or with the Modifier List, which is more memorable. (You should know both methods exist, and use whichever you like.) Note that the XForm object has two sub-objects: Gizmo and Center.
2. Expand the XForm item in the modifier stack, and select its Center sub-object.
3. Click the Align tool, then click the ball. You will see a dialog box. Make sure that all three axes (x, y, and z) are checked. Click the the choice that says Center under Target Object, and click OK.

The text pauses to make it clear that an object can have only one pivot point. You have not added another pivot point, you have just added a center point to the object that it can rotate around. (I wonder if there is some judge watching us to make sure we don't violate a copyrighted feature or some such.)

So, now that you have the XForm modifier configured, you need to use it. Continue on page 126.

1. Turn on Auto Key. Click the Select and Rotate tool.
2. Click the XForm's Gizmo sub-object. The text reveals that this is necessary to rotate around the XForm center instead of the ball's pivot point (default).
   
   Before you move ahead, think! Which way should the ball rotate? Which viewport should you use to rotate it? I have seen too many balls spin backwards. Don't do that.
   
   
3. Put the time slider at frame 100 (the last frame). Rotate the ball 360 degrees on its y-axis. (You may want to use the transform type-in box for this.) Click the XForm object to leave sub-object mode, and test the animation.
   Question 2: Explain, in your own words, why the XForm modifier was needed for this exercise.

This section of the text ends with an overview of how to edit any of the keyframes used above.

Project: anticipation and momentum in a thrown knife

Chapter 6 contains a series of exercises to animate a knife thrown at at target. Begin as indicated on page 129, by copying the project file to your hard drive, and setting the project root folder.

Project Exercise 1: Blocking the scene

1. Open the start file. Move the time slider to frame 30, and turn on Auto Key.
2. Move the knife into the target as illustrated at the top of page 130. I had to move it down a bit as well as horizontally to make it look right.
   This is the first time you will have seen that objects in 3DS Max can easily penetrate each other. Up to now, you have been guided around that fact.
3. Move the time slider to frame 15 and move the knife higher in the scene, as though it was at the peak of an arc. The text offers no measurement for this, so make a guess about a good z-axis value. The text does not show you a good trick until later. You should know about it here. Do this:
   1. Open the Display panel on the Command panel set.
   2. Scroll down to the Display Properties rollout.
   3. Turn on the checkbox for Trajectory.
   4. You should see a red line on the screen.
      Question 3: The red line is the knife's trajectory. What information does this line give you visually?
4. The step shows you how to increase or decrease the number of frames in a scene. (This is a very important skill to have, so learn the location and use of this button.) Click the Time Configuration button. (You will find it near the Viewport Navigation Controls, the fifth button from the bottom right corner of the workspace, unless they have changed it again.)
   Once the Time Configuration window is open, find the End Time field. The default value is 100 (frames). Change its value to 30. Note that the End Time value will match the Length value (30), and the Frame Count value will be one more (31). Click OK to save this setting. This is a useful technique for lengthening or shortening the number of frames in a scene. Remember it, because you will use it again.
   
5. The text asks you to play the animation, and to watch for the default ease out and ease in at the ends of the knife's path. This step also tries to provide a plan for the next several steps, but there is a typo in the way. Let's assume that we were just told that the knife should start moving at frame 10, not frame 0. To make this correction, open the Curve Editor. Find the x, y and z Position tracks in the Controller window, and use Ctrl-click to select all three of them. (Actually, they were all selected when I opened the curve editor.)
6. Drag a marquee selection around the keyframes at frame 0. Change the Select and Move tool on the Curve Editor toolbar to the Horizontal Move tool and use it to move the selected keyframes to frame 10. Why use the Horizontal Move tool? Because you only want to move those keyframes in time. The Horizontal Move tool is supposed to constrain movement to the time axis, leaving the values on the position axes unchanged. Well, that was a good idea in earlier versions of the program. When I tried it this time, I found that the mouse would move the keys vertically anyway. When you do it, note the vertical value of one of the keys. Drag all the keys at once, but try to set them down in the same relative vertical position at Frame 10.
7. The action in step 6 changed the length of the action. The new middle frame is 20, not 15. Use the method in step 6 to move the keyframes currently at frame 15 to frame 20.

The text introduces another "new" concept on page 132: trajectories. We have already touche on it. In 3DS Max, a trajectory is the path an object takes through a scene, made visible. The trajectory of the knife in this scene is illustrated in the images at the bottom of page 132. To see a trajectory, select the Motion panel, and click Trajectories. I told you to do it earlier because it makes setting the path much easier.

On page 133, you are told to click the Sub-Object button on the motion panel to get to the Key subobjects for the trajectory. There is a step missing. You have to click the Trajectories button first, then click the Sub-Object button. (By default, my computer had the Parameters button clicked, which was a problem until I realized what to do). Use the procedure on these two pages, moving the key frames as subobjects, to experiment with adjusting the vertical rise in the knife's path.

Knives that are thrown for any distance tend to spin. The text continues the lesson by adding a rotation to the knife. Again, plan this! Which viewport and which axis to rotate on?

Project Exercise 2: Adding rotation

1. Move the time slider to frame 30, and select the Select and Rotate tool. Make sure the Auto Key feature is on. Select the knife and rotate it on its y-axis by 443 degrees. (If you have Angle Snap turned on, 445 degrees will also be fine.) The change in degrees is positive, which means the knife rotates counter clockwise in the camera's current view.
2. Open the Curve Editor. Find and select the x, y, and z Rotation tracks. This brings up an interesting point. The Curve Editor shows rotation on the x-axis, not the y-axis.When the knife rotates correctly, it rotates on the y-axis and through the x-axis.
   Refer to the exercise above for the method you should use to move the keyframes at frame 0 to frame 10. Turn off Auto Key when you have done so.
3. Play the animation as instructed. You still have an ease in and ease out, which are not appropriate here. Why is this a step? You need to learn to look for things to fix or improve. You should always do this as a troubleshooting step.
4. Okay, they have been complaining about the ease in and ease out that you get by default. It is time to correct that for this model. Several sub-steps here.
   In the Curve Editor, select the x-Position track. Select all the keyframes on that track. Switch the tangency for all those keyframes to Linear.
   Select the z-Position track. Use the handles on the individual keys (they appear when each key is selected) to adjust the curve to be more like the reference illustration in the middle of page 134.
5. The authors provide more tweaks to the animation in this step and the next. Try them, but be aware that you may not see the improvement that the authors expect in this short animation. There is an error here, but I will address it at the end of the project.

A person who throws a knife tends to move their hand backward before moving it forward. This movement is referred to as anticipation. Even though there is no hand in the scene at this time, we will add an anticipation to the knife's movement.

Project Exercise 3: Adding anticipation

1. Move the time slider to frame 0. Open the Curve Editor and select the x-Rotation track for the knife. Click the Add Keys button. Add a keyframe at frame 0. (Note, in the image on page 135, the time slider is in the wrong place.)
2. Select the Move tool as instructed, and click the keyframe at frame 10. In the Editor's Key Stats area, change the value of that key to 240. This will begin the process of animating the knife before the throw.
3. The tangent at frame 0 is correct. Change the tangent at frame 10 to Linear. Play this animation and try to see why the authors don't like it.
4. Use the keyboard command to undo your last change: Ctrl-Z. (The authors say you may have to hit it more than once. I had to hit it twice.) Change the Move tool to the Vertical Move tool. Select the In tangent for keyframe 10. The In tangent is the handle on the left side of a keyframe. (The Out tangent would be the handle on the right side of a keyframe.) You may have to scroll the Curve Editor window to find it.
5. Hold a shift key down as you drag the keyframe's In tangent down to make the curve resemble the one shown at the top of page 136. If you look carefully at the image on that page, you will see that the authors pulled the handle down and to the left a bit.
6. Play the animation. If yours looks as bad as mine did, you may realize that you need to adjust the other Bezier control for the key at frame 10 as well. The authors did this, but they did not mention it. Do so, so the knife continues to move with some realism.
7. Save again, to avoid problems.

Project Exercise 4: Follow-Through

1. This next part of the project leads up to a transfer of momentum from the knife to the target that moves the target (rocks it) just a bit. In this exercise, you will add some frames and work on the knife.
   In step 1, open the Time Configuration window again, and change the End Time value to 45. As the text explains, this will add fifteen frames to the end of the current animation.
2. Select the knife. Move the time slider to frame 30. Open the Curve Editor. Select the x-Position track for the knife. Add a keyframe using the methods above at frame 35.
3. The authors ask you to check the value of the new keyframe by looking at the type-in boxes in the Curve Editor. In their case, the value was about -231, and they advise changing it to -224 (a difference of 7), to sink the knife farther into the target. My initial value was very different, and yours may be as well. Adjust your value up and down a bit to get a depth into the target that you like, making sure that the knife is not bouncing out of the target.
4. Check the animation to make sure the knife is moving as desired. You may want to try adding just a little bounce here. A very small one. How? Pull the Bezier handle for the last key so there is just a little bump in the curve between the keys at 30 and 35. (A bump goes up, a dip goes down.  Yes, more vocabulary.)
5. The authors want to add a bit of follow-through (after the main action) rotation to the knife. Select the x-Rotation track in the Curve Editor. Add a key on this curve at frame 35. Note the change the authors used between their keys at frames 30 and 35, and adjust the value of your key at frame 35 by a similar amount. The effect may not be noticeable.
6. Save again.

Project Exercise 5: Momentum

This last part of the project in the text addresses another transfer of momentum to the target. The target has to move a bit, being pushed back by the knife's mass. If you have a feeling for the physics of the situation, you can imagine what has to happen. However, what happens if we animate just the target? Not good: the knife has to move as well if it is in the target. We have to animate the target and the knife together, which takes us to a hierarchy.

1. Move the time slider to frame 30. Click the Select and Link tool. Select the knife, and link it to the target by dragging a line from the knife to the target. (We do not want them linked in a hierarchy before this frame.) This will make the knife a child object of the target, which means the knife will move along with the target.
2. Move the time slider to frame 34. Turn on Auto Key. Choose the Select and Rotate tool. Rotate the target about 5 degrees back, and be glad that the authors already moved the target's pivot point.
3. Open the Curve Editor. Select the y-Rotation track for the target. Select the keyframe at frame 0, and move it to frame 30. Next, shift-drag (copy) that keyframe from frame 30 to frame 37. In both of these operations, be careful not to change the value (vertical position) of the original or copy frame.
4. Change the tangent at frame 30 to Fast.
5. Select the y-Rotation track for the target again. Use Add Key to add keyframes at frame 40 and frame 44. (This seems like nonsense, since there are only 41 frames in the animation.) Use the Vertical Move tool or the Value entry field to set the value of the key at frame 40 to about 1.7.
6. Choose the Select and Move tool. Move the time slider to frame 37. Move the target "just a bit" on the x-axis. This is to show that the knife not only rocked the target, it pushed it back a little. Open the Curve Editor again, and select the x-Position curve of the target. Next, select the keyframe at frame 0, and move it to frame 30. Change the tangent for frame 30 to Fast.
7. Save the file incrementally.

Project Exercise 6: Another Tweak

Presently, the knife continues rotating even after it has penetrated the target. If the target were plastic foam, maybe it would. If the target is made of anything else, this is not realistic. This is not in the book. It is my requirement for completing the exercise.

1. Select the knife.
2. Turn on Auto Key.
3. Open the Curve Editor. The knife should stop rotating at frame 29, not frame 30. Change the last Rotation key in each axis so that it happens at frame 29, with the same value that it currently has in frame 29. Do not just move the key horizontally, since this will keep the value that it currently has in frame 30. Move it vertically as well, to stop rotation upon full contact with the target.
4. Save again, and play it for me in the application.