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Pick up a clicker, find the right channel, and enter Student ID. Upcoming Deadlines. Homework #9 – Stop-motion character Animation Due Thursday, November 10 th (Next week) 20 points (10 points if late); 20 point bonus to top 3 For full schedule, visit course website: - PowerPoint PPT Presentation

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Uniform Motion

Upcoming DeadlinesHomework #9 Stop-motion character AnimationDue Thursday, November 10th (Next week)20 points (10 points if late); 20 point bonus to top 3

For full schedule, visit course website:ArtPhysics123.pbworks.comPick up a clicker, find the right channel, and enter Student ID1Survey QuestionMany videos are shown in this class; would you say that the number of videos is:Too many. Use the class time for other stuff.About the right balance.Not enough. Add more and leave out other stuff.

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Review QuestionIn the passing position the pelvis drops slightly on the non-weight bearing side. This motion is called:Pelvic rotationPelvic listKnee flexionHip hula-hulaThe Twist

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Pelvic ListPelvic list keeps the center of gravity from rising as much when the body passes over the weight-bearing leg, keeping the center of gravity on a flatter path of action. CGStridePassing PositionPassing PositionPassing PositionStrideCGWalking is more efficient with pelvic list.Path of Action ofCG without ListWith Pelvic ListWalking ForwardB) Pelvic list4Stride WidthShifting the center of gravity from left to right requires work so a wide stride is less efficient.

LessEfficientMoreEfficient5

8-Loop & U-LoopThe center of gravity shifts up & down but also side-to-side. CG makes a Figure-8 loop when walking slow

Makes a U-shape loop when walking fast.

SlowFastSide-to-SideUp & DownWalking ForwardFigure 8Loop6

Look (2009)This music video is one long walk cycle, focusing on the motion of the hips.http://www.youtube.com/watch?v=KX82DXvmQu47Step LengthWhen walking, why dont we take longer (or shorter) steps?We naturally adjust our step length to minimize the energy output required to maintain our desired walking speed.Step length

8Energy is required to:

Move the leg forward in the stride; longer steps take less energy.

Raise the body in the passing position; longer steps take more energy.

MoveRaiseXCGXCGEnergy & Step Length9Optimum Step Length

Work done per minuteStep Length (meters)Treadmill data of metabolic rate while walking at 2 mphOptimum Step LengthLonger Steps, Slower CadenceShorter Steps, Quicker CadenceThe body adjusts the step length to minimize the total energy expended while maintaining desired speed.10Shoulder Rotation

The shoulders rotate opposite from the hips, swinging over the planted leg.11Arm Swing

The arm swings back and forth, also like a pendulum, roughly 180o out of phase with the leg. The arm and leg are roughly the same length so they swing back and forth with about the same period.12Hand and AnkleHand and ankle on opposite sides follow similar triangular or half-teardrop pattern.

13Richard Williams ASKWilliams shows a similar half-teardrop path of action in the motion of the ankle.

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Rotation BalanceIt takes less effort if you balance the rotation of the lower body with an opposite rotation of your upper body.Moving your legs (and hips) as you walk requires a torque (rotational force) to turn them.Katie Corna15Demo: The TwistTry dancing The Twist in the normal way, moving the hips opposite from the shoulders. Then try to dance it the wrong way, moving hips and shoulders together, back and forth.

16Joints & Levers

17Toy Story (1995)Pixars Toy Story, directed by John Lasseter, was the first full-length feature film using computer animation.

Tin Toy (1988, Pixar), also directed by Lasseter, won an Oscar in 1988 for Animated Short Film.18Tin Toy (1988)http://www.youtube.com/watch?v=vNZtl5SZvbM

19The Polar Express (2004)The Polar Express was first full-length feature film made entirely with motion-capture animation.

20Uncanny ValleyParadoxically, as computer generated characters get more realistic they start to be creepy.Realism Appeal

Emily Project

PolarExpressShrek 1BeowulfToy StoryTin Toyhttp://www.youtube.com/watch?v=GBgURIUQ70021Realism TightropeThe uncanny valley occurs when some elements are more realistic than others.

Our human instincts warn us something is wrong.Realistic Image Appeal Realistic MotionCompletely NaturalTolerableRepulsive

RepulsiveRobotZombieTolerable22Articulated Figures

In computer animation characters are articulated figures, like marionette puppets.

The challenge for animators is to move all the elements (arms, legs, hands, etc.) believably from frame to frame.23JointsRevolute JointPrismatic Joint (Slider)Two kinds of joints: Revolute (rotation) and Prismatic (extension/contraction).Nearly all joints in animals are revolute joints24Axis of RotationRotation occurs around a line called the axis of rotation.The axle is the axis of rotation for a set of wheels.25Revolute JointsRevolute joints may have a single axis of rotation, like hinge joints and pivot joints, or a variable axis, such as the ball and socket joint.

ElbowShoulder

Forearm26Forward Kinetics

With forward kinetics (FK) the animator has to specify the axis of rotation and the angle of rotation for each joint on a moving limb.Lift the arm by a shoulder rotationMove forearm by an elbow rotation27

Forward KineticsForward kinetics (FK) is a tedious process for the animator and it is difficult to maintain certain constraints, such as the planted foot in a walk.28

Inverse KineticsWith inverse kinetics (IK) the animator positions the end effector, such as the hand, and the computer calculates the required joint rotations.29Inverse KineticsRotations calculated by the computer using IK are not always natural poses performed by a person. Furthermore, the timing may not be correct.Ball & SocketBall & SocketHingexxRaising hand into High Five poseAwkwardIK PoseElbowWristShoulder30Understanding RotationJust like any other type of motion, rotation is governed by Newtons laws:

Law of Inertia Law of Acceleration Action-Reaction Principle

Lets see how inertia, force, reaction, etc. appear in the context of rotational motion.

Sir Isaac Newton31Mass is a measure of inertia for linear motion.

Rotational inertia is similar concept for rotation.

InertiaMmGold brickNormal brickDifficult to moveEasy to movexxWood BatPlastic Pee-wee BatDifficult to RotateEasy to Rotate32Rotational InertiaRotational inertia depends on: Total mass of the objectHow the mass is distributed

The farther the objects mass is from the axis of rotation, the larger the rotational inertia. 33Demo: Inertia SticksTwo metal pipes of the same massRotateLeadweightsEasytoRotateHardtoRotateAxis ofRotation34Human Rotational InertiaIn which pose does the dancer have a larger rotational inertia?

Axis of RotationABPose APose BSame for A & B since mass is unchanged.

35Human Rotational Inertia

Axis of RotationABB) Pose B

Pose B has larger rotational inertia since the leg is extended, putting mass further from the axis of rotation.36Demo: Long LegsLong legs have greater rotational inertia than short legs so long legged animals have a slow walking stride.

37Drag of Articulated LimbsFast SwingSlow SwingSlowFast

The greater rotational inertia of longer limbs results in drag, just like with hair and fabrics. 38

Demo: Drop the StickTwo meter sticks stand upright against a wall; one has a hunk of clay on the end. Which stick will swing down and hit the floor first?The one without the hunk of clay.Why?Clay increases rotational inertia, which slows the rotation.Axis of Rotation39

Demo: Drop the StickAxis of RotationX CGX CGAnother way to understand why the weighted stick takes longer to fall is that its center of gravity is higher.

The higher it is, the longer it takes for an object to fall to the ground.Longer stick tips over more slowly40

Tripping and FallingAxis of RotationX CGX CGIf small child trips, he hits the ground more quickly than an adult.Can view this two ways:*Child has small rotational inertia.*Childs center of gravity is initially closer to the ground.41Demo: Hammer Balance

BAAxis of RotationIn which case is the hammer easier to balance on your finger?

Case ACase BThe same for A & B

42Demo: Hammer BalanceB) Case BIn Case B the rotation is slower and thus easier to balance.In case B the rotational inertia is greater because most of the mass is far from the axis of rotation (at your fingertip).

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