Animation,Motion Capture,KeyframingAdrien Treuillesource: http://scaq.blogspot.com/2006_11_01_archive.htmlOverviewAnimation Intro Cell AnimationKeyframingPhysical SimulationPDEsOverviewAnimation IntroCell AnimationKeyframingPhysical SimulationPDEsWhat is animation?GraphicsAnimation = × TimeCell AnimationSquash and StretchUse distortions to convey flexibilityKeyframingData-driven AnimationPhysics-based AnimationWhat do you need to know?•No project on this material.•No need to memorize the mathematics in this lecture.•Need to understand the basic ideas.•Need to understand mathematics of subsequent lectures:•PDEs / Particle SystemsOverviewAnimation IntroCell AnimationKeyframingPhysical SimulationPDEsOverviewAnimation IntroCell AnimationKeyframingPhysical SimulationPDEsTraditional Cel Animation• Film runs at 24 frames per second (fps)– That’s 1440 pictures to draw per minute• Artistic issues:– Artistic vision has to be converted into a sequence of still frames– Not enough to get the stills right--must look right at full speed» Hard to “see” the motion given the stills » Hard to “see” the motion at the wrong frame rate• Each frame is drawn by handTraditional Animation: The Process• Key Frames– Draw a few important frames in pencil» beginning of jump, end of jump and a frame in the air• Inbetweens– Draw the rest of the frames• Painting– Redraw onto clear sheet of plastic called a cel, color them in- Use one layer for background, one for object- Can have multiple animators working simultaneously on different layers, avoid re-drawing and flickering- Draw each separately- Stack them together on a copy stand- Transfer onto film by taking a photograph of the stackExamplePrinciples of Traditional Animation[Lasseter, SIGGRAPH 1987]• Stylistic conventions followed by Disney’s animators and others• From experience built up over many years– Squash and stretch -- use distortions to convey flexibility– Timing -- speed conveys mass, personality– Anticipation -- prepare the audience for an action– Followthrough and overlapping action -- continuity with next action– Slow in and out -- speed of transitions conveys subtleties– Arcs -- motion is usually curved– Exaggeration -- emphasize emotional content– Secondary Action -- motion occurring as a consequence– Appeal -- audience must enjoy watching itSquash and StretchUse distortions to convey flexibilityPrinciples of Traditional AnimationSquash and StretchUse distortions to convey flexibilityDefines the rigidity of the material Gives the sense that the object is made out of a soft, pliable material.Elongating the drawings before and after the bounce increases the sense of speed, makes it easier to follow and givesmore snap to the action.The ball on the left moves at a constant speed with no squash/stretch. The ball in the center does slow in and out with a squash/stretch.The ball on the right moves at a constant speed with squash/stretch.ExampleTiming & MotionSpeed conveys mass, personalityA heavier object takes a greater force and a longer time to accelerate and decelerateA larger object moves more slowly than a smaller object and has greater inertiaMotion also can give the illusion of weight For example, consider a ball hitting a boxhttp://www.siggraph.org/education/materials/HyperGraph/animation/character_animation/principles/timing.htmAnticipationPrepare the audience for an actionDon’t surprise the audienceDirect their attention to what’s importantFollow Through and Overlapping Action The termination of an action and establishing its relationship to the next action Audience likes to see resolution of actionDiscontinuities are unsettlingSecondary ActionMotion occurring as a consequenceThe Mathematics of Squash and StretchOverviewAnimation IntroCell AnimationKeyframingPhysical SimulationPDEsOverviewAnimation IntroCell AnimationKeyframingPhysical SimulationPDEsKeyframing BasicsHow Do You Interpolate Between Keys?Keyframing BasicsKeyframing BasicsKeyframe basics•For each variable, specify its value at the “important” frames. Not all variables need agree about which frames are important.•Hence, key values rather than key frames.•Create path for each parameter by interpolating key values.paramsframeskey valuesinterpolated valuesKeyvalueInterpolationFramesParamsProblems with Interpolation• Splines don’t always do the right thing• Classic problems–Important constraints may break between keyframes»feet sink through the floor»hands pass through walls–3D rotations»Euler angles don’t always interpolate in a natural way• Classic solutions:–More keyframes!–Quaternions help fix rotation problemsOverviewAnimation IntroCell AnimationKeyframingPhysical SimulationPDEsOverviewAnimation IntroCell AnimationKeyframingPhysical SimulationPDEsExamplesBird FlightPublished in ACM Transactions on Graphics (SIGGRAPH 2003)angle of attackspreadfeatherwrist bendtail bendelbow bendforearm twistshoulder(quaternion joint)tail spreadtail twistFigure 2: The bird skeleton. Note that in order to model both twistand bend movement, the forearms and the tail are each divided intotwo links. The actuated joints are shoulder × 2, elbow bend × 2,forearm twist × 2, wrist bend × 2, tail bend, tail twist, and tailspread. The shoulder joint has 3 DOFs and the other joints each has1 DOF. The trunk has 6 DOFs representing its global position andorientation.bend springstwist springaerodynamicforces Figure 3: Left: Angular springs on a feather. Right: Becauseof vane asymmetry, air pressure may create different amounts offorces on both sides of the shaft and cause the feather to rotatearound its shaft.torque. To avoid the concentration of mass at the front edge of thewing because of the massless feathers, links with feathers are ex-tended in the direction of feather growth for a more accurate massdistribution.4.1 Wingbeat parameterizationIn order to represent the desired DOF patterns q∗(t) for a wing-beat, we use a set of wingbeat parameters u. The size of u definesthe dimensionality of the search space for the optimization and di-rectly impacts the performance of the optimization process. It is,therefore, important that we specify each wingbeat using as fewparameters as possible while still giving the bird enough maneuver-ability. The parameters are shown in Table 1. The superscripts uand d indicate upstroke and downstroke parameters. Most of theseparameters are replicated for the left and
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