september6.ppt
- 1. Now Playing: Blue Monk from āNights of Ballads and Bluesā Recorded March 4, 1963 McCoy Tyner - Piano Steve Davis - Bass Lex Humphries - Drums Music By Thelonius Monk
- 2. 3D Transforms & Computer Animation Rick Skarbez, Instructor COMP 575 September 6, 2007
- 3. Announcements ā¢ Homework 1 is out today ā¢ Due at the end of class next Thursday ā¢ Tabitha Peck (tpeck@cs.unc.edu) is here to ask you to participate in her user study
- 4. ā¢ Introduced the concept of vector spaces ā¢ Learned the basic 2D transforms ā¢ Translation ā¢ Scaling ā¢ Rotation ā¢ Shearing ā¢ Talked about why we use homogeneous coordinates and transform matrices ā¢ Talked about how to compose transforms Last Time
- 5. Today ā¢ Discuss robot arm example from last class ā¢ Extend transforms to 3D ā¢ Aside: Talk about some principles of computer animation
- 6. Robotic Arm Example ā¢ Fingers first ā¢ Then wrist ā¢ Then elbow ā¢ Finally, shoulder
- 7. x y T1 R1 R2 R3 P Find the new location of P (Pā) after some translations T1, T2, T3, T4 and rotations R1, R2, and R3. Express in terms of a matrix product, i.e. Pā = R1R2R3P T2 T3 T4 Robotic Arm Example
- 9. x y Robotic Arm Example Pā Pāā = R3Pā = R3T4P Pāā R3
- 10. x y Robotic Arm Example Pāāā = T3Pāā = T3R3T4P Pāā T3 Pāāā
- 11. x y Robotic Arm Example P4 = R2Pāāā = R2T3R3T4P Pāāā P4 R2
- 12. x y Robotic Arm Example P4 T2 P5 P5 = T2P4 = T2R2T3R3T4P
- 13. x y Robotic Arm Example P5 P6 R1 P6 = R1P5 = R1T2R2T3R3T4P
- 14. x y Robotic Arm Example P6 P7 T1 P7 = T1P6 = T1R1T2R2T3R3T4P
- 15. x y Robotic Arm Example P6 P7 T1 P7 = T1P6 = T1R1T2R2T3R3T4P T1 R1 R2 R3 T2 T3 T4
- 16. x y Robotic Arm Example P7 = T1P6 = T1R1T2R2T3R3T4P P7 T1 R1 R2 R3 T2 T3 T4
- 17. 3D Transforms x y T x y z T Pretty much exactly the same as 2D transforms
- 18. Homogenous Coordinates in 3D Reminder: w = 1 for points w = 0 for vectors 2D 3D 3D 2D ā¢ Just as with 2D, need to add a w term ā¢ Normalizing is done in the same way as before
- 19. Cross Products ā¢ We talked about the cross product operator in the math lecture ā¢ Defined as ā¢ The cross product of 2 vectors is a vector perpendicular to both of the other two vectors ā¢ Wasnāt really applicable in 2D ā¢ Note that 2 vectors can make this true
- 20. Cross Product Direction ā¢ The direction of the resulting vector from a cross product can be determined by the āright hand ruleā ā¢ With your right hand, for P x Q ā¢ Point your thumb in the direction of P ā¢ Point your index finger in the direction of Q ā¢ Rotate your middle finger to be perpendicular to the thumb and index ā¢ This is the direction of P x Q
- 21. Coordinate Systems ā¢ This is why coordinate systems are sometimes referred to as left or right handed ā¢ Given x and y vectors, the direction of the z vector specifies its handedness +x +y +z +x +y +z Left-Handed Right-Handed
- 22. Translation in 3D ā¢ We will represent translation with a matrix of the following form: t is the x-offset u is the y-offset v is the z-offset
- 23. Scaling in 3D ā¢ We will represent scaling with a matrix of the following form: Ī± is the scale factor in the x-direction Ī² is the scale factor in the y-direction Ī³ is the scale factor in the z-direction
- 24. Rotation in 3D ā¢ Extending rotation to 3D is somewhat more complicated than either translation or scaling ā¢ In 2D, you could only rotate around 1 point ā¢ In 3D, you can rotate around any of the 3 axes ā¢ Each axis produces a slightly different rotation matrix
- 25. Rotation in 3D ā¢ Rotation about the z-axis is most familiar ā¢ Essentially, this is what we already did, in the z=0 plane
- 26. Rotation in 3D Rotation About The Z-Axis Rotation About The X-Axis Rotation About The Y-Axis
- 27. Rotation about any axis in 3D ā¢ How can we extend this to rotation about any axis, not just the principle axes? ā¢ Need to move the axis we want to rotate about to one of the principle axes (say, the z axis) ā¢ First, apply a rotation about x, to move the axis into the yz-plane (Rx) ā¢ Then, apply a rotation about y, to move the axis onto the z-axis (Ry) ā¢ Then apply your desired rotation, followed by the inverses of the other two (to reverse
- 28. Rotation about any axis in 3D Rtotal = Rx -1Ry -1RzRyRx
- 29. Rotation about any point and any axis in 3D ā¢ To rotate about a non-origin point, extend in the same way as in 2D ā¢ First, translate to the origin (Txyz -1) ā¢ Then apply your rotation (in the most general case, Rx -1Ry -1RzRyRx) ā¢ Then translate back (Txyz) Rtotal = Txyz Rx -1Ry -1RzRyRx Txyz -1
- 30. Transforms Recap ā¢ Robot Arm example ā¢ 3D transforms ā¢ Very similar to 2D transforms ā¢ Rotation is a bit more complex ā¢ Can rotate about any axis ā¢ Cross products ā¢ Coordinate systems ā¢ Left vs. right handed
- 31. Computer Animation ā¢ Can think of animation as objects being transformed over time ā¢ We have a ātimelineā that says what transforms are applied at what times ā¢ Each rendered image is one frame ā¢ The duration of each frame (say, 1/60 of a second for 60fps) is a single time step
- 32. āPrinciples of Traditional Animation Applied to 3D Computer Graphicsā ā¢ Lasseter noticed a trend ā¢ Computers were making animation easier than ever before ā¢ But animation was not getting better ā¢ Actually, it was often worse ā¢ Why? John Lasseter (Pixar), SIGGRAPH 1987
- 33. The Problem with Good Tools ā¢ Why was there so much bad animation? ā¢ New tools were allowing users with no experience to animate
- 34. The Illusion of Life ā¢ Many of the principles behind traditional animation were developed by Disney animators in the 1930s ā¢ The Illusion of Life ā¢ Lasseterās talk was intended to extend these principles to computer animation
- 35. The Principles 1. Squash and Stretch 2. Timing and Motion 3. Anticipation 4. Staging 5. Follow-through and Overlapping Action 6. Straight-ahead and Pose-to-pose Action 7. Slow In and Out 8. Arcs 9. Exaggeration 10.Secondary Action
- 36. Squash and Stretch ā¢ In the real world, only totally rigid objects (i.e. chairs, rocks) remain rigid when moving ā¢ Living things deform ā¢ So, if you want something to look āaliveā, you canāt just rigidly slide it around ā¢ Squash and stretch to emphasize motion
- 37. Squash and Stretch ā¢ Squash on contact ā¢ Stretch with motion (more ā faster) ā¢ Need to conserve volume ā¢ That is, if youāre stretching in x, need to squash in y and z
- 38. Squash and Stretch ā¢ Hinged objects (i.e. Luxo Jr.) can squash and stretch without deforming
- 39. Squash and Stretch Slow Motion Fast Motion Fast Motion w/S&S If objects overlap between frames, the eye can smooth the motion
- 40. Timing ā¢ The speed of motion gives us cues about ā¢ Weight ā¢ Size ā¢ Meaning ā¢ Motion must be āreadableā ā¢ Must take long enough for the viewer to see and understand ā¢ Must be quick enough to hold
- 41. Timing ā¢ Small and light objects should be fast and nimble ā¢ Large and heavy objects should be slow and lumbering
- 42. Keyframes and In- Betweening ā¢ Keyframes are frames in a sequence of animation that mark the beginning and end of a smooth transition ā¢ In-Betweens are the frames between a beginning and end keyframe ā¢ The in-betweens make the animation sequence appear smooth
- 43. Keyframes and In- Betweening Before After In-betweens
- 44. Timing ā¢ Imagine an animation where a person is looking over his left shoulder, then his right ā¢ No in-betweens: Hit by a strong force, head nearly snapped off ā¢ 1 in-between: Hit by a frying pan ā¢ 3 in-betweens: Dodging a flying object ā¢ 5 in-betweens: Giving an order (āCome over hereā) ā¢ 7 in-betweens: Looking around for something ā¢ 10 in-betweens: Stretching a sore neck ā¢ All from the same 2 keyframes!
- 45. Anticipation ā¢ There are 3 parts to any action 1. The preparation for the action (anticipation) 2. The action 3. The termination of the action (follow- through) ā¢ Can be anatomical preparation ā¢ Pulling back your foot before kicking ā¢ Or just to draw the viewersā attention ā¢ A character looking at something off- screen
- 46. Anticipation From Andre & Wally B, Lucasfilm CG, 1984
- 47. Anticipation From Luxo Jr., Pixar, 1987
- 48. Staging ā¢ When an action occurs ā¢ Make sure it is clear ā¢ Make sure it is visible ā¢ Only stage 1 important action at a time ā¢ In Luxo Jr, it is always clear which character is the center of attention ā¢ Action is more clearly visible in silhouette
- 49. Follow-through and Overlapping Action ā¢ When throwing a ball, your hand doesnāt just stop after the ball is released ā¢ When a multi-part object moves, usually one part will lead and the others will follow ā¢ i.e. In walking, motion starts at the hip, then the leg moves, then finally the foot ā¢ Therefore, sub-objects will begin and end their motions at different times
- 50. Follow-through and Overlapping Action ā¢ Overlapping means that you start a second motion before the first has completely finished ā¢ Blend the follow-through of one action into the anticipation of the next ā¢ āWhen a character knows what he is going to do he doesnāt have to stop before each individual action and think to do it. He has planned in advance in his mind.ā - Walt Disney
- 51. Straight-Ahead and Pose-to-Pose Action ā¢ Straight-ahead action is when an animator hand-composes all the frames in a scene ā¢ Sort of like a scene of all keyframes ā¢ Action looks wild and out-of-control ā¢ Pose-to-pose action is when an animator carefully composes individual important poses, and then tweens them ā¢ Used when timing and smoothness matter
- 52. Pose-to-Pose Action ā¢ To achieve smooth motions, you would normally work hierarchically ā¢ First, draw the keyframes ā¢ Then draw some inbetweens ā¢ Finally, draw all the remaining inbetweens
- 53. Pose-to-Pose Action ā¢ Computer animation is naturally hierarchical, but slightly different ā¢ Consider a jump ā¢ Create translation keyframes for the entire model ā¢ Add rotation/translation keyframes for arms ā¢ Add rotation/translation keyframes for legs ā¢ etc.
- 54. Slow In and Out ā¢ Refers to the spacing of the in- betweens ā¢ Instead of having an object move with constant velocity, allow the velocity to vary ā¢ Enforce continuity of 2nd and 3rd Slow Slow Fast
- 55. Arcs ā¢ Motion in nature almost always occurs in an arc ā¢ Not in straight lines ā¢ Even if you think the motion should be in a straight line, adding some variation will make it look more natural
- 56. Exaggeration ā¢ Can exaggerate ā¢ Shape of objects ā¢ Motion of objects ā¢ Sound ā¢ Character emotions ā¢ Exaggeration is āaccentuating the essence of an ideaā ā¢ Not just amplification, but removal of distraction
- 57. Exaggeration ā¢ Exaggeration should be used carefully ā¢ Use it too little, and the exaggerated things will stand out too much ā¢ Use it too much, and the scene will become unrealistic
- 58. Secondary Action ā¢ Include the actions that happen as a result of the primary action ā¢ One example would be the facial expression, while the body expresses the primary action ā¢ Another would be Luxo Jr.ās cord, which moves because it is attached to a moving body
- 59. Personality ā¢ The sum total of all the principles discussed before ā¢ The goal of animation is to produce something that a viewer wants to watch ā¢ The animator should have a consistent personality in mind when decided how to apply the principles ā¢ Need to know what you want before you start
- 60. Personality Simple things, like breaking symmetry add an level of complexity (and subtlety) to the character
- 61. Next Time ā¢ Introduction to OpenGL programming