1. COMPUTER GRAPHICS CHAPTER 35 CS 482 – Fall 2017 ANIMATION
ANIMATION PROCESSES
INTERPOLATION-BASED ANIMATION
HARDWARE ISSUES
KINEMATICS
DYNAMICS

2. ANIMATION PROCESSES MOTION PERCEPTION CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 257

3. TRADITIONAL ANIMATION PROCESS
ANIMATION PROCESSES
TRADITIONAL ANIMATION PROCESS
Storyboards
Dialogue
Sketching
In-Betweening
Inking
Painting
Backgrounds
Photographing
Editing
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 258

4. COMPUTER ANIMATION PROCESS
ANIMATION PROCESSES
COMPUTER ANIMATION PROCESS
Storyboards
Staging
Set Modeling
Keyframing
Shading
Effects
Lighting
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 259

5. INTERPOLATION-BASED ANIMATION
KEYFRAMES
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 260

6. INTERPOLATION-BASED ANIMATION
ARTICULATION VARIABLES
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 261

7. HARDWARE ISSUES SCREEN REFRESH
Among the tasks of the video controller is the refreshing of the display.
Two primary approaches have arisen over the years: progressive scan, in which scanlines are refreshed in a top to bottom fashion, and interlaced scan, in which refreshes alternate between the odd-numbered and even-numbered scanlines.
The interlaced approach cuts the required bandwidth in half, and is therefore preferred by most television broadcasters.
Progressive scan reduces the “comb” effect and “twitter” in the image, and is therefore preferred by most computer and software manufacturers.
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 262

8. HARDWARE ISSUES DOUBLE BUFFERING
When a display refreshes faster than the processor can render the next frame, the swapped buffer contains a “torn” image (with some pixels filled with the previous frame’s image and some from the current one).
When vertical synchronization is activated, the buffer swap is delayed until the current frame has been completely processed, eliminating the image quality issue, but the animation suffers latency problems.
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 263

9. HARDWARE ISSUES TRIPLE BUFFERING
By keeping two back buffers at all times, and alternating their being filled, the front buffer can be swapped with the most recently filled back buffer, reducing latency while maintaining image quality.
Double Buffering w/o vsync:
Double Buffering w/vsync:
TRIPle Buffering:
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 264

10. KINEMATICS STANDARD JOINT TYPES Revolute Joint (1 DOF)
Translational Joint (1 DOF)
Cylindrical Joint (2 DOF)
Spherical Joint (3 DOF)
Planar Joint (3 DOF)
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 265

11. TREE-BASED HIERARCHICAL MODEL
KINEMATICS
TREE-BASED HIERARCHICAL MODEL
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 266

12. KINEMATICS SKELETON HIERARCHY CS 482 – Fall 2017 CHAPTER 35: ANIMATION
PAGE 267

13. KINEMATICS TWO APPROACHES Inverse Kinematics Forward Kinematics
The modeler rotates or moves individual joints to pose and animate the joint chains
Inverse Kinematics
The modeler moves a handle to pose the entire joint chain
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 268

14. KINEMATICS FORWARD KINEMATICS
When rigging a character using forward kinematics, any given joint can only affect parts of the skeleton that fall below it on the joint hierarchy.
For example, rotating a character's shoulder changes the position of the elbow, wrist, and hand. However, moving the hand only moves the hand and fingers.
When using forward kinematics, an animator typically needs to set the rotation and position of each joint individually.
To achieve a desired pose, the animator works through the joint hierarchy sequentially: root, spine, shoulder, elbow, etc.
The final position of a terminating joint (like a knuckle) thus depends on the joint angles of every joint above it in the hierarchy.
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 269

15. KINEMATICS INVERSE KINEMATICS
Inverse kinematics is the reverse process from forward kinematics, and is often used as an efficient solution for rigging a character's arms and legs.
With inverse kinematics, the terminating joint is directly placed by the animator, while the joints above it on the hierarchy are automatically interpolated by the software.
For example, when moving the hand's inverse kinematics controls, all unconstrained joints above the hand will be affected.
Inverse kinematics is most appropriate when the animation calls for a terminating joint to be placed very precisely; the animator merely positions certain body parts in a goal position rather than the having to adjust their position joint-by-joint.
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 270

16. CASE STUDY: TWO-LINK ARM
KINEMATICS
CASE STUDY: TWO-LINK ARM
Forward Kinematics:
𝑥= 𝐿 1 cos 𝜃 1 + 𝐿 2 cos 𝜃 1 + 𝜃 2
𝑦= 𝐿 1 sin 𝜃 1 + 𝐿 2 sin⁡( 𝜃 1 + 𝜃 2 )
Inverse Kinematics:
𝑥 2 = 𝐿 cos 2 𝜃 1 +2 𝐿 1 𝐿 2 cos 𝜃 1 cos ( 𝜃 1 + 𝜃 2 ) + 𝐿 cos 2 ( 𝜃 1 + 𝜃 2 )
𝑦 2 = 𝐿 sin 2 𝜃 𝐿 1 𝐿 2 sin 𝜃 1 sin ( 𝜃 1 + 𝜃 2 ) + 𝐿 sin 2 ( 𝜃 1 + 𝜃 2 )
𝑥 2 + 𝑦 2 = 𝐿 𝐿 𝐿 1 𝐿 2 cos 𝜃 1 cos 𝜃 1 cos 𝜃 2 − sin 𝜃 1 sin 𝜃 sin 𝜃 1 ( sin 𝜃 1 cos 𝜃 2 + cos 𝜃 1 sin 𝜃 2 )
= 𝐿 𝐿 𝐿 1 𝐿 2 cos 𝜃 2
𝜃 2 = cos −1 𝑥 2 + 𝑦 2 − 𝐿 1 2 − 𝐿 𝐿 1 𝐿 2 L2
tan 𝜃 3 = 𝑦 𝑥 tan 𝜃 4 = 𝐿 2 sin 𝜃 2 𝐿 2 cos 𝜃 2 + 𝐿 1
𝜃 1 = 𝜃 3 − 𝜃 4
tan 𝜃 1 = tan ( 𝜃 3 − 𝜃 4 ) = tan 𝜃 3 − tan 𝜃 tan 𝜃 3 tan 𝜃 4 = 𝑦 𝑥 − 𝐿 2 sin 𝜃 2 𝐿 2 cos 𝜃 2 + 𝐿 𝑦 𝑥 𝐿 2 sin 𝜃 2 𝐿 2 cos 𝜃 2 + 𝐿 1
= 𝑦 𝐿 2 cos 𝜃 2 + 𝐿 1 −𝑥 𝐿 2 sin 𝜃 2 𝑥 𝐿 2 cos 𝜃 2 + 𝐿 1 +𝑦 𝐿 2 sin 𝜃 2
𝜃 1 = tan −1 𝑦 𝐿 2 cos 𝜃 2 + 𝐿 1 −𝑥 𝐿 2 sin 𝜃 2 𝑥 𝐿 2 cos 𝜃 2 + 𝐿 1 +𝑦 𝐿 2 sin 𝜃 2 y L1 2 4 3 1 x
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 271

17. DYNAMICS MASS-SPRING SYSTEMS
Various movements may be simulated by means of spring models.
Musculature
Curly Hair
Energy Storage & Release During Running
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 272

18. DYNAMICS COLLISION DETECTION
Animation frequently requires the detection of collisions occurring between objects in the scene.
Determining collisions against a bounding box or a bounding sphere is computationally simple, but might detect collisions that might not be accurate against the original mesh
Determining collisions against the convex hull (the smallest convex polyhedron containing the original mesh) is a reasonable compromise – more precise than using a bounding box or sphere, and less computationally complex than using the original mesh
Determining precise collisions with a non-convex polyhedron is usually too computationally complex to implement
CS 482 – Fall 2017
CHAPTER 35: ANIMATION
PAGE 273