Computer Graphics · Cluster
Animation
Keyframes, skinning, and simulation.
- 01 Keyframe Interpolation and the Cubic Hermite Segment How a sparse animation channel becomes a continuous function of time, why cubic tangents carry units of value per second, and which degenerate segments an evaluator must survive.
- 02 Slerp, Squad, and the Cost of Interpolating Rotations Why component-wise quaternion interpolation fails, what slerp computes and what it costs, and how squad and exponential maps extend the same idea to a whole curve.
- 03 From Joint Hierarchy to Skinning Palette How parent-relative joint transforms compose into world matrices, why the bind pose is stored as an inverse, and what a skeleton costs to upload every frame.
- 04 Linear Blend Skinning and the Candy-Wrapper Collapse Why averaging joint matrices produces volume loss and pinching on twisted limbs, how dual quaternions replace the average, and why dual quaternion skinning is not always the better choice.
- 05 Keyframe Reduction and the Error Metric That Decides It How a dense sampled curve becomes a sparse key list, why the error must be measured against the reconstructed curve and not the original samples, and where per-channel reduction breaks a skeleton.
- 06 Inverse Kinematics and the Jacobian It Iterates How an end-effector target becomes joint angles, why the Jacobian transpose and pseudoinverse solve the same problem differently, and where singularities make both of them fail.
- 07 Additive Animation Layers and the Weights That Normalize Them How a delta pose composes onto a base without double-counting, why blend weights need a normalized space, and how the same arithmetic mixes clips, layers, and states.
- 08 Stability Limits of Explicit Integration in Dynamics Why forward Euler and Verlet diverge above a step size bound, where the bound comes from, and how a hair or cloth solver stays stable past the limit that breaks a rigid-body integrator.
- 09 Position-Based Dynamics and the Projection It Iterates How a cloth or rope is simulated by moving points to satisfy constraints directly, why the solver iterates rather than solving, and how stiffness becomes an iteration count.
- 10 Sequential Impulse and the Contact It Solves One Pair at a Time How a rigid-body contact constraint is solved as a sequence of per-contact impulses, why warm starting makes the solver converge, and what happens when too many contacts share one body.