Knowledge / Animation / VFX / Game Design / Rigging and character animation

Rigging and character animation

Animation / VFX / Game Design (B.Sc / B.Des) · 3D · free study notes for exams, placements and interviews

In short

Rigging builds the controllable skeleton, deformers and control handles that let a static 3D model move; character animation is the keyframed or captured motion applied through that rig. The two are examined together because a rig is judged only by the poses it can hold without breaking, and animation is limited by the rig it drives. Indian university B.Sc/B.Des syllabi examine skeleton hierarchy, FK/IK, skinning and weighting, deformers, blend shapes, the 12 principles, cycles and the graph editor; placement tests ask for a clean rig file, a weighted arm bend and an 11-second acting shot or a walk cycle. Rigging TD and animator roles at DNEG India, Framestore Mumbai, Prana, 88 Pictures, Cosmos-Maya, Green Gold, Toonz, Phantom FX, Basilic Fly, Lakshya Digital and Ubisoft/Rockstar India hire on exactly these skills. Industry software is Maya, Blender, 3ds Max, Houdini, MotionBuilder, Unreal and Unity, with FBX, Alembic, USD and glTF as interchange formats.

Explained

Skeleton, joints and transform hierarchy

Forward and inverse kinematics, constraints, drivers

Skinning and weighting

Facial rigging

The 12 principles and animation workflow

Motion capture, retargeting and game pipelines

Key points

Formulas and examples

World matrix: M_world = M_local · M_parent_local · … · M_root_local (row-vector convention, as in Maya); a point transforms as p' = p · M_world. Units: scene units, usually 1 unit = 1 cm or 1 m — fix this before rigging.
Linear blend skinning: v' = Σᵢ wᵢ (Mᵢ Bᵢ⁻¹) v, with Σᵢ wᵢ = 1, wᵢ ≥ 0. v = rest position, Bᵢ = joint i's bind (rest) world matrix, Mᵢ = its current world matrix, wᵢ = weight.
Axis-angle to quaternion: q = (cos(θ/2), n sin(θ/2)), n = unit axis, θ = angle (degrees or radians — keep one). Slerp: q(t) = [sin((1−t)Ω) q₁ + sin(tΩ) q₂] / sin Ω, cos Ω = q₁·q₂.
Two-bone IK (lengths L₁, L₂; target distance d, clamped to |L₁−L₂| ≤ d ≤ L₁+L₂):
cos(elbow interior angle) = (L₁² + L₂² − d²) / (2 L₁ L₂)
cos(shoulder offset angle) = (L₁² + d² − L₂²) / (2 L₁ d)
Timing: frames = seconds × fps; seconds = frames / fps. Ballistic jump: h = ½ g t², t_up = √(2h/g), total air time = 2 t_up, g = 9.81 m/s².
Locomotion: speed = (steps per cycle × stride length) / (cycle frames / fps); root travel per frame = speed / fps.
Animation data size (game): bytes ≈ joints × channels × keys × bytes per key.

Example 1 — LBS at an elbow and the volume-loss artefact. Rest vertex v = (2, 0, 0) m near the elbow. Upper-arm joint A stays at identity; forearm joint B rotates 90° about Z through the origin. Weights wA = 0.7, wB = 0.3.

Example 2 — two-bone IK for an arm. Upper arm L₁ = 30 cm, forearm L₂ = 25 cm, hand target at d = 40 cm from the shoulder.

Example 3 — jump timing at 24 fps. A character's hips rise 0.5 m during a jump.

Example 4 — walk cycle speed and foot slide. A 24-frame cycle at 24 fps, 2 steps per cycle, stride 0.75 m per step.

Example 5 — game animation budget. A 70-joint skeleton, rotation only as quaternions (4 channels × 2 bytes compressed = 8 bytes per key), 30 keys per second, 2-second clip, keys on every frame.

FKIK
InputJoint rotationsEffector position
Best forArcs, free limbs, overlapFoot plants, props, contact
Failure modeHand drifts off a surfaceSnap/pop at reach limit, flipping knee
CostTrivialSolver per frame
Linear blend skinningDual quaternion skinning
BlendsMatrices linearlyRotations as dual quaternions
Twist 180°Candy-wrapper collapseHolds volume
BendVolume loss, creasingSlight bulge
Cost / supportCheapest, universal in enginesSlightly costlier, supported in Maya/Blender, limited in some engines
Joint-based faceBlend-shape face
DataFew extra jointsMany sculpted targets
ControlRotations, cheap, mocap-friendlyExact artist-authored shapes
Real-timeExcellentHeavier, but ARKit/MetaHuman standard
Typical useGames, crowdsFilm hero faces

Where it is used

Interview questions

Common mistakes

Related topics

3D modelling, texturing and UV mapping · Lighting, rendering and shaders · Principles of animation and storyboarding · Motion capture and virtual production · Game engines: Unity and Unreal · Cloth, hair and dynamics simulation

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