procedural-character-animation

name	procedural-character-animation
description	Animate a humanoid character entirely from continuous state — no spritesheet, no clips, no blend tree — using a joint skeleton, forward kinematics and two-bone IK. Use when building locomotion, crouch/prone, climbing, ladders, aiming or melee for a side-view character, when a walk "slides" or "looks canned", or when you need to judge animation quality without being able to watch it.

Animating a character with arithmetic

A pose is a list of ANGLES. The skeleton turns those into joint POSITIONS. The drawing turns positions into pixels. Change the numbers and the drawing follows for free — which is the whole reason to do it this way instead of drawing frames, because a clip cannot answer "he is moving at 2.7 m/s, aiming 31° up, three quarters of the way into a crouch", and that is the only question a player ever asks.

Rule 1 — the phase is advanced by DISTANCE, not by time

phase += travelled / stride        // NOT phase += dt * rate

A clip played at a rate is wrong the instant the rate changes, wrong on a slope, and wrong in a slide. A phase driven by odometry cannot be. This is the single line that stops the feet sliding, and foot slide is the one thing that tells a player an animation is canned.

It also means a change of gear needs no blend: the phase is continuous through it because the odometer is.

Rule 2 — the feet lead and the hips follow

The intuitive way round — swing the thigh, let the foot land where it lands — slides by construction. Instead:

1. Give each foot a TARGET. Planted, it is motionless in the world; swinging, it arcs forward. While planted its position relative to the body moves backward at exactly body speed, which is one line and is the whole trick.
2. Put the pelvis at whatever height keeps the planted leg inside its own length: sqrt(L² - x²). The rise and fall of walking, and the dip through double support, come out of the geometry. Never tune a bob.
3. Solve the legs backwards from the feet with two-bone IK.

Rule 2b — a held object is the target, and the HANDS follow it

Rule 2 applied one level up. Pose the arms from joint angles and then draw a weapon between the two hands, and everything is wrong for the same reason a swung thigh slides: the hands are half a forearm apart, so a few degrees of noise between them swings the muzzle thirty degrees, and nothing in the chain knows what the character is aiming at. A line of men all shooting at the same thing came out holding sticks at unrelated angles.

Invert it. Decide the aim direction, place the object along it, anchor it where it is actually held (a rifle's buttpad sits in the shoulder pocket — anchor at the grip and let it extend both ways and a quarter of a body length of stock hangs out behind the spine, through the chest), then solve BOTH hands onto it with two-bone IK, elbows biased down. Draw it from the same anchor and axis the hands were solved to, so the thing on screen and the thing being held cannot disagree.

Order matters and the fault is invisible in a still. The torso attitude — lean, twist, neck — moves the shoulders, and the shoulders are what the arms are solved FROM. Set them before solving the skeleton you IK against; set them after and you rotate the upper body out from under hands that were placed a moment earlier, differently for every character depending on his lean. The symptom is weapons at inconsistent heights across identical poses, and it reads as jitter in a transform rather than as the ordering bug it is.

Rule 3 — cadence is the primitive, stride is derived

cadence = f(speed)        stride = speed / cadence

Modelling stride directly and dividing for cadence looks equivalent and is not: it lets contact time grow with speed, and contact time × speed is exactly how far a planted foot travels relative to the hips. At sprint that came out at 1.3 m of travel for a 0.9 m leg, so the geometry answered by putting the hips at 0.44 of leg length — a duck-walk, measurable long before it was visible.

Corollary: leg length and stride are coupled. Shortening the legs to fix proportions will over-extend an existing stride and sink the hips. That is the geometry telling you the stride was too long.

Rule 4 — the ankle rolls, and the roll constant lives in ONE place

A straight leg from a hip to an ankle pinned on the floor forces the hips down at both ends of every step, and the figure squats along. Real ankles rise at heel-strike and toe-off (about ⅛ of leg length); the toe stays planted while the ankle pivots over it, so it costs no foot slide.

This constant is needed in two places — the stance solution and the flight arc's take-off height — and the two disagreed twice, each time putting a step of a fifth of a leg into the hips at the seam. Put it in one function.

Rule 5 — flight is ballistics, not a number that looked right

A body in free flight for t seconds rises g·t²/8, where t is the flight window over the cadence. Inventing the height put twelve pixels of rise into a window three hundredths of a second wide at the walk/run boundary — a pop, at exactly the moment the gait changes character. The true answer was one pixel; a sprinter's centre of mass really does only rise a couple of centimetres.

Rule 6 — a walk and a run differ by ONE number

Stance fraction: the share of the cycle each foot spends on the ground. Above a half, both feet are down for part of the cycle and it is a walk. Below it there is a window with neither and it is a run. Nothing else distinguishes them — not speed, not amplitude. Six "gears" is one gait sampled at six speeds.

Rule 7 — every non-walking state needs its own geometry

Do not reach for the walk with the numbers turned down.

• Prone has no clearance under the pelvis, so the walk's foot targets are unreachable and the IK folds the legs into the chest. Crawling is its own gait: legs nearly straight BACK along the ground at almost full extension (tucking them in leaves the knee nowhere to fold but through the floor), arms reaching forward of the shoulder — relative to the pelvis they land under his own chest, because prone the shoulder is a third of a body length ahead of the hips.
• Prone heads must be solved absolutely, and it is the FACE you are solving, not the skull. Inheriting the torso's lean when the torso is horizontal means staring at the floor. But solving the skull to point forward points the face at the floor too, because the face direction is PERPENDICULAR to the skull's axis — to look ahead off a horizontal body the neck cranes and the skull comes up toward vertical, which is what a man on his belly actually does. Getting this wrong twice in a row costs two rounds of "still looking down".
• A head held up off a prone body is the neck carrying it. Look ahead while moving; let it down to rest when stationary, lifting occasionally to check. Free, and it is the difference between a body and a mannequin lying down.
• Climbing: hang the body FROM the hands. They stay on the edge; the shoulders sit however far below them the arms are extended; folding the arms is what raises him. Setting y along a curve and letting the arms follow is the same thing backwards and looks exactly like a man being levitated past a ledge. And put the feet on the wall — hand-posed legs that never touch the surface are what make a climb read as a teleport with arm movement. Then clamp those foot targets to the ground beneath him: on a knee-high crate the "hang" position is below the floor, and the legs go into the terrain.
• A vault is not a slow climb. Below about half body height there is nothing to hang from: you plant a hand, drive off the legs and step over the top in one arc. Hanging off a knee-high crate looks like a man who has never seen a crate. Pick the move from the obstacle's height above what he is standing on, not from its height above the ledge.
• A kneel is the rear KNEE on the ground, and it is a contact point like a foot. Solve for where the FEET go and let the knees land where they may — the obvious approach, and the same mistake as swinging the thigh — and you get two horizontal thighs and two vertical shins: a man sitting on an invisible chair. Drop the pelvis until the thigh alone spans hip to floor, put the rear foot back far enough that the shin lies along the ground, and plant the front foot under the front knee.
• Ladders: four limbs IK'd to one vertical line, two beats out of phase, with the phase advanced by distance climbed. Same principle as Rule 1.

Rule 7b — a death is a SIMULATION, not a pose function

Everything above is a pose function because a walk is a cycle and a cycle has a parameter. A death is not a cycle: it never repeats, and what makes it read as death rather than as an animation is that it answers to how the character was standing, how fast he was going and which way he was facing at that instant.

So: a verlet ragdoll, its particles born on the joints of the pose he died in, distance constraints for the bones, gravity, a floor. Nobody authors a falling-over animation and nobody can, because there are as many of them as there are ways to be standing. Two things that are not obvious:

• The impulse goes in as a difference between position and PREVIOUS position — that is what velocity is in verlet. Setting the position instead teleports the body a pixel and leaves it standing still in the air.
• The floor is a constraint too, so it goes INSIDE the relaxation loop. Solving the bones and then clamping to the ground afterwards is the obvious order and it is wrong: the clamp gets the last word every tick, so it can pull a foot up while the hip stays put and leave that bone permanently over length. Interleaved, worst drift went from 25% to 9%.

Rule 8 — measure it, because you cannot watch it

Animation is the one thing a screenshot cannot show, and an agent cannot watch it at all. Assert on the properties a viewer would complain about:

• a planted foot does not move HORIZONTALLY (vertical movement is the roll)
• no knee ever bends backwards
• the hips never sink below ~0.8 of leg length
• hip height is CONTINUOUS across the cycle (this catches seams)
• the hips actually rise and fall
• the barrel points where the mouse is, to a fraction of a radian
• an arm is never longer than an arm
• a blocked pedestrian turns a few times a second, not sixty
• a climb never moves more than a few px PER FRAME (measure per frame, not per fraction of the move — a duration-blind metric passes a seven-pixel hop)

The trap: "hips stay up", "never levitate" and "height is continuous" are ALL perfectly satisfied by a dead-level line. A too-generous ankle roll once cancelled the geometric dip exactly, the figure glided, and every assertion stayed green. Assert the presence of motion, not only its absence of faults.

Rule 10 — vary it per step, or it reads as a machine

A gait computed from speed alone is exactly periodic, and exact periodicity is what reads as robotic. The give-away is not that any one step looks wrong — it is that every step looks identical.

Hash the variation on the STEP NUMBER, not a stream, so a replay reproduces it and two characters at the same speed do not wobble in unison; interpolate between this step's value and the next so nothing jumps at the plant.

What may vary and what may not: anything feeding back into where a foot is PLANTED must not, or the plant moves between the swing that placed it and the stance that holds it — foot slide, reintroduced through the back door. So leave stride and stance alone and put the variation into lift, swing amplitude, lean and the carriage of the head. Add a constant left/right asymmetry too: one leg lifting a little higher and the pair a hair off antiphase is most of what separates a person from a mechanism, and it costs one number.

Assert it: consecutive steps must differ (sampled during SWING — in stance the foot is planted and the knee is correctly identical every step), the same walk must repeat exactly, and the two legs must not be mirror images.

Also useful: contact sheets. One gait sampled across a full cycle, side by side. Foot slide, a limping knee and a hitch at the loop point are obvious in a row of stills and invisible in one.

Rule 9 — get an art critique from a vision model, repeatedly

You cannot see whether it looks like the character. Put a game frame beside a reference frame in front of a vision model and ask for a ranked, quantitative critique; implement; repeat. Five rounds found, among others:

• boots drawn DARKER than the background, so they read as holes
• shoulder span at half the reference's, which made the head look too big when the head was correct
• a highlight brighter than the reference's brightest fabric AND brighter than the background, so highlights read as objects stuck on
• the head outlined twice, nesting a black crescent inside its own silhouette
• the fist pinned in front of the body for every frame of the cycle — an animation bug no assertion caught
• the identity feature (a tri-lens goggle array) rotated ninety degrees

Drawing with discs, from the same reviews

If limbs are runs of overlapping circles, the review has concrete answers:

• Constant radius, never interpolated. Equal discs give a union with two straight parallel edges; an interpolated run is a cone, and a cone tapers at both ends, which is what reads as soft.
• Offset a highlight to TANGENCY, not to the centre. Put its centreline (limbR - hiR) off the axis so the discs touch the silhouette on the lit side. The lit edge then coincides with the outline and you get one hard edge free. Centred, you get two soft edges and none.
• Terminate runs at joints, never mid-limb: an end at a joint reads as a seam, an end mid-limb reads as a smear.
• An even value ladder beats a big jump. A reference garment steps about sixteen lightness at a time and never more than eighteen; ours jumped fifty-five in one step and read as plastic. And anchor the ladder high enough that the steps above the base are visible — the same ladder with the base too low buries the modelling inside the figure's own darkness.
• Gear is the character. A plate carrier is three stacked constant-radius runs; that plus shoulder caps, knee pads and a belt is four gear pieces and the biggest recognition gain available.

Two reviewers, not one, and give them no context. An art director asked about palette, value structure, composition and environment, and an animator asked ONLY about the figures and how they hold things — in terms a programmer can turn into a joint angle or an IK target ("the rear elbow should be below the weapon line", "the head leads the hips by half a head"). Hand each of them the game frame and the reference and nothing else: no explanation of what was built, no defence of it, no list of known issues. The animator found the arms-solved-before-the-lean ordering bug above, which no assertion caught and which had survived a dozen screenshots.

Ask for measurements, not impressions. Expect rounds to contradict each other as each reacts to the last overcorrection — converge, and let the geometry break ties where it can.