Spatial Reasoning

3D Spatial Reasoning

Core spatial math for placing objects correctly in OpenUSD scenes.

Coordinate System

• Stage: Z-up, metersPerUnit=1.0 (meters)
• All placement coordinates are in meters
• Rotations: always AddRotateXYZOp() — never individual axis ops

metersPerUnit Conversion (CRITICAL)

Assets have their own metersPerUnit. Common values:

• 1.0 = meters (robots, environments)
• 0.01 = centimeters (most KION lightspeed assets, SimModelAnimation, compositions)

Rule: Before referencing any asset, read its metersPerUnit:

asset_stage = Usd.Stage.Open(asset_path)  # Must use Usd.Stage, NOT Sdf.Layer
mpu = UsdGeom.GetStageMetersPerUnit(asset_stage)

Sdf.Layer.FindOrOpen() FAILS SILENTLY on binary .usd crate files — always returns None. Never use it for mpu detection.

Getting real-world size of an asset:

bbox_cache = UsdGeom.BBoxCache(Usd.TimeCode.Default(), [UsdGeom.Tokens.default_])
raw_range = bbox_cache.ComputeWorldBound(default_prim).ComputeAlignedRange()
raw_size = raw_range.GetMax() - raw_range.GetMin()
real_size_meters = [raw_size[i] * mpu for i in range(3)]

Transform Matrix Order (CRITICAL)

When placing an asset with scale + rotation + translation:

# CORRECT: Translate * Rotate * Scale
# Scale shrinks asset to meters, Rotate orients it, Translate positions it
scale_mat = Gf.Matrix4d().SetScale(Gf.Vec3d(mpu, mpu, mpu))
rot_mat = Gf.Matrix4d().SetRotate(Gf.Rotation(Gf.Vec3d(0,0,1), heading_deg))
trans_mat = Gf.Matrix4d().SetTranslate(Gf.Vec3d(x, y, z))
xf.MakeMatrixXform().Set(trans_mat * rot_mat * scale_mat)

WRONG: scale * translate scales the translation vector too — a 3m offset becomes 0.03m for mpu=0.01.

Placement Helper

def place(stage, prim_path, asset_path, x, y, z=0, rot_z=0, mpu=0.01):
    """Place an asset with correct metersPerUnit scaling."""
    prim = stage.DefinePrim(prim_path, "Xform")
    prim.GetReferences().AddReference(asset_path)
    xf = UsdGeom.Xformable(prim)
    S = Gf.Matrix4d().SetScale(Gf.Vec3d(mpu, mpu, mpu))
    R = Gf.Matrix4d().SetRotate(Gf.Rotation(Gf.Vec3d(0,0,1), rot_z))
    T = Gf.Matrix4d().SetTranslate(Gf.Vec3d(x, y, z))
    xf.MakeMatrixXform().Set(T * R * S)
    return prim

Look-At Camera Math

def look_at_rotation(cam_pos, target_pos):
    """Compute XYZ Euler rotation for camera to look at target. Z-up stage."""
    dx = target_pos[0] - cam_pos[0]
    dy = target_pos[1] - cam_pos[1]
    dz = target_pos[2] - cam_pos[2]
    horiz = math.sqrt(dx*dx + dy*dy)
    pitch = math.degrees(math.atan2(horiz, -dz))
    yaw = math.degrees(math.atan2(dx, -dy))
    return Gf.Vec3f(pitch, 0, yaw)

Grid Layout

def grid_positions(n_items, spacing, origin=(0,0)):
    """Generate grid positions for n items with given spacing."""
    cols = min(8, math.ceil(math.sqrt(n_items * 1.5)))
    positions = []
    for i in range(n_items):
        row, col = divmod(i, cols)
        x = origin[0] + col * spacing
        y = origin[1] + row * spacing
        positions.append((x, y))
    return positions, cols

Baked Waypoint Animation

See bake_waypoints() in scripts/spatial.py (28 lines).

Zone Boundary Check

def in_zone(x, y, zone):
    """Check if (x,y) is within a zone dict with 'x':[min,max], 'y':[min,max]."""
    return zone['x'][0] <= x <= zone['x'][1] and zone['y'][0] <= y <= zone['y'][1]

Shell vs Interior Coordinate Alignment (CRITICAL)

The KION mega warehouse shell at mpu=0.01 is ~170×100m in stage meters. When placing interior cubes/assets at specific zone coordinates (e.g., racks at X=30-60), the camera must be positioned WITHIN the layout zone, not at the building origin.

Hero camera rule: Place camera at (zone_start_x + 3, zone_center_y, 2.5) looking INTO the zone — never at (0, y, z) which will be inside the shell wall geometry.

Top-down camera rule: Place at (layout_center_x, layout_center_y, max(W,D)*0.9) with focal 12mm. This is the money shot for layout validation — always render this first.

Camera-to-layout match: Before rendering, verify camera pos is inside the bounding box of your placed content, not just inside the shell.

Render File Size Validation

If all renders within a stage have identical byte counts, the camera path switch didn't take effect. Fix: create a fresh camera prim for each shot (remove + redefine), not just change the path.

KION Asset Scale Map (CRITICAL — 2026-03-14)

The KION asset tree has MIXED units. ALWAYS validate with Usd.Stage.Open() + UsdGeom.BBoxCache:

Rule: ONLY Shell + Lighting need 0.01. ALL other KION assembly assets are in meters.

Placing meter-scale assets at mpu=0.01 makes them 100× too small (invisible). This bug silently breaks scenes — assets "exist" in USD but render as sub-centimeter specs.

Validation command:

stage = Usd.Stage.Open(asset_path)
bbox = UsdGeom.BBoxCache(0, [UsdGeom.Tokens.default_]).ComputeWorldBound(stage.GetPseudoRoot()).ComputeAlignedRange()
size = bbox.GetMax() - bbox.GetMin()
# If any dimension > 1000 → centimeters (use 0.01)
# If all dimensions < 100 → meters (use 1.0)

Common Gotchas

0a. Shell interior bounds ≠ shell bbox — sm_warehouse_mega bbox is (-13.2,-5.2)→(172.6,136.8) but Corner module starts at X=0.6 and Center (floor) at X=11.6. Actual usable interior: X=3-170, Y=0-134. Always check module children bboxes, not just root. 0b. UsdGeom.Cube extent is [-1,1]³ (size 2) — scale by w/2, d/2, h/2 NOT w, d, h. Using full dimensions makes every block 2× its intended size. This caused 14,570 phantom clashes in uber warehouse v2. 0b. SetTranslateOnly() WIPES scale from Gf.Matrix4d — if you set mat[0][0]=0.01 then call mat.SetTranslateOnly(...), the scale reverts to identity. Build the matrix with explicit 16 floats: Gf.Matrix4d(sx,0,0,0, 0,sy,0,0, 0,0,sz,0, tx,ty,tz,1). This caused a 100× shell scaling bug.

1. Sdf.Layer.FindOrOpen fails on binary .usd crate files — use Usd.Stage.Open
2. Matrix order: T * R * S not S * R * T
3. Cameras default look along -Z in camera space = straight down in Z-up stage (no rotation needed for top-down)
4. xformOp:translate already exists in xformOpOrder → use MakeMatrixXform() instead of AddTranslateOp()
5. DHGen humans already have xformOps defined — must use MakeMatrixXform() which clears and replaces
6. Shell is ~170×100m — layout area is usually a subset. Camera must be inside the layout area, not at origin.
7. Isaac Sim vp.camera_path sometimes silently fails between rapid renders — always create fresh camera prim with stage.RemovePrim() + UsdGeom.Camera.Define() for each shot
8. RT2 needs 200+ settle frames for convergence. Less = noisy/incomplete renders.

Lessons Learned — GSRC Integration (2026-03-12)

Scaling Awareness

• When placing large equipment (50m+ footprint), the facility MUST grow proportionally
• A 58×83m module in a 120×80m warehouse = impossible overlap
• Always calculate: equipment_area / facility_area — if > 30%, facility needs to grow

Collision Prevention

• Before placing a new zone, check all existing zone bounding boxes
• Zone overlaps are the #1 failure mode when scaling up quickly (V7/V8 had overlaps)
• Use coordinate-based collision detection: if new_x_range overlaps existing_x_range AND new_y_range overlaps existing_y_range → collision

Variation Workflow

• Build ONE variation at a time — render — show — get feedback — iterate
• Don't batch multiple variations without showing intermediate results
• Each variation should have a distinct spatial philosophy, not just moved zones

Occupancy Map as Validation

• Generate occupancy map after each variation as a spatial sanity check
• If free_space% < 40%, the layout is too dense for robot navigation
• If free_space% > 80%, the layout has too much wasted space
• Sweet spot for warehouses: 55-70% free space

Advanced Topics

See advanced.md for details.