🚀 Support Field

Collision detection for convex shapes in Genesis relies heavily on support functions. Every iteration of the Minkowski Portal Refinement (MPR) algorithm asks questions of the form:

“Given a direction d, which vertex of the shape has the maximum dot-product v·d?”

A naïve implementation has to iterate over all vertices every time – wasteful for models containing thousands of points. To avoid this, Genesis pre-computes a Support Field for every convex geometry during scene initialisation. The implementation lives in genesis/engine/solvers/rigid/support_field_decomp.py.

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How It Works

1. Uniform Direction Grid – The sphere is discretised into support_res × support_res directions using longitude/latitude (θ, ϕ). By default support_res = 180, giving ≈32 k sample directions.

2. Offline Projection – For each direction we project all vertices and remember the index with the largest dot-product. The resulting arrays are:

   • support_v ∈ ℝ^{N_dir×3} – the actual vertex positions in object space.

   • support_vid ∈ ℕ^{N_dir} – original vertex indices (useful to warm-start SDF queries).

   • support_cell_start[i_g] – prefix-sum offset into the flattened arrays per geometry.

3. Taichi Fields – The arrays are copied into GPU-resident Taichi fields so that kernels can access them without host round-trips.

v_ws, idx = support_field._func_support_world(dir_ws, i_geom, i_batch)

The above gives you the extreme point in world-space for any query direction in O(1).

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Data Layout

Field	Shape	Description
support_v	(N_cells, 3)	vertex positions (float32/64)
support_vid	(N_cells,)	corresponding vertex index (int32)
support_cell_start	(n_geoms,)	offset into flattened arrays

!!! info “Memory footprint” With the default resolution each convex shape uses ≈ 32 k × (3 × 4 + 4) = 416 kB. For collections of small primitives this is significantly cheaper than building a BVH per shape.

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Advantages

• Constant-time look-ups during MPR ⇒ fewer diverging branches on the GPU.

• GPU friendly – the support field is a simple SOA array, no complex pointer chasing.

• Works for any convex mesh – no need for canonical-axes or bounding boxes.

Limitations & Future Work

• The direction grid is isotropic but not adaptive – features smaller than the angular cell size may map to the wrong vertex.

• Preprocessing and memory consumption would be expensive if the number of geometry is large in a scene.

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API Summary

from genesis.engine.solvers.rigid.rigid_solver_decomp import RigidSolver
solver   = RigidSolver(...)
s_field  = solver.collider._mpr._support  # internal handle

v_ws, idx = s_field._func_support_world(dir_ws, i_geom, i_env)

v_ws is the world-space support point while idx is the vertex ID in the original mesh (global index).

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Relation to Collision Pipeline

The Support Field is an acceleration structure exclusively used by the convex–convex narrow phase. Other collision paths – SDF, terrain, plane–box – bypass it because they either rely on analytical support functions or distance fields.

For details on how MPR integrates this structure see Collision, Contacts & Forces.