Cutting-surface reconstruction: matched mechanisms and remaining gaps#

This page evaluates visual topology and motion binding only. A visible kerf is not evidence of correct mechanical separation; native particle connectivity, contact and momentum remain independently scored.

Implemented from paper III-F#

Tofu and banana now share one reference-configuration surface reconstruction:

  1. primal links of a uniform reference grid store Hermite intersection points and unit normals for the original boundary and recorded blade surfaces;

  2. a candidate link disconnects only after native particle histories locally contain side digits 1 and 2 for that cut, so unassigned material below a partial cut remains connected;

  3. while material remains connected, remaining-link components are computed per cell with one QEF dual vertex per local region; once saved native mechanical components are disjoint, each is rebuilt as a closed local volume clipped by its recorded cut half-spaces, so a triangle cannot share incompatible motion fields;

  4. a complete cut creates coincident faces with opposing normals for adjacent components;

  5. every surface representative inherits a native mechanical component and persistent cut code, then follows a compatible TLMPM motion field through fixed trilinear weights.

Analytical acceptance covers original Hermite points on the zero level set, unit normals, a closed uncut surface, two components after a complete cut, four components after orthogonal intersecting cuts, a connected lower bridge for partial cuts, opposing cap normals, no open edges and no degenerate triangles. Replay adds no visual opening; the currently published parallel complete-cut tasks also do not mix native mechanical components within one triangle.

Surface stability and RTX presentation#

The cut-push gallery uses a repaired display surface and OVRTX path tracing. The old QEF solve retained weak tangent directions on the curved banana and clipped unstable representatives to cell edges. The repair drops singular directions below 10% of the leading value, retains the Hermite mass point in those directions, and triangulates concave dual quads using the better projected diagonal. Exact cut planes and native component membership remain constraints. This changes the reconstructed display mesh, not the saved particles or their mechanics.

Partial cut labels must not clip unlabelled material on the other side of a still-connected component. At 4.70 s, the banana’s third cut initially labelled only five particles on one side; the previous display incorrectly hid the right segment for one frame. Frame 94 was rerendered from native sample 470 after correcting this condition, with its neighboring states checked. Scanning all 161 banana and 121 tofu display states found no other affected frame. The receipt retains the original render hashes and the frame-specific repair; no neighboring frame was copied or interpolated.

In the initial banana diagnostic, inward-facing triangles against the analytic normal decreased from 540 to 8; the remaining flags lie at the non-differentiable authored end caps. The smooth flanks have none. Maximum reference-boundary residual decreased from 1.233 mm to 0.454 mm. Across the selected 0, 0.8 and 8 s probes, the largest vertex change from the old display was 1.834 mm in world coordinates. These are display-reconstruction diagnostics, not material-accuracy estimates. Selected-frame measurements retain both versions.

Soft area lights, PBR roughness and material-space fibre/cut-face textures describe appearance only. No vertex smoothing, temporal motion interpolation or new physics step is used. Cached disconnected reference topology is reused only while all native cut codes and component labels match; current saved x/F motion is evaluated again for every frame. OVRTX mesh points and object/camera transforms are read back for every rendered frame. The complete 20 fps replay covers 161 banana and 121 tofu frames; GIF playback remains uniformly slowed to 120 ms per frame.

Banana RTX receipt · Tofu RTX receipt. Original particle media and physical scores remain unchanged; historical gallery entries retain their original renderer hashes.

Remaining differences from the paper#

Paper capability

Current boundary

The finite blade edge sweeps each substep and disconnects the reference links it actually intersects online.

Replay recovers axis-aligned x/y planes from the saved blade path and combines them with persistent side labels. Lateral sweep beyond half a material-sampling spacing is rejected; arbitrary curved or tilted paths are unsupported.

Only cells affected during the current step are updated.

CPU replay rebuilds changed reference topology and reuses unchanged disconnected topology; it does not implement the authors’ local GPU update path.

Surface representatives embed directly in the compatible TLMPM motion field at that time.

Historical records did not save logical-grid motion fields. DexLab reconstructs each needed node by a local Gaussian average of the saved x/F affine predictions from compatible particles in the same mechanical component; a common affine field remains exact. Once a saved state is disconnected, this implementation also rebuilds each native mechanical component as a closed local volume instead of exactly reproducing the paper’s online per-cell update. Topology follows native history, while coarse particle deformation can still produce small outer-surface artifacts.

The authors’ surface-grid resolution and geometry assets.

These are unpublished. DexLab independently uses surface spacing equal to one quarter of the mechanical grid spacing; the banana remains an authored shape rather than the authors’ asset or a scanned specimen.

Independent motion after fully intersecting through-cuts.

Analytical tests cover four independent closed regions, but no formal record and public video yet qualify motion around the intersection line. The current crossed-scoring task covers shallow cuts whose lower bridge remains connected.

A new partial crack forming inside an already separated piece.

Complete cuts remain closed and split again when the next cut completes. The intermediate state where a later cut has started but not passed through a piece separated by an earlier cut is not independently qualified, so the final frame does not establish exact frame-by-frame equivalence to the paper.

Compact active states on GPU and real-time performance.

Unimplemented. Surface reconstruction runs offline in NumPy/SciPy, with VTK or OVRTX presentation, and cannot reproduce the paper’s timing result.

The supported straight-cut tasks may therefore be described as using paper-style linked volumes, Hermite data and local dual contouring. They are not a complete reproduction of the BladeMaster surface system. Each public media directory records source hashes, renderer hashes, resolution, frame mapping and these limits in provenance.json.

Cutting-fidelity matrix · Crossed shallow scoring · Continuous cutting and blade pushing · BladeMaster III-F