trueform

About | TS

Research

The theory and publications behind trueform's algorithms.

Geometry pipelines accumulate defects. Sculpting, remeshing, format conversion—each step can introduce non-manifold flaps, inconsistencies, and surface artifacts. By the time geometry reaches your algorithm, it is rarely the ideal manifold most methods assume.

trueform is built around a simple idea: a mesh should be understood as an intended surface, observed through the noise of floating-point arithmetic and prior processing.

These defects are additive—they attach to the surface without creating holes. The underlying structure remains recoverable.

\mathcal{M}':\left\{\;\begin{smallmatrix} T' \\ G' \end{smallmatrix}\;\right\}

\mathcal{M}:\left\{\;\begin{smallmatrix} T' \cup T_\Delta \\ G' + G_\Delta \end{smallmatrix}\;\right\}

\cup\, \textcolor{#14b8a6}{T_\Delta} \sim \mathcal{D}_T

+\, \textcolor{#14b8a6}{G_\Delta} \sim \mathcal{D}_G

\mathcal{F}

Processing adds artifacts to the underlying mesh $\mathcal{M}'$ : topological noise $\textcolor{#14b8a6}{T_\Delta}$ (flaps, bad winding) and geometric noise $\textcolor{#14b8a6}{G_\Delta}$ (displaced vertices). Idealization $\mathcal{F}$ recovers $\mathcal{M}'$ from $\mathcal{M}$ .

This perspective shapes the algorithms:

Topological consistency. The intersection graph is reduced to its unique canonical form. The reduction diagram maps each intersection to its simplest representative in the ε-topology, ensuring consistency under floating-point uncertainty.
Artifacts are modeled as independent noise. Geometric inconsistencies decompose locally across polygon regions; topological artifacts decompose globally across manifold edge-connected components—enabling robust classification of the intended structure.

The goal is commutative correctness: operations that commute with mesh idealization. Chain operations freely on non-ideal meshes and clean up once at the end.

Boolean operation $\mathcal{B}$ commutes with mesh idealization $\mathcal{F}$ . Top: $\mathcal{B}$ on a mesh with artifacts produces a result with artifacts; the intersection graph $\mathcal{G}_\mathcal{I}$ contains a branching edge. Bottom: $\mathcal{B}$ on idealized meshes produces a clean result; $\mathcal{G}_\mathcal{I}$ is a simple closed curve. Apply $\mathcal{F}$ at any point—both paths yield equivalent geometry.

Publications

tf::tree: A General-Purpose Spatial Hierarchy for Real-Time Geometry Queries. Žiga Sajovic, Dejan Knez, and Robert Korez. (IEEE), June 2025. https://doi.org/10.36227/techrxiv.174952959.92977743/v1
Real-Time Mesh Booleans that Commute with Mesh Idealization. Žiga Sajovic and Dejan Knez. (IEEE), May 2025. https://doi.org/10.36227/techrxiv.174667714.42575478/v1

Citation

If you use trueform in your work, please cite:

@software{trueform2025,
    title={trueform: Real-time Geometric Processing},
    author={Sajovic, {\v{Z}}iga and {et al.}},
    organization={XLAB d.o.o.},
    year={2025},
    url={https://github.com/polydera/trueform}
}

Raycast Rendering

Batch ray casting with Lambertian shading, producing a BMP image entirely with NDArray operations.

Contributing

Guidelines for contributing code, documentation, and examples.