Filmsticking++: Explicit Surface Reconstruction

• The paper introduces a novel formulation using weighted Restricted Power Diagrams and transient virtual sites to robustly interpolate input points onto an evolving guiding surface.
• It achieves watertight, manifold surface meshes that accurately capture deep cavities, thin structures, noise, and non-uniform sampling in low-quality point clouds.
• The method iteratively refines the mesh with a final Poisson-based correction step, ensuring sharp feature preservation and proper topology throughout reconstruction.

Filmsticking++ is an explicit, interpolation-based surface reconstruction method that deforms a watertight guiding mesh onto an unoriented point cloud by replacing Restricted Voronoi Diagram-based filmsticking with a Restricted Power Diagram formulation, augmenting the evolution with virtual sites, and using a smoothness-based manifold fix. Its stated objective is to reconstruct an explicit surface mesh that exactly interpolates the given points while remaining watertight and manifold, even for low-quality inputs with deep internal cavities, thin plates, thin tubes, noise, non-uniform sampling, and missing data (Wang et al., 11 Feb 2026).

1. Definition and problem setting

Explicit surface reconstruction seeks a triangle mesh $\mathbf G$ whose vertices and faces explicitly represent the target surface. In the interpolation-based setting considered by Filmsticking++, the defining requirement is that the output mesh exactly interpolates the input points, so that each point lies on the reconstructed surface up to non-manifold constraints. The paper emphasizes that this requirement is particularly important when the samples themselves are treated as ground-truth geometric measurements and when preserving sharp features, thin plates, tubes, and fine details is more important than the smoothing behavior typical of approximation-oriented implicit methods (Wang et al., 11 Feb 2026).

The difficulty arises from geometric ambiguity, combinatorial complexity, low-quality inputs, and complex topology. A sparse or noisy point cloud admits many possible interpolating meshes; deciding which triplets of points should form triangles while preserving a watertight 2-manifold is inherently hard; and deep internal cavities, thin plates, and tubular structures induce failure modes in which front and back surfaces are confused or cavities are never reached. The immediate predecessor discussed in the paper is an RVD-based filmsticking method that evolves a guiding surface from a bounding sphere through repeated Restricted Voronoi Diagram and Restricted Delaunay Triangulation updates, followed by volumetric sculpting. Filmsticking++ is presented as a direct response to the inherent Euclidean-distance limitation of that approach, which prevented some deep cavity points from ever acquiring restricted cells on the evolving surface (Wang et al., 11 Feb 2026).

2. Geometric formulation: from Restricted Voronoi to Restricted Power Diagrams

The central mathematical change is the replacement of Euclidean Voronoi cells by weighted power cells. For a site set $\mathbf P = \{p_i\} \subset \mathbb R^3$, the Voronoi cell of $p_i$ is

$$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$

For a weighted site $(p_i,w_i)$, Filmsticking++ uses the power distance

$\pi_{w_i}(x) = \|x - p_i\|^2 - w_i,$

with power cell

$$PC_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\|^2 - w_i \leq \|p_j - x\|^2 - w_j,\ \forall j \neq i\}.$$

The Restricted Power Diagram is the intersection of these 3D power cells with the current guiding surface $\mathbf G$, and the dual Restricted Delaunay Triangulation is formed on $\mathbf G$ when three restricted power regions meet at a vertex. This substitution is the mechanism by which distant interior points can be made to dominate regions on the guiding surface and thus enter the dual triangulation (Wang et al., 11 Feb 2026).

For a single off-surface point $q \in \mathbf Q$, with projection $\mathbf P = \{p_i\} \subset \mathbb R^3$0 onto $\mathbf P = \{p_i\} \subset \mathbb R^3$1, and with all on-surface vertex weights fixed to zero, the paper derives a safe interval for the weight $\mathbf P = \{p_i\} \subset \mathbb R^3$2:

$\mathbf P = \{p_i\} \subset \mathbb R^3$3

The lower bound ensures that $\mathbf P = \{p_i\} \subset \mathbb R^3$4 dominates a neighborhood around its projection $\mathbf P = \{p_i\} \subset \mathbb R^3$5 on the guiding surface; the upper bound prevents its power cell from engulfing existing surface vertices and destroying local structure. For multiple off-surface sites $\mathbf P = \{p_i\} \subset \mathbb R^3$6, the construction sets

$\mathbf P = \{p_i\} \subset \mathbb R^3$7

where $\mathbf P = \{p_i\} \subset \mathbb R^3$8 is the projection onto $\mathbf P = \{p_i\} \subset \mathbb R^3$9. Under the distinct-projection assumptions stated in the paper, this guarantees that at least one such site is attracted in each iteration. The intended consequence is that deep interior points, which would remain hidden under Euclidean RVD, eventually reach the guiding surface under the weighted RPD formulation (Wang et al., 11 Feb 2026).

3. Iterative algorithm and guiding-surface evolution

Filmsticking++ begins from a watertight bounding sphere used as the initial guiding surface $p_i$0. The algorithm then treats both the real point cloud and a set of virtual sites as sites in a repeated update loop. At each iteration, it computes closest projections of sites onto $p_i$1, assigns zero weights to sites already on the surface and squared-distance weights to off-surface sites, computes the Restricted Power Diagram on $p_i$2, builds the dual Restricted Delaunay Triangulation, and updates the guiding surface by incorporating newly attracted sites (Wang et al., 11 Feb 2026).

The manifold structure of the evolving surface is not left implicit. The paper lists three manifold conditions for the RDT-based update: every restricted cell must be homeomorphic to a disk, any two neighboring cells must share exactly one common edge, and every cell must have at least three neighbors. These conditions are enforced as part of each Filmsticking++ step so that $p_i$3 remains watertight and manifold throughout the evolution (Wang et al., 11 Feb 2026).

After the iterative stage has attracted almost all real points onto $p_i$4, the method performs a field-based dangling removal step. The specific field-based method used in the paper is Poisson reconstruction, driven not by noisy input normals but by normals assigned from the final guiding surface. A final Filmsticking++ step is then applied to recover the explicit interpolating mesh with the corrected topology. This staging is significant because it replaces the repeated sculpting cycles of the previous RVD-based method with a single field-based correction pass (Wang et al., 11 Feb 2026).

4. Virtual sites and expulsion of the external medial axis

A second major innovation is the introduction of virtual sites. The paper observes that, as the guiding surface increasingly approximates the target shape, the external medial axis is gradually expelled outside the guiding surface. Filmsticking++ accelerates this process by placing virtual sites inside the initial guiding surface, allowing them to participate in RPD computation, and removing each virtual site immediately after it reaches the guiding surface (Wang et al., 11 Feb 2026).

The virtual sites are sampled from Voronoi vertices of the point cloud, which the paper uses as an approximation to medial-axis structure. Voronoi vertices inside the bounding sphere are collected, and farthest point sampling is used to obtain about 1K virtual sites. The stated rationale is empirical: too many virtual sites slow computation, while too few do not sufficiently accelerate evolution in deep cavities. Once included as weighted sites, these auxiliary points can pull the surface toward cavity interiors that would otherwise require many more filmsticking iterations to reach (Wang et al., 11 Feb 2026).

The deletion rule is equally important. A virtual site that touches the guiding surface in one iteration is removed before the next iteration, and its former domain is repartitioned among neighboring sites. This makes the virtual sites transient accelerators rather than permanent geometric constraints. The paper further notes that some sampled Voronoi vertices may lie on the inner medial axis or arise from noisy regions, but such sites are often blocked by real points and are therefore difficult to attract; if a few are attracted accidentally because of missing data, their immediate removal allows the topology to recover in later iterations (Wang et al., 11 Feb 2026).

5. Manifold fixing, robustness, and handling of thin structures

When a site dominates multiple disconnected regions on the guiding surface, the dual triangulation can become non-manifold. This is especially problematic for thin plates, where Euclidean proximity alone may confuse front and back surfaces. Filmsticking++ resolves this with a local smoothness criterion rather than a purely distance-based choice. For a vertex $p_i$5, the paper defines

$p_i$6

where $p_i$7 is the average normal at $p_i$8, $p_i$9 is the normal of an incident triangle $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$0, and $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$1 is the angle at $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$2 in that triangle. The ring with smaller $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$3 is kept. In the paper’s interpretation, this encodes a preference for the simpler and smoother configuration and avoids gluing the two sides of a thin plate together (Wang et al., 11 Feb 2026).

The method is explicitly designed to operate without input normals. Its core steps use only Euclidean and power distances between sites and the guiding surface. Normals are introduced only in the field-based dangling-removal stage, and those normals are taken from the guiding surface rather than estimated directly from the noisy cloud. This design is presented as one reason for robustness under noisy, sparse, and non-uniform sampling, and as a contrast to implicit methods whose behavior depends more directly on normal estimation quality (Wang et al., 11 Feb 2026).

The same section of the paper attributes robustness to three additional factors: the attraction process is constrained by manifoldness, so isolated distant noisy points do not necessarily gain stable power cells; the safe-weight construction expands off-surface cells without allowing catastrophic neighborhood changes; and the virtual-site mechanism reduces the number of iterations needed in complex concavities, thereby making the algorithm less sensitive to irregular local sampling. This suggests that Filmsticking++ is not merely a faster variant of the previous method, but a reformulation that alters both completeness and failure behavior (Wang et al., 11 Feb 2026).

6. Evaluation, computational profile, and limitations

The paper evaluates Filmsticking++ on synthetic models from Thingi10K, synthetic irregularly sampled shapes such as the Vase test, high-genus tubular networks, a thin-plate Shield model, real scan datasets from Huang et al. 2022 and the EPFL Statue models, large-scale multi-view stereopsis data, and new scans from SHINING 3D Einscan SE (Wang et al., 11 Feb 2026).

On the quantitative Thingi10K benchmark with 500 random models, the reported metrics are Normal Consistency (NC), Chamfer Distance (CD), and F-Score (F1). For 10K-point inputs, Filmsticking++ reports NC $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$4, CD $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$5, and F1 $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$6, which the paper states are the best values among the compared methods. For 5K-point inputs, it reports NC $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$7, CD $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$8, and F1 $$C_i = \{x\in \mathbb{R}^3 \;\big|\; \|p_i - x\| \leq \|p_j - x\|,\ \forall j\neq i\}.$$9, again giving the lowest CD and the best or near-best overall performance among the listed baselines (Wang et al., 11 Feb 2026).

The runtime profile is presented as $(p_i,w_i)$0 with $(p_i,w_i)$1, after $(p_i,w_i)$2 kd-tree and Delaunay preprocessing. The paper gives the following representative comparisons between the previous RD method and Filmsticking++:

Model	RD	Filmsticking++
Girl (5K)	5 filmsticking + 3 sculpting, 2.6s	4 iterations + 1 Poisson, 1.9s
Flower (20K)	20 filmsticking + 10 sculpting, 17.94s	8 iterations + 1 Poisson, 3.69s
Disk (20K)	10 + 7, 10.75s	7 + 1, 3.1s
Dragon (150K)	fails to scale	17 iterations + 1 Poisson, 698s

For large multi-view stereo scans with 1–4M points, the paper reports about 3 hours on 1.3 GHz i9 + RTX 3090 for single-view subsets (Wang et al., 11 Feb 2026).

The reported limitations are also specific. The current algorithm is designed for closed surfaces, tends to overestimate minimum thickness, may close small openings, and cannot reconstruct open meshes. Extremely thin necks can cause the inward offset of the guiding surface to break into disconnected components, which can then induce incorrect topology. Very sparse point clouds remain difficult, and multi-million point clouds still present runtime and memory costs for both Filmsticking++ and the Poisson stage (Wang et al., 11 Feb 2026).

Taken together, the method’s encyclopedic significance lies in a precise combination of ingredients: weighted Restricted Power Diagrams to overcome Euclidean visibility failure in deep cavities, transient virtual sites to accelerate medial-axis expulsion, a smoothness-based manifold fix for thin structures, and a final field-based correction driven by normals derived from the evolving surface rather than the raw cloud. Within the reconstruction literature represented here, that combination defines Filmsticking++ as a state-of-the-art explicit, watertight, manifold, interpolation-based method for point clouds without normals (Wang et al., 11 Feb 2026).