Surface reconstruction from unorganized points

Hugues HoppeTony DeRoseTom DuchampJohn McDonaldWerner Stuetzle

article1992SIGGRAPH3,523 citations

Presents a foundational method for reconstructing 3D surfaces of arbitrary topology and boundary configurations from unorganized point clouds by estimating a signed distance function through consistently oriented local tangent planes and extracting the resulting zero-set mesh.

Listen

The paper presents an algorithm for reconstructing an unknown surface from an unorganized collection of points sampled on or near it. The method addresses practical needs in range scanning of complex objects, medical imaging from contours, and free-form surface design, where data lack ordering, normals, or prior knowledge of topology and boundaries.

The work set out to produce a simplicial surface that approximates the unknown manifold, inferring its geometry, topology, and boundary status automatically from the points alone.

The approach defines a signed distance function by first fitting local tangent planes to each point’s k-nearest neighbors, then orienting those planes consistently through a graph that connects nearby centers and propagates orientation along a minimum spanning tree. A contouring procedure then extracts the zero set of the distance function as a triangular mesh, marking boundaries where the function becomes undefined beyond a density threshold. The method was tested on several thousand to twenty thousand points drawn from meshes, simulated multi-view range data, real cylindrical scans, and stacked contours.

It reliably recovered surfaces of varying topology and genus, correctly identified boundaries such as the open base of a cat model, and produced meshes free of spurious components. Execution times ranged from under a minute for small sets to roughly half an hour for larger ones on contemporary hardware, with post-processing to improve triangle quality.

These results show that a single procedure can replace specialized techniques that exploit ordering or planarity, enabling direct use of merged or sketched point data without manual cleanup. The output meshes provide a compact starting point for further modeling or analysis.

Further development should focus on formal conditions guaranteeing correct topology, automatic selection of neighborhood size, and extension of the same framework to higher-dimensional manifolds. Using the resulting meshes as input to spline fitting would improve geometric accuracy and storage efficiency.

The algorithm succeeded on all presented examples, yet lacks proven correctness bounds and assumes a single connected component; performance also depends on the chosen neighborhood size and noise estimates.

University of Washington geometry reconstruction topology Surface Reconstruction Unorganized Point Tangent Plane

hhoppe/Mesh-processing-library Hoppe et al (1992).pdf

Paper: Least-Squares Fitting of Two 3-D Point Sets, K. S. Arun et al. (1987). Understanding least-squares rigid transformations provides the essential geometric alignment foundation utilized during point-set pre-processing.

Paper: PointNet: Deep Learning on Point Sets for 3D Classification and Segmentation, Charles R. Qi et al. (2017). PointNet directly extends surface reconstruction and point processing concepts into an end-to-end deep learning framework for unstructured point clouds.

Cover for Surface reconstruction from unorganized points

Abstract

We describe and demonstrate an algorithm that takes as input an unorganized set of points {x1, . . . , xn} ⊂ IR3 on or near an unknown manifold M, and produces as output a simplicial surface that approximates M. Neither the topology, the presence of boundaries, nor the geometry of M are assumed to be known in advance — all are inferred automatically from the data. This problem naturally arises in a variety of practical situations such as range scanning an object from multiple view points, recovery of biological shapes from two-dimensional slices, and interactive surface sketching.

Topics

geometry reconstruction topology viewpoint interactive surfaces multiple views 3d reconstruction control point

Keywords

Surface Reconstruction Unorganized Point Tangent Plane Signed Distance Function Riemannian Graph Minimal Spanning Tree Contour Tracing Marching Cubes Boundary Detection Noise Estimation

1 Introduction
1.1 Terminology
1.2 Problem Statement
2 Related Work
2.1 Surface Reconstruction
2.2 Surface Reconstruction vs Function Reconstruction
3 A Description of the Algorithm
3.1 Overview
3.2 Tangent Plane Estimation
3.3 Consistent Tangent Plane Orientation
3.4 Signed Distance Function
3.5 Contour Tracing
4 Results
5 Discussion
5.1 Tangent Plane Approximation
5.2 Algorithm Complexity
6 Conclusions and Future Work
References

Knowls

Knowl 1 — Surface Reconstruction Pipeline from Unorganized Points
algorithm
The surface reconstruction algorithm takes as input an unorganized point set $X = \{x_1, \dots, x_n\} \subset \mathbb{R}^3$ sampled on or near an unknown manifold surface $M$ , together with neighborhood size $k$ , boundary distance threshold $\rho + \delta$ , and cubical grid cell size. It infers the topology, geometry, and boundaries of $M$ automatically and outputs an approximating simplicial surface (triangular mesh).
Input: Point set $X = \{x_1, \dots, x_n\} \subset \mathbb{R}^3$ , integer $k$ , boundary parameter $\rho + \delta$ , cell size $s$
Output: Simplicial surface $M'$ approximating $M$
Partition $\mathbb{R}^3$ into a cubical grid and hash points $X$ by cube index
for each point $x_i \in X$ do
    Find $k$ -nearest neighbors $Nbhd(x_i) \subset X$
    Compute center $o_i$ and normal $\hat{n}_i$ via PCA on $Nbhd(x_i)$
end for
Build Euclidean Minimum Spanning Tree (EMST) over centers $\{o_1, \dots, o_n\}$
Add edge $(i, j)$ if $o_i \in Nbhd(o_j)$ or $o_j \in Nbhd(o_i)$ to form Riemannian Graph $G$
Assign weight $w(i, j) = 1 - |\hat{n}_i \cdot \hat{n}_j|$ to every edge $(i, j) \in G$
Compute Minimum Spanning Tree $T$ of $G$
Select initial root plane $o_{\text{root}}$ (maximizing $z$ ) and orient $\hat{n}_{\text{root}}$ such that $\hat{n}_{\text{root}} \cdot (0, 0, 1)^T > 0$
Traverse $T$ in depth-first order to consistently orient all normals $\hat{n}_i$
Initialize empty cube queue $Q$ and visited set $V$
Find initial cubes intersecting $X$ and push to $Q$
while $Q$ is not empty do
    Pop cube $C$ from $Q$
    for each vertex $p$ of cube $C$ do
        Evaluate signed distance function $f(p)$
    end for
    Decompose $C$ into tetrahedra
    for each tetrahedron in $C$ do
        if $f$ is defined at all 4 vertices and exhibits a sign change then
            Compute zero-crossing edge intersections by linear interpolation
            Generate triangular face(s)
        end if
    end for
    Push unvisited adjacent cubes intersecting the zero-set into $Q$ and mark visited in $V$
end while
Simplify resulting simplicial mesh by collapsing edges according to an aspect ratio priority queue
return Simplified simplicial surface $M'$
Knowl 2 — Consistent Tangent Plane Orientation via Minimum Spanning Tree Propagation
algorithm
Assigning consistent orientations to tangent plane normals so that $\hat{n}_i \cdot \hat{n}_j \approx +1$ for neighboring planes is equivalent to graph optimization and is NP-hard by reduction to MAX-CUT. A heuristic orientation propagation algorithm resolves this ambiguity by propagating orientations along paths of maximal geometric flatness:
Input: Tangent plane centers $\{o_1, \dots, o_n\}$ , unoriented unit normals $\{\pm \hat{n}_1, \dots, \pm \hat{n}_n\}$ , neighbor parameter $k$
Output: Consistently oriented unit normals $\{\hat{n}_1, \dots, \hat{n}_n\}$
Construct EMST $T_{\text{Euclid}}$ on centers $\{o_1, \dots, o_n\}$
Initialize Riemannian Graph $G = (V, E)$ with $V = \{1, \dots, n\}$ and $E = E(T_{\text{Euclid}})$
for each $i \in \{1, \dots, n\}$ do
    for each $j$ such that $o_j$ is in the $k$ -neighborhood of $o_i$ do
        Add edge $(i, j)$ to $E$
    end for
end for
for each edge $(i, j) \in E$ do
     $w(i, j) \leftarrow 1 - |\hat{n}_i \cdot \hat{n}_j|$
end for
Compute Minimum Spanning Tree $T_{\text{MST}}$ of $G$ using weights $w$
Find index $r = \arg\max_i (o_i \cdot (0, 0, 1)^T)$
if $\hat{n}_r \cdot (0, 0, 1)^T < 0$ then
     $\hat{n}_r \leftarrow -\hat{n}_r$
end if
Traverse $T_{\text{MST}}$ starting at root $r$ using depth-first search:
for each directed tree edge $(u, v)$ traversed from parent $u$ to child $v$ do
    if $\hat{n}_u \cdot \hat{n}_v < 0$ then
         $\hat{n}_v \leftarrow -\hat{n}_v$
    end if
end for
return $\{\hat{n}_1, \dots, \hat{n}_n\}$
Assigning edge cost $1 - |\hat{n}_i \cdot \hat{n}_j|$ favors propagation across regions of low surface curvature first, preventing orientation conflicts from crossing sharp edges or ambiguous high-curvature boundaries.
Knowl 3 — Local Tangent Plane Estimation via Principal Component Analysis
model/method
For each point $x_i$ in the sample set $X = \{x_1, \dots, x_n\} \subset \mathbb{R}^3$ , an oriented tangent plane $Tp(x_i)$ is defined by a center point $o_i \in \mathbb{R}^3$ and a unit normal vector $\hat{n}_i \in \mathbb{R}^3$ .

Let $Nbhd(x_i) \subset X$ denote the $k$ -neighborhood (the $k$ nearest points in $X$ to $x_i$ ). The center $o_i$ is chosen as the centroid of $Nbhd(x_i)$ :

$o_i = \frac{1}{k} \sum_{y \in Nbhd(x_i)} y$

The normal vector $\hat{n}_i$ is computed via principal component analysis by forming the symmetric $3 \times 3$ positive semi-definite covariance matrix:

$CV = \sum_{y \in Nbhd(x_i)} (y - o_i) \otimes (y - o_i)$

where $\otimes$ is the vector outer product operator, yielding $(y - o_i)(y - o_i)^T$ . Let $\lambda_i^1 \ge \lambda_i^2 \ge \lambda_i^3$ denote the eigenvalues of $CV$ , and let $\hat{v}_i^1, \hat{v}_i^2, \hat{v}_i^3$ be their associated orthonormal unit eigenvectors. The unoriented normal direction is set to the eigenvector corresponding to the smallest eigenvalue:

$\hat{n}_i \in \{\hat{v}_i^3, -\hat{v}_i^3\}$

The plane $\{p \in \mathbb{R}^3 \mid (p - o_i) \cdot \hat{n}_i = 0\}$ is the best least-squares approximating plane to $Nbhd(x_i)$ .
Knowl 4 — Signed Distance Function Definition and Boundary Detection
model/method
The signed distance function $f(p)$ from an arbitrary query point $p \in \mathbb{R}^3$ to the unknown manifold $M$ is estimated using the local oriented tangent planes $Tp(x_i) = (o_i, \hat{n}_i)$ :
1. Find the tangent plane index $i$ whose center $o_i$ is closest to $p$ :
$i = \arg\min_{j \in \{1, \dots, n\}} \|p - o_j\|$
1. Compute the orthogonal projection $z$ of $p$ onto $Tp(x_i)$ :
$z = o_i - ((p - o_i) \cdot \hat{n}_i) \hat{n}_i$
1. Check data proximity: If the Euclidean distance from $z$ to the sample set $X$ satisfies $d(z, X) < \rho + \delta$ , the signed distance is assigned as:
$f(p) = (p - o_i) \cdot \hat{n}_i$

Otherwise, $f(p)$ is set to undefined.

Here $\rho$ is the sampling density bound and $\delta$ is the noise magnitude bound. When $f(p)$ is undefined at any vertex of a grid cube, isosurface extraction generates no surface within that cell, enabling the automatic reconstruction of true surface boundaries.
Knowl 5 — Noise and Density Model for Unorganized Surface Samples
definition
Let $M \subset \mathbb{R}^3$ be a compact, connected, orientable two-dimensional manifold (possibly bordered). A set of sampled points $X = \{x_1, \dots, x_n\} \subset \mathbb{R}^3$ is modeled under two parameters:
- $\delta$ -noise: The sample $X$ is $\delta$ -noisy if each point $x_i \in X$ satisfies $x_i = y_i + e_i$ , where $y_i \in M$ and the error vector $e_i \in \mathbb{R}^3$ satisfies $\|e_i\| \le \delta$ .
- $\rho$ -density: A noiseless point set $Y = \{y_1, \dots, y_n\} \subset M$ is $\rho$ -dense if every open sphere in $\mathbb{R}^3$ with radius $\rho$ centered at any point of $M$ contains at least one sample point $y_j \in Y$ . A $\delta$ -noisy sample $X$ is $\rho$ -dense if there exists a noiseless $\rho$ -dense sample $Y \subset M$ such that $\|x_i - y_i\| \le \delta$ for all $i = 1, \dots, n$ .
Under this model, any point $z \in M$ satisfies $d(z, X) \le \rho + \delta$ . Therefore, any projected point $z$ with $d(z, X) > \rho + \delta$ cannot lie on $M$ .
Knowl 6 — Boundary-Preserving Isosurface Extraction and Mesh Post-Processing
model/method
The zero set $Z(f) = \{p \in \mathbb{R}^3 \mid f(p) = 0\}$ is extracted using a modified marching cubes algorithm with tetrahedral decomposition and post-processing:
1. Tetrahedral Marching Cubes: The 3D bounding box is partitioned into a cubical grid. To avoid evaluating $f$ across all of space, a queue tracks only cubes intersecting $Z(f)$ . Cubes are decomposed into tetrahedra to ensure unambiguous, continuous piecewise linear isosurface facets.
2. Boundary Handling: If $f(p)$ is undefined at one or more vertices of a cube (indicating that the projected point lies farther than $\rho + \delta$ from $X$ ), no triangular facets are generated within that cell. This naturally leaves open boundaries along regions unsupported by data.
3. Mesh Simplification / Aspect-Ratio Optimization: The resulting mesh may contain poorly proportioned triangles. A priority queue of edges sorted by the objective metric:
$\text{Cost}(e) = \text{length}(e) \times \min(\text{inscribed\_radius}(F_1), \text{inscribed\_radius}(F_2))$

is iteratively processed, where $F_1, F_2$ are the faces adjacent to edge $e$ . Edges with the lowest cost are collapsed while verifying topological consistency to improve triangle aspect ratios without altering surface topology.
Knowl 7 — Computational Complexity with Spatial Hash Partitioning
theoretical result
By structuring the bounding box of $X$ with a uniform 3D cubical grid indexed via a hash table, point-location queries become localized:
- $k$ -Nearest Neighbor Search: Finding the $k$ -nearest neighbors for a query point runs in empirical $O(k)$ time.
- Riemannian Graph Construction: Constructing the graph (containing the EMST and $k$ -neighborhood edges) takes $O(nk)$ time. The graph contains at most $n + nk = O(n)$ edges.
- MST and Orientation Propagation: Computing the Minimum Spanning Tree of the Riemannian Graph takes $O(n \log n)$ time, and the depth-first traversal to orient tangent planes takes $O(n)$ time.
- Signed Distance Evaluation: Evaluating $f(p)$ at any grid vertex $p$ takes $O(1)$ time because finding the nearest tangent plane origin $o_i$ and verifying $d(z, X)$ are restricted to neighboring hash cells.
- Contouring Time: Contouring complexity is proportional to the number of cubes visited that intersect the zero set $Z(f)$ .

Knowl 8 — Empirical Reconstruction Performance and Hyperparameters

data/table

The algorithm was evaluated on point sets from five distinct sources: sampled simplicial meshes, multi-view ray tracing of CSG solids, cylindrical laser range images, and planar CT contours. Runtimes were measured on a 20 MIPS workstation.

Object	$n$	$k$	$\rho + \delta$	cell size	time (seconds)
cat	1000	15	0.06	1/30	19
knot	10000	20	$\infty$	1/50	137
mechpart	4102	12	$\infty$	1/40	54
spock	21760	8	0.08	1/80	514
femur	18224	40	0.06	1/50	2135

The parameter $\rho + \delta$ and the marching cubes cell size are expressed as fractions of the object's bounding diameter. For closed surfaces (such as knot and mechpart), $\rho + \delta$ is set to $\infty$ . cat demonstrates reconstruction of an open bordered surface homeomorphic to a disk; knot has simple topology but complex self-entangled geometry; mechpart is a CSG solid of genus 3 reconstructed from simulated 8-view range rays; spock is a subsampled (25%) physical range scan; and femur combines 39 planar CT slice contours.

Knowl 9 — Extension to Codimension-1 Manifolds in Arbitrary Dimensions
model/method
The signed distance reconstruction algorithm generalizes directly to reconstructing $(d-1)$ -dimensional manifolds embedded in $\mathbb{R}^d$ for any dimension $d \ge 2$ :
- In $\mathbb{R}^2$ ( $d=2$ ), the algorithm reconstructs 1D curves (open or closed) from unorganized planar point sets using 1D tangent lines and 2D grid contouring.
- In $\mathbb{R}^3$ ( $d=3$ ), it reconstructs 2D surfaces from 3D points.
- In $\mathbb{R}^4$ ( $d=4$ ), it reconstructs 3D hypersurfaces/volumes from unorganized 4D points.
In all dimensions $d$ , local $k$ -neighborhoods yield a $(d-1)$ -dimensional best-fitting hyperplane via the eigenvector of the $d \times d$ covariance matrix associated with its smallest eigenvalue $\lambda_i^d$ .
Knowl 10 — Neighborhood Size Selection and Eigenvalue Monitoring
model/method
The neighborhood size $k$ governs the trade-off between noise filtering and local geometric fidelity:
- When $k$ is too small, noise dominates: the covariance eigenvalues $\lambda_i^1, \lambda_i^2, \lambda_i^3$ are similar in magnitude, and the estimated normal $\hat{v}_i^3$ fails to reflect the true surface normal.
- When $k$ is too large, the neighborhood loses locality: non-zero surface curvature increases the third eigenvalue $\lambda_i^3$ (the neighborhood "thickness").
An adaptive neighborhood strategy selects $k$ dynamically by incrementally gathering points while monitoring $\lambda_i^3$ , stopping when $\lambda_i^3$ exceeds a threshold set by local or global noise estimates.

Coverage note — None was omitted; all key algorithmic phases, mathematical formulas, sampling definitions, complexity derivations, experimental parameters and tables, and proposed dimensional extensions are fully represented.

References

1.E. L. Allgower and P. H. Schmidt. An algorithm for piecewise linear approximation of an implicitly defined manifold. SIAM Journal of Numerical Analysis, 22:322–346, April 1985.
2.J. L. Bentley. Multidimensional divide and conquer. Comm. ACM, 23(4):214–229, 1980.
3.Y. Breseler, J. A. Fessler, and A. Macovski. A Bayesian approach to reconstruction from incomplete projections of a multiple object 3D domain. IEEE Trans. Pat. Anal. Mach. Intell., 11(8):840–858, August 1989.
4.James F. Brinkley. Knowledge-driven ultrasonic three-dimensional organ modeling. IEEE Trans. Pat. Anal. Mach. Intell., 7(4):431–441, July 1985.
5.David P. Dobkin, Silvio V. F. Levy, William P. Thurston, and Allan R. Wilks. Contour tracing by piecewise linear approximations. ACM TOG, 9(4):389–423, October 1990.
6.John A. Eisenman. Graphical editing of composite bezier curves. Master’s thesis, Department of Electrical Engineering and Computer Science, M.I.T., 1988.
7.T.A. Foley. Interpolation to scattered data on a spherical domain. In M. Cox and J. Mason, editors, Algorithms for Approximation II, pages 303–310. Chapman and Hall, London, 1990.
8.Michael R. Garey and David S. Johnson. Computers and Intractability. W. H. Freeman and Company, 1979.
9.T. Hastie and W. Stuetzle. Principal curves. JASA, 84:502–516, 1989.
10.Averill M. Law and W. David Kelton. Simulation Modeling and Analysis. McGraw-Hill, Inc., second edition, 1991.
11.Marshal L. Merriam. Experience with the cyberware 3D digitizer. In NCGA Proceedings, pages 125–133, March 1992.
12.David Meyers, Shelly Skinner, and Kenneth Sloan. Surfaces from contours: The correspondence and branching problems. In Proceedings of Graphics Interface ’91, pages 246–254, June 1991.
13.Doug Moore and Joe Warren. Approximation of dense scattered data using algebraic surfaces. TR 90-135, Rice University, October 1990.
14.Doug Moore and Joe Warren. Adaptive mesh generation ii: Packing solids. TR 90-139, Rice University, March 1991.
15.Shigeru Muraki. Volumetric shape description of range data using “blobby model”. Computer Graphics (SIGGRAPH ’91 Proceedings), 25(4):227–235, July 1991.
16.Gregory M. Nielson, Thomas A. Foley, Bernd Hamann, and David Lane. Visualizing and modeling scattered multivariate data. IEEE CG&A, 11(3):47–55, May 1991.
17.Barrett O’Neill. Elementary Differential Geometry. Academic Press, Orlando, Florida, 1966.
18.Vaughan Pratt. Direct least-squares fitting of algebraic surfaces. Computer Graphics (SIGGRAPH ’87 Proceedings), 21(4):145–152, July 1987.
19.Emanuel Sachs, Andrew Roberts, and David Stoops. 3-Draw: A tool for designing 3D shapes. IEEE Computer Graphics and Applications, 11(6):18–26, November 1991.
20.Hanan Samet. Applications of Spatial Data Structures. Addison-Wesley, 1990.
21.Philip J. Schneider. Phoenix: An interactive curve design system based on the automatic fitting of hand-sketched curves. Master’s thesis, Department of Computer Science, U. of Washington, 1988.
22.R. B. Schudy and D. H. Ballard. Model detection of cardiac chambers in ultrasound images. Technical Report 12, Computer Science Department, University of Rochester, 1978.
23.R. B. Schudy and D. H. Ballard. Towards an anatomical model of heart motion as seen in 4-d cardiac ultrasound data. In Proceedings of the 6th Conference on Computer Applications in Radiology and Computer-Aided Analysis of Radiological Images, 1979.
24.Stan Sclaroff and Alex Pentland. Generalized implicit functions for computer graphics. Computer Graphics (SIGGRAPH ’91 Proceedings), 25(4):247–250, July 1991.
25.G. Taubin. Estimation of planar curves, surfaces and nonplanar space curves defined by implicit equations, with applications to edge and range image segmentation. Technical Report LEMS-66, Division of Engineering, Brown University, 1990.
26.B. C. Vemuri. Representation and Recognition of Objects From Dense Range Maps. PhD thesis, Department of Electrical and Computer Engineering, University of Texas at Austin, 1987.
27.B. C. Vemuri, A. Mitiche, and J. K. Aggarwal. Curvature-based representation of objects from range data. Image and Vision Computing, 4(2):107–114, 1986.
28.G. Wyvill, C. McPheeters, and B. Wyvill. Data structures for soft objects. The Visual Computer, 2(4):227–234, August 1986.

Citation

MLA

Hoppe, H., et al. “Surface Reconstruction from Unorganized Points”. Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, 1992, pp. 71–78, https://doi.org/10.1145/133994.134011.

APA

Hoppe, H., DeRose, T., Duchamp, T., McDonald, J., & Stuetzle, W. (1992). Surface reconstruction from unorganized points. Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, 71–78. https://doi.org/10.1145/133994.134011

Chicago

Hoppe, H., T. DeRose, T. Duchamp, J. McDonald, and W. Stuetzle. 1992. “Surface Reconstruction from Unorganized Points”. Proceedings of the 19th Annual Conference on Computer Graphics and Interactive Techniques, 71–78. https://doi.org/10.1145/133994.134011.

Harvard

Hoppe, H. et al. (1992) “Surface reconstruction from unorganized points”, Proceedings of the 19th annual conference on Computer graphics and interactive techniques. ACM, pp. 71–78. Available at: https://doi.org/10.1145/133994.134011.

Vancouver

1. Hoppe H, DeRose T, Duchamp T, McDonald J, Stuetzle W (1992) Surface reconstruction from unorganized points. In: Proceedings of the 19th annual conference on Computer graphics and interactive techniques. ACM, pp 71–78

BibTeX

@inproceedings{Hoppe_1992, series={SIGGRAPH92}, title={Surface reconstruction from unorganized points}, url={http://dx.doi.org/10.1145/133994.134011}, DOI={10.1145/133994.134011}, booktitle={Proceedings of the 19th annual conference on Computer graphics and interactive techniques}, publisher={ACM}, author={Hoppe, Hugues and DeRose, Tony and Duchamp, Tom and McDonald, John and Stuetzle, Werner}, year={1992}, month=July, pages={71–78}, collection={SIGGRAPH92} }

Metadata:Crossref

Source Code

This paper has an official code repository available. Click below to access the source code.

View Repository

Access the Paper

This paper is available from its original source. Click below to access the PDF.

Open PDF

Surface reconstruction from unorganized points

Abstract

Topics

Keywords

Table of Contents

Knowls

Knowl 1 — Surface Reconstruction Pipeline from Unorganized Points

Knowl 2 — Consistent Tangent Plane Orientation via Minimum Spanning Tree Propagation

Knowl 3 — Local Tangent Plane Estimation via Principal Component Analysis

Knowl 4 — Signed Distance Function Definition and Boundary Detection

Knowl 5 — Noise and Density Model for Unorganized Surface Samples

Knowl 6 — Boundary-Preserving Isosurface Extraction and Mesh Post-Processing

Knowl 7 — Computational Complexity with Spatial Hash Partitioning