The paper presents an algorithm for surface reconstruction from unorganized points in $\mathbb{R}^3$. The algorithm aims to produce a simplicial surface that approximates an unknown manifold $M$ without assuming any prior knowledge about its topology, boundaries, or geometry. The input is a set of points $\{x_1, \ldots, x_n\}$ on or near $M$, and the output is a simplicial surface that captures the shape of $M$. The problem arises in various practical scenarios, such as range scanning from multiple viewpoints, recovering biological shapes from two-dimensional slices, and interactive surface sketching. The algorithm consists of two stages: 1. **Tangent Plane Estimation**: For each data point, an oriented tangent plane is estimated using the nearest neighbors. The orientation of these planes is crucial for defining a consistent global orientation. 2. **Signed Distance Function**: A signed distance function $f$ is defined using the tangent planes to estimate the signed geometric distance to the unknown surface $M$. The zero set $Z(f)$ is used to approximate $M$. 3. **Contour Tracing**: The contouring algorithm is used to approximate $Z(f)$ by a simplicial surface. This involves sampling the signed distance function over a 3D grid and reconstructing the surface from the intersections. The paper discusses the theoretical foundations, including the use of the implicit function theorem and the Riemannian Graph for consistent orientation. It also addresses the challenges of handling noisy and boundary-present surfaces. Experimental results demonstrate the algorithm's effectiveness on various datasets, including mesh data, ray-traced points, range images, and contours. Future work includes developing formal guarantees for the correctness of the reconstruction and improving geometric accuracy through spline surface fitting.The paper presents an algorithm for surface reconstruction from unorganized points in $\mathbb{R}^3$. The algorithm aims to produce a simplicial surface that approximates an unknown manifold $M$ without assuming any prior knowledge about its topology, boundaries, or geometry. The input is a set of points $\{x_1, \ldots, x_n\}$ on or near $M$, and the output is a simplicial surface that captures the shape of $M$. The problem arises in various practical scenarios, such as range scanning from multiple viewpoints, recovering biological shapes from two-dimensional slices, and interactive surface sketching. The algorithm consists of two stages: 1. **Tangent Plane Estimation**: For each data point, an oriented tangent plane is estimated using the nearest neighbors. The orientation of these planes is crucial for defining a consistent global orientation. 2. **Signed Distance Function**: A signed distance function $f$ is defined using the tangent planes to estimate the signed geometric distance to the unknown surface $M$. The zero set $Z(f)$ is used to approximate $M$. 3. **Contour Tracing**: The contouring algorithm is used to approximate $Z(f)$ by a simplicial surface. This involves sampling the signed distance function over a 3D grid and reconstructing the surface from the intersections. The paper discusses the theoretical foundations, including the use of the implicit function theorem and the Riemannian Graph for consistent orientation. It also addresses the challenges of handling noisy and boundary-present surfaces. Experimental results demonstrate the algorithm's effectiveness on various datasets, including mesh data, ray-traced points, range images, and contours. Future work includes developing formal guarantees for the correctness of the reconstruction and improving geometric accuracy through spline surface fitting.