Related papers: Point-Normal Subdivision Curves and Surfaces
Normal estimation for 3D point clouds is a fundamental task in 3D geometry processing. The state-of-the-art methods rely on priors of fitting local surfaces learned from normal supervision. However, normal supervision in benchmarks comes…
Normalizing flows are a powerful technique for obtaining reparameterizable samples from complex multimodal distributions. Unfortunately, current approaches are only available for the most basic geometries and fall short when the underlying…
This paper presents a hybrid algorithm that combines features form both Sqrt(3) and Loop Subdivision schemes. The algorithm aims at preserving sharp features and trim regions, during the surfaces subdivision, using a set of rules. The…
In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…
This paper proposes a fast and accurate surface normal estimation method which can be directly used on depth maps (organized point clouds). The surface normal estimation process is formulated as a closed-form expression. In order to reduce…
We consider the problem of B\'{e}zier curves/surfaces subdivision using blossoms. We propose closed-form formulae for blossoms evaluation, as needed for the calculation of control points. This approach leads to direct and efficient way to…
A new family of combined subdivision schemes with one tension parameter is proposed by the interpolatory and approximating subdivision schemes. The displacement vectors between the points of interpolatory and approximating subdivision…
This paper proposes a method for computing the visible occluding contours of subdivision surfaces. The paper first introduces new theory for contour visibility of smooth surfaces. Necessary and sufficient conditions are introduced for when…
Many applications of geometry modeling and computer graphics necessite accurate curvature estimations of curves on the plane or on manifolds. In this paper, we define the notion of the discrete geodesic curvature of a geodesic polygon on a…
Recovering high quality surfaces from noisy point clouds, known as point cloud denoising, is a fundamental yet challenging problem in geometry processing. Most of the existing methods either directly denoise the noisy input or filter raw…
In this paper subdivision schemes, which are used for functions approximation and curves generation, are considered. In classical case, for the functions defined on the real line, the theory of subdivision schemes is widely known due to…
In computed tomography, the approximation quality of a scan of a physical object is typically limited by the acquisition modalities, especially the hardware including X-ray detectors. To improve upon this, we experiment with a…
Normal estimation on 3D point clouds is a fundamental problem in 3D vision and graphics. Current methods often show limited accuracy in predicting normals at sharp features (e.g., edges and corners) and less robustness to noise. In this…
The purpose of this paper is to present simple and fast methods for computing control points for polynomial curves and polynomial surfaces given explicitly in terms of polynomials (written as sums of monomials). We give recurrence formulae…
Interpolatory subdivision schemes generate smooth curves from piecewise-linear control polygons by repeatedly inserting new vertices. Classical schemes rely on a single global tension parameter and typically require separate formulations in…
Point clouds are popular 3D representations for real-life objects (such as in LiDAR and Kinect) due to their detailed and compact representation of surface-based geometry. Recent approaches characterise the geometry of point clouds by…
This paper introduces Neural Subdivision, a novel framework for data-driven coarse-to-fine geometry modeling. During inference, our method takes a coarse triangle mesh as input and recursively subdivides it to a finer geometry by applying…
In the process of projecting the surface of a three-dimensional object onto a two-dimensional surface, due to the perspective distortion, the image on the surface of the object will have different degrees of distortion according to the…
Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To…
Using the normalized B-bases of vector spaces of trigonometric and hyperbolic polynomials of finite order, we specify control point configurations for the exact description of higher dimensional (rational) curves and (hybrid) multivariate…