Vectorfield isosurface-based reconstruction from oriented points

Context. With the contemporary development of topological optimization, and parametric and AI-guided design, the problem of implicit surface representation became prominent in additive manufacturing. Although more and more software packages use implicit modeling for design, there is no common standard way of writing, storing, or passing a set of implicit surfaces or curves over the network. The object of the study is one of the possible ways of such representation, specifically: modeling implicit curves and surfaces using pseudo-Gaussian interpolation.Objective. The goal of the work is the development of a modeling method that improved the accuracy of the implicit object representation wothout significant increase in memory used or processing time spent.Method. One of the conventional ways to model an implicit surface would be to represent its signed distance function (SDF) with its values defined on a regular grid. Then a continuous SDF could be obtained from the grid values by means of interpolation.What we propose instead is to store not SDF values but the coefficients of a pseudo-Gaussian interpolating function in the grid, which would enable picking the exact interpolation points before the SDF model is written. In this way we achieve better accuracy in the regions we’re interested the most in with no additional memory overhead.Results. The developed method was implemented in software for curves in 2D and validated against several primitive implicit curves of different nanture: circles, sqaures, rectangles with different parameters of the model. The method has shown improved accuaracy in general, but there were several classes of corner cases found for which it deserves further development.Conclusions. Pseudo-Gaussian interpolation defined as a sum of radial basis functions on a regular grid with points of interpolation defined in the proximity of the grid points generally allows to model an implicit surface more accurately than a voxel model interpolation does. The memory intake or computational toll isn’t much different in these two approaches. However, the interpolating points selection strategy and the choice of the best modeling parameters for each particular modeling problem remain an open quesition.

Autonomous UAVs operating in GPS-denied environments rely heavily on onboard perception for safe navigation, yet traditional LiDAR and camera-based systems falter in poor lighting and weather situations. In contrast, millimetre wave (mmWave) radar offers superior robustness and low power consumption but produces extremely sparse, noisy, and low-resolution measurements that limit its utility for dense 3D understanding. This work proposes a novel radar-only inference framework that reconstructs dense LiDAR-like point clouds by leveraging a stereo millimeter-wave radar (IWR6843AoP) data with hallucinated Time-of-Flight (ToF) representations. Rather than relying on explicit ToF sensors, our method learns to infer mid-range depth priors through an auxiliary supervised hallucination network trained with radar inputs only. A unified PointNet-based architecture fuses stereo radar features with the hallucinated ToF embedding to generate dense Cartesian point clouds in real time. A large-scale, high-fidelity multimodal dataset of approximately 50,000 frames is generated in NVIDIA Isaac Sim to emulate realistic UAV sensor configurations. Experimental evaluations demonstrate strong robustness to radar noise and reliable geometric consistency suitable for downstream tasks such as ICP-based odometry. The resulting framework delivers LiDAR-like geometric structure using only radar at runtime, offering a computationally efficient, deployable, and resilient solution for UAV navigation in GPS-denied and harsh environmental conditions.

In the recent era, a lot of interest is attracted by the autonomous vehicles which can sense surroundings and navigate without human intervention. Object detection and recognition form a major part of autonomous driving systems. Lidar sensors can be used to capture point clouds of driving environment. Detecting multiple 3D objects in point clouds in real time and defining their boundaries with the help of 3D bounding boxes are critical in motion planning by self driving systems. This paper proposes a LiDAR-based 3D object detection system that operates in real-time, with emphasis on autonomous driving scenarios. A state-of-the-art 2D standard object detector for RGB images, YOLOv4, is used as the base for object detection. The multi-class 3D bounding boxes are generated using a complex regression approach. An Euler-Region-Proposal Network (E-RPN) is used to predict the pose of the object. The proposed model receives point cloud data as input and outputs 3D bounding boxes with classes in real-time. The experiments done on the KITTI benchmark dataset proves that the proposed system outperforms existing methods in terms of accuracy and performance.

In this paper, we present a scheme for analyzing structures which have complex shape models. The targets of the structural analysis usually consist of a combination of simple shape models senerated using modeling tools such as CAD systems. On the other hand, in the field of computer graphics, there have been proposed a number of techniques that make it possible to create complex shape models from point clouds obtained by three-dimensional (3D) range scanners. One suitable representation for the reconstructed shape is an implicit surface model. One typical advantage of the implicit representation is first inside/outside distinction. For the analysis of a structure represented as an implicit surface model, we use tlie Element-Free Galerkin Method (EFGM), which is suitable for the analysis of a structure with an implicit surface representation. For the analysis with the EFGM. internal nodes spread in the object are required and the nodes can be generated easily using the property of fast inside/outside distinction. We also note that the EFGM does not require any information about connectivity between adjoining nodes inside the model. We also present some numerical results of 3D stress problems.

Addresses the problem of texture mapping implicit surfaces. Recent work in providing 2D mappings for implicit surfaces maps points from an auxiliary parametric (support) surface to the implicit surface. In this work, we extend this method by observing that all commonly used skeletal elements are easily parameterized and can be used as their own support surfaces. In areas of a surface defined by the combination of multiple skeletal primitives, we compute a mapping through relations found with the zero-level surface of a primitive by using the gradient field.

We propose an algorithm for fluid simulation in three-dimensional scenes with obstacles represented as implicit surfaces. The fluid simulation is performed based on the smoothed particle hydrodynamics method and the behavior of fluid particles in the vicinity of obstacles is defined by introducing a new model of particle motion specific to implicitly representation. For effective parallelization on the graphics processing units, we apply the grid of polynomial method to express the implicitly defined obstacles. The proposed method takes advantage of the properties of implicit representation such as smoothness, shape modelling and the expression of deforming objects.

Implicit Surface-Based Geometric Fusion

A new surface based approach to implicit surface polygonisation is introduced. This is applied to the reconstruction of 3D surface models of complex objects from multiple range images. Geometric fusion of multiple range images into an implicit surface representation was presented in previous work. This paper introduces an efficient algorithm to reconstruct a triangulated model of a manifold implicit surface, a local 3D constraint is derived which defines the Delaunay surface triangulation of a set of points on a manifold surface in 3D space. The 'marching triangles' algorithm uses the local 3D constraint to reconstruct a Delaunay triangulation of an arbitrary topology manifold surface. Computational and representational costs are both a factor of 3-5 lower than previous volumetric approaches such as marching cubes.

We describe algebraic methods for creating implicit surfaces using linear combinations of radial basis interpolants to form complex models from scattered surface points. Shapes with arbitrary topology are easily represented without the usual interpolation or aliasing errors arising from discrete sampling. These methods were first applied to implicit surfaces by Savchenko, et al. and later developed independently by Turk and O'Brien as a means of performing shape interpolation. Earlier approaches were limited as a modeling mechanism because of the order of the computational complexity involved. We explore and extend these implicit interpolating methods to make them suitable for systems of large numbers of scattered surface points by using compactly supported radial basis interpolants. The use of compactly supported elements generates a sparse solution space, reducing the computational complexity and making the technique practical for large models. The local nature of compactly supported radial basis functions permits the use of computational techniques and data structures such as k-d trees for spatial subdivision, promoting fast solvers and methods to divide and conquer many of the subproblems associated with these methods. Moreover, the representation of complex models permits the exploration of diverse surface geometry. This reduction in computational complexity enables the application of these methods to the study of shape properties of large complex shapes.

In this paper, a new procedure for implicit surface reconstruction from oriented points is presented. A normal constraints based implicit polynomials fitting method and the partition of unity approach are fused into our framework. Firstly, a large scale input data is subdivided into some overlapping patches by octree. Then the global implicit surface is transferred into local implicit patch fitting and blending of them. To fit the local implicit polynomials, we build an energy by three steps corresponding to enforcement of the interpolatory constraints, satisfying of normal constraints and enhancement of fitting stability. The unkowns in an implicit polynomial are determined by minimizing this quadratic energy function. It is demonstrated in some experiments with several real data sets that this combination provides an intuitive and effective means to approximate the scattered point data associated normals.

Abstract. The Project ADFEX (Adaptive Federative 3D Exploration of Multi Robot System) pursues the goal to develop a time- and cost-efficient system for exploration and monitoring task of unknown areas or buildings. A fleet of unmanned aerial vehicles equipped with appropriate sensors (laser scanner, RGB camera, near infrared camera, thermal camera) were designed and built. A typical operational scenario may include the exploration of the object or area of investigation by an UAV equipped with a laser scanning range finder to generate a rough point cloud in real time to provide an overview of the object on a ground station as well as an obstacle map. The data about the object enables the path planning for the robot fleet. Subsequently, the object will be captured by a RGB camera mounted on the second flying robot for the generation of a dense and accurate 3D point cloud by using of structure from motion techniques. In addition, the detailed image data serves as basis for a visual damage detection on the investigated building. This paper focuses on our experience with use of a low-cost light-weight Hokuyo laser scanner onboard an UAV. The hardware components for laser scanner based 3D point cloud acquisition are discussed, problems are demonstrated and analyzed, and a quantitative analysis of the accuracy potential is shown as well as in comparison with structure from motion-tools presented.

Three-dimensional (3D) registration or matching is a crucial step in 3D model reconstruction. In this work, we develop a real-time 3D point cloud registration technology. Firstly, in order to achieve real-time 3D data acquisition, the stereo phase unwrapping method is utilized to eliminate the ambiguity of the wrapped phase, assisted with the depth constraint strategy without projecting any additional patterns or embedding any auxiliary signals. Then we implement SLAM-based coarse registration and ICP-based fine registration to match the point cloud data after the rapid identification of two-dimensional (2D) feature points. In order to improve the efficiency of 3D registration, the relative motion of the measured object at each coarse registration is quantified, through which only one fine registration is performed after several coarse registrations. The experiment shows that, the complex model can be registered in real time to reconstruct its whole 3D model with our method.

Randomly sampling points on surfaces is an essential operation in geometry processing. This sampling is computationally straightforward on explicit meshes, but it is much more difficult on other shape representations, such as widely‐used implicit surfaces. This work studies a simple and general scheme for sampling points on a surface, which is derived from a connection to the intersections of random rays with the surface. Concretely, given a subroutine to cast a ray against a surface and find all intersections, we can use that subroutine to uniformly sample white noise points on the surface. This approach is particularly effective in the context of implicit signed distance functions, where sphere marching allows us to efficiently cast rays and sample points, without needing to extract an intermediate mesh. We analyze the basic method to show that it guarantees uniformity, and find experimentally that it is significantly more efficient than alternative strategies on a variety of representations. Furthermore, we show extensions to blue noise sampling and stratified sampling, and applications to deform neural implicit surfaces as well as moment estimation.

This paper proposes spherical product functions to define implicit spherical product surfaces. A spherical product function is composed of a contour function and a profile function and its iso-surface's shape is generated by modulating and translating the iso-curve of the contour function through the points on the iso-curve of the profile function. This paper also shows if contour and profile functions are ray-linear, then an implicit spherical product surface can be parameterized and hence have both the advantages of implicit and parametric surfaces. Moreover, this paper proposes ray-linear two-branch and one-branch linear and super-hyperbolic functions that can be used to construct new contour and profile functions with asymmetric or symmetric iso-curves. Based on them, an implicit spherical product surface can has asymmetric or symmetric contour and profile and also has a parametric representation. P( α , β ) =(X( α , β ), Y( α , β ), Z( α , β )),

Explicit surfaces, such as triangulations or wireframe models, have been extensively used to represent the deformable 3D models that are used to fit 3D point and 2D silhouette data. The resulting approaches, however, suffer from the fact that fitting typically involves finding the facets that are closest to the 3D data points or most likely to be silhouette facets. This requires searching, which is slow, and dealing with the non-differentiability of the distance function. By contrast, implicit surface representations allow fitting without search, since one can simply evaluate a differentiable field function at every data point. However, implicit representations are not necessarily the most intuitive ones and users, such as graphics designers, tend to prefer explicit models.