Oscar Ruiz-Salguero

Hessian Eigenfunctions for Triangular Mesh Parameterization

Hessian Locally Linear Embedding (HLLE) is an algorithm that computes the nullspace of a Hessian functional n nH for Dimensionality Reduction (DR) of a sampled manifold M. This article presents a variation of n nclassic HLLE for parameterization of 3D triangular meshes. Contrary to classic HLLE which estimates local n nHessian nullspaces, the proposed approach follows intuitive ideas from Differential Geometry where the local n nHessian is estimated by quadratic interpolation and a partition of unity is used to join all neighborhoods. In n naddition, local average triangle normals are used to estimate the tangent plane TxM at x 2 M instead of PCA, n nresulting in local parameterizations which reflect better the geometry of the surface and perform better when n nthe mesh presents sharp features. A high frequency dataset (Brain) is used to test our algorithm resulting in a n nhigher rate of success (96:63%) compared to classic HLLE (76:4%).

Inverse Kinematics for Upper Limb Compound Movement Estimation in Exoskeleton-Assisted Rehabilitation.

Robot-Assisted Rehabilitation (RAR) is relevant for treating patients affected by nervous system injuries (e.g., stroke and spinal cord injury). The accurate estimation of the joint angles of the patient limbs in RAR is critical to assess the patient improvement. The economical prevalent method to estimate the patient posture in Exoskeleton-based RAR is to approximate the limb joint angles with the ones of the Exoskeleton. This approximation is rough since their kinematic structures differ. Motion capture systems (MOCAPs) can improve the estimations, at the expenses of a considerable overload of the therapy setup. Alternatively, the Extended Inverse Kinematics Posture Estimation (EIKPE) computational method models the limb and Exoskeleton as differing parallel kinematic chains. EIKPE has been tested with single DOF movements of the wrist and elbow joints. This paper presents the assessment of EIKPE with elbow-shoulder compound movements (i.e., object prehension). Ground-truth for estimation assessment is obtained from an optical MOCAP (not intended for the treatment stage). The assessment shows EIKPE rendering a good numerical approximation of the actual posture during the compound movement execution, especially for the shoulder joint angles. This work opens the horizon for clinical studies with patient groups, Exoskeleton models, and movements types.

Mesh segmentation and texture mapping for dimensional inspection in Web3D

Traditionally, the data generated by industrial metrology software is stored as static reports that metrology experts produce for engineering and production departments. Nevertheless, industry demands new approaches that provide ubiquitous and real time access to overall geometry, manufacturing and other data. Web3D technologies can help to improve the traditional metrology methods and offer new ways to convey this information in web-based continuous friendly manner. However, enriched point clouds may be massive, thus presenting transmission and display limitations. To partially overcome these limitations, this article presents an algorithm that computes efficient metrology textures, which are then transferred and displayed through Web3D standards. Texture coordinates are computed only once for the reference CAD mesh on the server using in-house thermal-based segmentation and Hessian-based parameterization algorithms. The metrology data is then encoded in a texture file, which becomes available instantly for interactive visual inspection through the Web3D platform.

FEA Structural Optimization Based on Metagraphs.

Evolutionary Structural Optimization (ESO) seeks to mimic the form in which nature designs shapes. This paper focuses on shape carving triggered by environmental stimuli. In this realm, existing algorithms delete under - stressed parts of a basic shape, until a reasonably efficient (under some criterion) shape emerges. In the present article, we state a generalization of such approaches in two forms: (1) We use a formalism that enables stimuli from different sources, in addition to stress ones (e.g. kinematic constraints, friction, abrasion). (2) We use metagraphs built on the Finite Element constraint graphs to eliminate the dependency of the evolution on the particular neighborhood chosen to be deleted in a given iteration. The proposed methodology emulates 2D landmark cases of ESO. Future work addresses the implementation of such stimuli type, the integration of our algorithm with evolutionary based techniques and the extension of the method to 3D shapes.

Fast Analytic Simulation for Multi-Laser Heating of Sheet Metal in GPU

Interactive multi-beam laser machining simulation is crucial in the context of tool path planning and optimization of laser machining parameters. Current simulation approaches for heat transfer analysis (1) rely on numerical Finite Element methods (or any of its variants), non-suitable for interactive applications; and (2) require the multiple laser beams to be completely synchronized in trajectories, parameters and time frames. To overcome this limitation, this manuscript presents an algorithm for interactive simulation of the transient temperature field on the sheet metal. Contrary to standard numerical methods, our algorithm is based on an analytic solution in the frequency domain, allowing arbitrary time/space discretizations without loss of precision and non-monotonic retrieval of the temperature history. In addition, the method allows complete asynchronous laser beams with independent trajectories, parameters and time frames. Our implementation in a GPU device allows simulations at interactive rates even for a large amount of simultaneous laser beams. The presented method is already integrated into an interactive simulation environment for sheet cutting. Ongoing work addresses thermal stress coupling and laser ablation.

Geometry simplification of open-cell porous materials for elastic deformation FEA

Estimation of mechanical properties of porous materials is central for their medical and industrial application. However, the massive size of accurate boundary representations (B-Rep) of the foams makes the numerical estimations intractable. Even for small domain sizes, the mesh generation for finite element analysis (FEA) may not terminate. Current efforts for simulating porous materials use statistical predictions of the material structure. The simulated and actual materials present different geometry and topology, with consequences on the simulation results. To overcome these limitations, this manuscript presents a method, which (1) synthesizes an accurate truss abstraction from the raw geometry data, (2) executes efficient FEA simulations, and (3) processes nodal displacements to estimate apparent mechanical moduli of the porous material. The method addresses materials whose ligaments have circular cross-sections. The iso-surface present in the Computer Tomography (CT) scan of the porous material is used to synthesize a truss graph whose edges are truncated cones. Then, optimization and simplification methods are applied to produce a topologically and geometrically correct truss representation for the foam domain. Comparative FEA load simulations are conducted between the full B-Rep and truss representations of the material. The truss model proves to be significantly more efficient for FEA, departing from the Full B-Rep FEA by a maximum of 16% in the estimation of equivalent mechanical moduli. Geometric assessments such as porosity and Hausdorff distance confirm that the truss abstraction is a cost-effective one. Ongoing efforts concentrate on point set geometric algorithms for enforcement of standardized material testing.

Hybrid geometry / topology based mesh segmentation for reverse engineering

Abstract Mesh segmentation and parameterization are crucial for Reverse Engineering (RE). Bijective parameterizations of the sub-meshes are a sine-qua-non test for segmentation. Current segmentation methods use either (1) topologic or (2) geometric criteria to partition the mesh. Reported topology-based segmentations produce large sub-meshes which reject parameterizations. Geometry-based segmentations are very sensitive to local variations in dihedral angle or curvatures, thus producing an exaggerated large number of small sub-meshes. Although small sub-meshes accept nearly isometric parameterizations, this significant granulation defeats the intent of synthesizing a usable Boundary Representation (compulsory for RE). In response to these limitations, this article presents an implementation of a hybrid geometry / topology segmentation algorithm for mechanical workpieces. This method locates heat transfer constraints (topological criterion) in low frequency neighborhoods of the mesh (geometric criterion) and solves for the resulting temperature distribution on the mesh. The mesh partition dictated by the temperature scalar map results in large, albeit parameterizable, sub-meshes. Our algorithm is tested with both benchmark repository and physical piece scans data. The experiments are successful, except for the well - known cases of topological cylinders, which require a user - introduced boundary along the cylinder generatrices.

Weighted area/angle distortion minimization for Mesh Parameterization

Purpose n n n n nMesh Parameterization is central to reverse engineering, tool path planning, etc. This work synthesizes parameterizations with un-constrained borders, overall minimum angle plus area distortion. This study aims to present an assessment of the sensitivity of the minimized distortion with respect to weighed area and angle distortions. n n n n nDesign/methodology/approach n n n n nA Mesh Parameterization which does not constrain borders is implemented by performing: isometry maps for each triangle to the plane Z = 0; an affine transform within the plane Z = 0 to glue the triangles back together; and a Levenberg–Marquardt minimization algorithm of a nonlinear F penalty function that modifies the parameters of the first two transformations to discourage triangle flips, angle or area distortions. F is a convex weighed combination of area distortion (weight: α with 0 ≤ α ≤ 1) and angle distortion (weight: 1 − α). n n n n nFindings n n n n nThe present study parameterization algorithm has linear complexity [𝒪(n), n = number of mesh vertices]. The sensitivity analysis permits a fine-tuning of the weight parameter which achieves overall bijective parameterizations in the studied cases. No theoretical guarantee is given in this manuscript for the bijectivity. This algorithm has equal or superior performance compared with the ABF, LSCM and ARAP algorithms for the Ball, Cow and Gargoyle data sets. Additional correct results of this algorithm alone are presented for the Foot, Fandisk and Sliced-Glove data sets. n n n n nOriginality/value n n n n nThe devised free boundary nonlinear Mesh Parameterization method does not require a valid initial parameterization and produces locally bijective parameterizations in all of our tests. A formal sensitivity analysis shows that the resulting parameterization is more stable, i.e. the UV mapping changes very little when the algorithm tries to preserve angles than when it tries to preserve areas. The algorithm presented in this study belongs to the class that parameterizes meshes with holes. This study presents the results of a complexity analysis comparing the present study algorithm with 12 competing ones.