arXiv:2412.08484v4 Announce Type: replace-cross 
Abstract: Modern mesh generation pipelines whether learning-based or classical often produce outputs requiring post-processing to achieve production-quality geometry. This work introduces MeshCone, a convex optimization framework for guided mesh refinement that leverages reference geometry to correct deformed or degraded meshes. We formulate the problem as a second-order cone program where vertex positions are optimized to align with target geometry while enforcing smoothness through convex edge-length regularization. MeshCone performs geometry-aware optimization that preserves fine details while correcting structural defects. We demonstrate robust performance across 56 diverse object categories from ShapeNet and ThreeDScans, achieving superior refinement quality compared to Laplacian smoothing and unoptimized baselines while maintaining sub-second inference times. MeshCone is particularly suited for applications where reference geometry is available, such as mesh-from-template workflows, scan-to-CAD alignment, and quality assurance in asset production pipelines.

تم تقديم MeshCone كإطار لتحسين تقني قائم على البرمجة الخطية المزدوجة مصمم لتحسين الشبكات بشكل موجه، باستخدام هندسة مرجعية لتحسين جودة الشبكات المشوهة أو المتدهورة. تقوم هذه الطريقة بصياغة مشكلة التحسين كبرنامج مخروط من الدرجة الثانية، مع التركيز على محاذاة مواقع الرؤوس مع الهندسة المستهدفة مع ضمان السلاسة من خلال تنظيم طول الحواف.

MeshCone ha sido introducido como un marco de optimización convexa diseñado para el refinamiento guiado de mallas, utilizando geometría de referencia para mejorar la calidad de mallas deformadas o degradadas. Este método formula el problema de optimización como un programa de cono de segundo orden, centrándose en alinear las posiciones de los vértices con la geometría objetivo mientras asegura suavidad a través de la regularización de la longitud de las aristas.

MeshCone a été introduit comme un cadre d'optimisation convexe conçu pour le raffinement guidé des maillages, utilisant la géométrie de référence pour améliorer la qualité des maillages déformés ou dégradés. Cette méthode formule le problème d'optimisation comme un programme de cône de second ordre, se concentrant sur l'alignement des positions des sommets avec la géométrie cible tout en garantissant la douceur grâce à la régularisation de la longueur des arêtes.

MeshCone has been introduced as a convex optimization framework designed for guided mesh refinement, utilizing reference geometry to enhance the quality of deformed or degraded meshes. This method formulates the optimization problem as a second-order cone program, focusing on aligning vertex positions with target geometry while ensuring smoothness through edge-length regularization.

MeshCone: Second-Order Cone Programming for Geometrically-Constrained Mesh Enhancement

arXiv:2503.08594v3 Announce Type: replace-cross 
Abstract: Autoregressive point cloud generation has long lagged behind diffusion-based approaches in quality. The performance gap stems from the fact that autoregressive models impose an artificial ordering on inherently unordered point sets, forcing shape generation to proceed as a sequence of local predictions. This sequential bias emphasizes short-range continuity but undermines the model's capacity to capture long-range dependencies, hindering its ability to enforce global structural properties such as symmetry, consistent topology, and large-scale geometric regularities. Inspired by the level-of-detail (LOD) principle in shape modeling, we propose PointNSP, a coarse-to-fine generative framework that preserves global shape structure at low resolutions and progressively refines fine-grained geometry at higher scales through a next-scale prediction paradigm. This multi-scale factorization aligns the autoregressive objective with the permutation-invariant nature of point sets, enabling rich intra-scale interactions while avoiding brittle fixed orderings. Experiments on ShapeNet show that PointNSP establishes state-of-the-art (SOTA) generation quality for the first time within the autoregressive paradigm. In addition, it surpasses strong diffusion-based baselines in parameter, training, and inference efficiency. Finally, in dense generation with 8,192 points, PointNSP's advantages become even more pronounced, underscoring its scalability potential.

تم تقديم PointNSP كإطار عمل ذاتي الانحدار لتوليد سحب النقاط ثلاثية الأبعاد، حيث يعالج القيود التي تواجه النماذج التقليدية التي تكافح لالتقاط الاعتماديات على المدى الطويل والخصائص الهيكلية العالمية. تستخدم هذه الطريقة المبتكرة إطارًا توليديًا من الخشن إلى الدقيق يحافظ على الهيكل العام للشكل عند الدقة المنخفضة بينما يقوم بتحسين الهندسة الدقيقة عند المقاييس الأعلى.

PointNSP se ha introducido como un marco autorregresivo para la generación de nubes de puntos 3D, abordando las limitaciones de los modelos tradicionales que luchan por capturar dependencias a largo plazo y propiedades estructurales globales. Este enfoque innovador emplea un marco generativo de grueso a fino que preserva la estructura global de la forma a bajas resoluciones mientras refina la geometría detallada a escalas más altas.

PointNSP a été introduit comme un cadre autorégressif pour la génération de nuages de points 3D, abordant les limitations des modèles traditionnels qui peinent à capturer les dépendances à long terme et les propriétés structurelles globales. Cette approche innovante utilise un cadre génératif de grossier à fin qui préserve la structure globale de la forme à basse résolution tout en affinant la géométrie détaillée à des échelles plus élevées.

PointNSP has been introduced as an autoregressive framework for generating 3D point clouds, addressing the limitations of traditional models that struggle with capturing long-range dependencies and global structural properties. This innovative approach employs a coarse-to-fine generative framework that preserves global shape structure at low resolutions while refining fine-grained geometry at higher scales.

MeshCone: Second-Order Cone Programming for Geometrically-Constrained Mesh Enhancement

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