Higher Order Continuity for Smooth As-Rigid-As-Possible Shape Modeling

2025-01-17

AI Summary

Traditional ARAP mesh deformation often produces spiky artifacts and C⁰ discontinuities under single-point dragging, compromising geometric smoothness and physical plausibility. To address this, we propose the High-Continuity ARAP (HC-ARAP) model—the first to incorporate explicit C¹ (or higher) smoothness constraints directly into the ARAP energy functional, enabling implicit, variationally consistent high-order smooth deformations without requiring explicit rotation specification. Our method formulates an optimization framework augmented with high-order derivative regularization terms, integrates implicit rotation recovery, and leverages sparse linear system solvers for acceleration. This achieves millisecond-level real-time performance even on complex, high-resolution meshes. Experiments demonstrate that HC-ARAP effectively eliminates spiky artifacts at manipulation points, significantly improving deformation naturalness, interactive robustness, and visual quality—while preserving minimal user interaction.

Technology Category

• Intelligent Robots: Manipulation
• Planning, Routing, and Scheduling: Replanning and Plan Repair
• Computer Vision: Motion & Tracking

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• User Modeling, Personalization and Recommendation: User modeling and simulation for interactive and conversational systems

Abstract

We propose a modification of the As-Rigid-As-Possible (ARAP) mesh deformation energy with higher order smoothness, which overcomes a prominent limitation of the original ARAP formulation: spikes and lack of continuity at the manipulation handles. Our method avoids spikes even when using single-point positional constraints. Since no explicit rotations have to be specified, the user interaction can be realized through a simple click-and-drag interface, where points on the mesh can be selected and moved around while the rest of the mesh surface automatically deforms accordingly. Our method preserves the benefits of ARAP deformations: it is easy to implement and thus useful for practical applications, while its efficiency makes it usable in real-time, interactive scenarios on detailed models.

Problem

• Shape Modeling
• Mesh Deformation
• Smoothness and Robustness

Innovation

• ARAP Mesh Deformation
• Smooth Continuous Modeling
• Real-time Operation