Learning Conjugate Direction Fields for Planar Quadrilateral Mesh Generation

TL;DR

This paper introduces a neural network-based method for generating conjugate direction fields on freeform surfaces to facilitate planar quadrilateral mesh creation, significantly improving efficiency and user control over traditional optimization approaches.

Contribution

We propose a data-driven neural network approach for controlled conjugate direction field generation, enabling interactive PQ mesh design with a new large-scale dataset and evaluation metrics.

Findings

Our method produces high-quality CDFs aligned with user strokes.

It significantly reduces computation time compared to traditional optimization.

Extensive experiments validate the effectiveness and generality of the approach.

Abstract

Planar quadrilateral (PQ) mesh generation is a key process in computer-aided design, particularly for architectural applications where the goal is to discretize a freeform surface using planar quad faces. The conjugate direction field (CDF) defined on the freeform surface plays a significant role in generating a PQ mesh, as it largely determines the PQ mesh layout. Conventionally, a CDF is obtained by solving a complex non-linear optimization problem that incorporates user preferences, i.e., aligning the CDF with user-specified strokes on the surface. This often requires a large number of iterations that are computationally expensive, preventing the interactive CDF design process for a desirable PQ mesh. To address this challenge, we propose a data-driven approach based on neural networks for controlled CDF generation. Our approach can effectively learn and fuse features from the freeform surface and the user strokes, and efficiently generate quality CDF respecting user guidance. To enable training and testing, we also present a dataset composed of 50000+ freeform surfaces with ground-truth CDFs, as well as a set of metrics for quantitative evaluation. The effectiveness and efficiency of our work are demonstrated by extensive experiments using testing data, architectural surfaces, and general 3D shapes.