3D Curve Sample Points for Watertight Shape Reconstruction
Find Innovative SolutionsGenerate Solutions
Solution Overview
Problem
Current computer-aided design systems face challenges in reconstructing closed, watertight 3D shapes from very sparse point clouds without orientation information, requiring dense point clouds or burdensome orientation vector definitions.
Innovation Solution
A computer-implemented method that uses optimization programs to determine orientation vectors normal to 3D curves, respecting a minimal rotation propagation condition, and fits sample points with an isovalue surface of a volumetric function, allowing for sparse point cloud reconstruction.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If point clouds are used to reconstruct 3D shapes, then the reconstruction can be performed from measurement data, but dense point clouds are required which increases data quantity and processing complexity
Solution Approach 1:
The patent transitions from 2D sketch curves to 3D shape reconstruction by introducing a volumetric function that operates in three-dimensional space. The system fits isovalue surfaces of the volumetric function to the 2D sketch data, effectively adding a dimensional transformation that enables sparse 3D reconstruction without requiring dense point clouds.
Solution Approach 2:
The patent changes the parameter representation from explicit point cloud coordinates to a volumetric function with associated isovalue surfaces. By optimizing the volumetric function parameters to match the sketch curves, the system achieves accurate shape reconstruction from sparse input data without needing dense sampling.
2Measurement precision
If orientation vectors are defined for each point to improve reconstruction quality, then the reconstruction accuracy improves, but the user burden and operational complexity increase
Solution Approach 1:
The system automatically computes orientation information from the optimized volumetric function gradient without requiring user input. The normal vectors are derived self-service from the mathematical structure of the volumetric function itself, eliminating the need for users to manually define orientation vectors at each point.
Solution Approach 2:
The volumetric function serves as an intermediary between the 2D sketch curves and the 3D shape reconstruction. It mediates the transformation by providing a continuous mathematical representation that implicitly defines both position and orientation information, removing the need for explicit orientation vector specification.
3Ease of manufacture
If curves are interpreted as representing a network topology to create B-Rep, then manufacturable objects can be created, but topological constraints and complexity increase
Solution Approach 1:
Instead of constructing a B-Rep boundary representation from curve networks with explicit topological constraints, the patent inverts the approach by using an implicit volumetric function representation. The isovalue surfaces of the volumetric function naturally define closed manifolds suitable for manufacturing without requiring explicit topological inference from curve crossings.
Data Source
AI summary
The invention notably relates to a computer-implemented method for designing a three-dimensional modeled object comprising providing sample points of 3D curves sketched by a user; determining a volumetric function, within a predetermined class of volumetric functions, as the optimum of an optimization program that explores orientation vectors defined at the sample points under the constraint that the explored orientation vectors be normal to the 3D curves and respect a minimal rotation propagation condition over each 3D curve, wherein the optimization program penalizes a distance from the explored orientation vectors; and fitting the sample points with an isovalue surface of the volumetric function.