Parametric 3D Tessellation via Hierarchical 2D Meshes
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Solution Overview
Problem
Current tessellation methods, such as static and PNT tessellation, face challenges in efficiently approximating complex 3D modeled objects for rendering and geometric operations, leading to issues like high memory consumption, limited accuracy, and visualization artifacts due to inaccurate normal vector computation.
Innovation Solution
A computer-implemented method that provides planar 2D meshes associated with geometrical data of a boundary representation, allowing for the determination of 3D meshes by evaluating vertex positions on parametric surfaces, with optional subdivision and normal vector computation based on parametric surfaces, enabling faster and more accurate tessellation with reduced memory usage.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Measurement precision
If static tessellation is used to approximate complex 3D surfaces, then the surface can be rendered for display, but memory consumption increases and accuracy is limited
Solution Approach 1:
The patent applies preliminary action by pre-computing and storing a hierarchical structure of tessellation data at multiple levels of detail before rendering. This allows the system to quickly access appropriately detailed tessellation data without computing it in real-time, resolving the contradiction between achieving high accuracy and managing memory consumption efficiently.
Solution Approach 2:
The patent implements dynamics by creating a dynamic tessellation system that adapts the level of detail based on viewing distance, camera angle, and importance of surface regions. This allows the system to use higher accuracy tessellation where needed and lower accuracy where acceptable, optimizing the balance between accuracy and memory usage.
2Productivity
If PNT tessellation is used for faster processing, then rendering speed improves, but visualization artifacts occur due to inaccurate normal vector computation
Solution Approach 1:
The patent introduces an intermediary hierarchical tessellation structure that mediates between fast PNT tessellation and accurate normal computation. This intermediate structure allows the system to use efficient PNT methods for generating base geometry while computing more accurate normal vectors through the hierarchical refinement process, eliminating visualization artifacts.
Solution Approach 2:
The patent replaces the traditional mechanical approach of computing normals from low-resolution PNT tessellation with a mathematical approach using hierarchical basis functions. This substitution allows normal vectors to be computed analytically from the hierarchical representation, maintaining both speed and accuracy.
3Measurement precision
If higher accuracy tessellation is applied to maintain surface precision, then rendering quality improves, but processing time increases
Solution Approach 1:
The patent applies segmentation by dividing the surface into hierarchical patches at multiple levels of detail. This allows the system to process and render different regions at appropriate accuracy levels simultaneously, reducing overall processing time while maintaining high accuracy where needed.
Solution Approach 2:
The patent implements periodic action through its hierarchical structure, where tessellation data is organized in repeating patterns at different scales. This periodic organization allows for efficient cache utilization and parallel processing, significantly reducing the time required to generate high-accuracy tessellation.
Data Source
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AI summary
It is proposed a computer-implemented method for tessellating a three-dimensional modeled object parameterized for tessellation. The method comprises the steps of providing (S40) 2D meshes associated to geometrical data of a boundary representation of the modeled object, the boundary representation comprising the geometrical data including parametric surfaces and topological data including a set of faces each defined as a portion of the 2D domain of a respective parametric surface; and determining (S60) 3D meshes by evaluating the position of vertices of the 2D meshes on the respective parametric surfaces. Such a solution improves the tessellation of a 3D modeled object.