Mesh Simplification Using Guide Planes for Vertex Alignment
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Solution Overview
Problem
Mesh simplification techniques, such as polychord collapse, often result in irregularly positioned vertices after edge collapse, leading to an unsuitable representation of the original mesh edges, which affects the smoothness and fidelity of the simplified mesh.
Innovation Solution
The use of guide planes to adjust the location of collapsed vertices, ensuring they align more accurately with the original edges by determining and smoothing parametric line values, thereby improving the smoothness and geometric fidelity of the simplified mesh.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Productivity
If mesh simplification is performed using traditional edge collapse techniques, then the complexity of the mesh is reduced with fewer faces, edges, and vertices, but the smoothness and geometric fidelity of the simplified mesh deteriorates due to irregularly positioned vertices
Solution Approach 1:
The patent introduces guide planes as intermediary geometric structures that mediate between the original mesh edges and the collapsed vertices. These guide planes serve as reference surfaces that constrain and guide the positioning of collapsed vertices, ensuring they align smoothly with the original mesh geometry rather than being placed irregularly. This intermediary structure resolves the contradiction by providing a geometric framework that maintains vertex positioning accuracy during the simplification process.
Solution Approach 2:
The patent transforms the vertex positioning problem from a discrete point placement issue into a continuous parameter optimization problem. By representing vertex positions using parametric equations along guide plane intersections and optimizing these parameters to minimize geometric deviation, the method achieves smooth vertex positioning while maintaining mesh simplification efficiency. This parameter-based approach allows for precise control over vertex locations without compromising simplification performance.
2Productivity
If vertices are collapsed during mesh simplification, then the number of vertices is reduced improving rendering performance, but the alignment with original edges deteriorates resulting in irregular positioning
Solution Approach 1:
The patent moves the vertex positioning problem from two-dimensional surface placement into a three-dimensional constraint system defined by intersecting guide planes. By introducing this additional spatial dimension with multiple constraining planes, the method achieves precise control over collapsed vertex positions, ensuring they align smoothly with original edges while still reducing vertex count for improved rendering performance.
3Manufacturing precision
If guide planes are introduced to improve vertex positioning, then the smoothness and fidelity of the simplified mesh is improved, but the complexity of the simplification process increases
Solution Approach 1:
The patent divides the mesh simplification process into distinct segments: (1) identifying candidate edges for collapse, (2) constructing guide planes for each candidate, (3) calculating optimal collapsed vertex positions using the guide planes, and (4) executing the collapse. This segmentation allows each sub-process to be optimized independently, managing overall complexity while achieving high vertex positioning accuracy through the guide plane mechanism.
Data Source
AI summary
A mesh that includes a polychord with edges may be received. A first mesh simplification operation may be performed with the mesh to remove the edges of the polychord and to generate a first simplified mesh. Guide planes may be generated based on the first simplified mesh. Furthermore, a second mesh simplification operation may be performed with a combination of the mesh with the guide planes to remove the edges of the polychord based on the guide planes and to generate a second simplified mesh.