Mesh Smoothing via Local Quadratic Surface Fitting
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Solution Overview
Problem
Existing mesh smoothing methods are ineffective for non-uniform vertex distributions and often result in model shrinkage, altering the shape of the object during the smoothing process.
Innovation Solution
A method that identifies neighboring vertices within a desired distance, determines a local coordinate system with the normal of the target vertex as the z-axis, and fits a quadratic surface function to each vertex using singular value decomposition to calculate new coordinates, ensuring effective smoothing without shape distortion.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If prior mesh smoothing methods are used, then noise can be removed from meshes with uniform vertex distributions, but the methods fail to perform well on non-uniform vertex distributions and cause model shrinkage
Solution Approach 1:
The patent applies local quality by establishing a local coordinate system for each vertex based on its neighboring vertices and triangles. The smoothing operation is performed independently at each vertex using its local geometry, allowing the method to adapt to non-uniform vertex distributions while effectively removing noise. This local approach ensures that each vertex is smoothed according to its specific local characteristics rather than using a global uniform method.
2Manufacturing precision
If prior mesh smoothing methods are used, then noise can be removed from meshes, but the model shrinks and shape is altered
Solution Approach 1:
The patent introduces a local coordinate system with an additional dimension (the normal direction) to handle the smoothing operation. By working in this extended local coordinate space and using quadratic surface fitting, the method can smooth vertices while preserving the overall model shape and size, avoiding the shrinkage effect of prior methods.
3Manufacturing precision
If geometric smoothing methods are used, then mesh vertices can be smoothed by averaging neighboring points, but the method is computationally intensive and time-consuming
Solution Approach 1:
The patent applies partial action by using a quadratic surface fit that only adjusts the necessary components (a, b, c, d, e, f parameters) rather than performing complete geometric smoothing operations on all vertices simultaneously. This partial approach reduces computational complexity while maintaining effective smoothing quality.
Data Source
AI summary
A method and apparatus for the smoothing of a mesh surface is disclosed whereby neighboring vertices of a target vertex are identified, for example, by identifying the neighboring vertices within a desired distance from the target vertex. A normal of the target vertex is determined as a function of, for example, the features of a set of neighbor triangles corresponding to the set of neighboring vertices. A local coordinate system is then established. Unknowns in a quadratic surface function are then solved as a function of the position of the neighboring vertices with respect to the local coordinate system and new x and y coordinates in the local coordinate system are determined for the target vertex. These new x and y coordinates are entered into the quadratic surface function to obtain a new smoothed z coordinate for the target vertex.