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Linear Correlations between Spatial and Normal Noise in Triangle Meshes.

Ying Yang, Norbert Peyerimhoff, Ioannis Ivrissimtzis

    IEEE Transactions on Visualization and Computer Graphics
    |April 18, 2012
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    We found a linear relationship between spatial noise in triangle mesh vertices and normal noise. This allows efficient computation of normal distortion, useful for dithered quantization analysis in 3D graphics.

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    Area of Science:

    • Computer Graphics
    • Computational Geometry
    • Digital Image Processing

    Background:

    • Triangle meshes are fundamental in 3D graphics.
    • Noise in vertex coordinates can lead to undesirable normal distortion.
    • Understanding this relationship is crucial for mesh processing and rendering.

    Purpose of the Study:

    • To investigate the relationship between vertex coordinate noise and normal noise in triangle meshes.
    • To develop efficient methods for quantifying normal distortion caused by spatial noise.
    • To analyze mesh vertex dithered quantization based on normal distortion tolerance.

    Main Methods:

    • Closed-form computation of normal angle change for single-vertex noise.
    • Approximation, lower, and upper bounds for normal angle change with multi-vertex noise.
    • Experimental validation of proposed bounds and approximations.
    • Analysis of linear correlation between spatial and normal noise.

    Main Results:

    • A linear correlation exists between normal angle distortion (θ) and functions of triangle heights for small spatial noise.
    • Efficient computation of θ is possible due to this linear correlation.
    • Spatial noise on vertices is analogous to dithered quantization.

    Conclusions:

    • The study provides a method to efficiently compute normal distortion from spatial noise in triangle meshes.
    • The findings enable the calculation of dithered quantization levels for mesh vertices given a normal distortion tolerance.
    • This research contributes to a better understanding of noise effects in 3D mesh representations.