The combination of polynomial regression with the control variable method is an effective approach for enhancing Monte Carlo integration for rendering local blocks.However, the high uncertainty and non-linear distribution of luminance in local blocks lead to higher computational errors in polynomial regression.To address this issue, we propose a new Monte Carlo estimation method.This method uses the bicubic B-spline surface to accurately fit the luminance of local blocks.The flexible node vectors of B-spline functions increase adaptability to non-linear distributions.The control variable method reduces errors in luminance estimation.We conduct experimental validation across multiple scenes in direct lighting environments.The results show that the Monte Carlo estimation method based on the bicubic B-spline surface and the control variable method significantly outperforms traditional polynomial regression fitting methods.The improvement is especially evident in blocks with significant luminance variations.

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The Application of the Bicubic B-Spline Fitting in Local Block Rendering

  • Jiatao Yao,
  • Shaobo Zhou,
  • Long Yang,
  • Shaojun Hu,
  • Zhiyi Zhang

摘要

The combination of polynomial regression with the control variable method is an effective approach for enhancing Monte Carlo integration for rendering local blocks.However, the high uncertainty and non-linear distribution of luminance in local blocks lead to higher computational errors in polynomial regression.To address this issue, we propose a new Monte Carlo estimation method.This method uses the bicubic B-spline surface to accurately fit the luminance of local blocks.The flexible node vectors of B-spline functions increase adaptability to non-linear distributions.The control variable method reduces errors in luminance estimation.We conduct experimental validation across multiple scenes in direct lighting environments.The results show that the Monte Carlo estimation method based on the bicubic B-spline surface and the control variable method significantly outperforms traditional polynomial regression fitting methods.The improvement is especially evident in blocks with significant luminance variations.