Treat the Steradian as the 2-Manifold - Githubissues

HanetakaChou / PatriotEngine

PatriotEngine aims to be a state-of-the-art real-time image synthesis engine.

https://hanetakachou.github.io/PatriotEngine

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Treat the Steradian as the 2-Manifold #64

Open HanetakaChou opened 3 years ago

HanetakaChou commented 3 years ago

1.To learn the Differential Geometry and try to treat the Steradian as the 2-Manifold which reduces the dimensions from 3(R^3) to 2(S^2) and simplifies the integral over the sphere surface when one calculates the lighting.
Try to understand the following papers from the perspective of the 2-Manifold:
- An Introduction to Manifolds / Example 23.11 (Integral over a sphere)
  [Tu 2011] Loring Tu. "An Introduction to Manifolds, Second Edition." Springer 2011.
- LTC
  [Heitz 2016] Eric Heitz, Jonathan Dupuy, Stephen Hill and David Neubelt. "Real-Time Polygonal-Light Shading with Linearly Transformed Cosines." SIGGRAPH 2016

1.学习微分几何(Differential Geometry)，尝试将球面度(Steradian)看作二维流形(2-Manifold)，从而更深刻地理解渲染中相关的公式，并尝试从微分几何的角度理解以下论文： /*重点目标*/**
- An Introduction to Manifolds / Example 23.11 (Integral over a sphere)
  [Tu 2011] Loring Tu. "An Introduction to Manifolds, Second Edition." Springer 2011.
- LTC
  [Heitz 2016] Eric Heitz, Jonathan Dupuy, Stephen Hill and David Neubelt. "Real-Time Polygonal-Light Shading with Linearly Transformed Cosines." SIGGRAPH 2016

HanetakaChou commented 3 years ago

To my pleasure, someone seems to have the similar idea which I find on the Google Scholar:
- [Herholz 2018] Sebastian Herholz, Oskar Elek, Jens Schindel, Jaroslav krivanek, Hendrik Lensch. "A Unified Manifold Framework for Efficient BRDF Sampling based on Parametric Mixture Models." EGSR 2018.
The traditional Euclidean-Space method may be replaced by the efficient 2-Manifold method in the next few years.