Rendering 3D Quadratic Bézier Curves by Accumulation

This paper first proposes a method for 3D curve rendering by modeling the appearance of a parametric curve as a uniform strip of point light emitters, whilst modeling each pixel on the observing screen as a receiver that receives light in the ray direction, resulting in evaluation of a double line integral. This outlines a general framework for 3D curve rendering that is easily portable to other applications. In terms of quadratic Bézier curves, we finally derive an analytic result from our method by choosing a suitable model for a point light, which does not involve any approximation or any numerical integration analysis. Based on this, we propose a novel rendering routine for 3D quadratic Bézier curves and provide a corresponding implementation using the wgpu API. Our approach offers solutions to ensure order-independence of curve segments and continuous light intensity values on the observing screen, while avoiding common artifacts. The implementation results demonstrate the feasibility and effectiveness of our method, highlighting its potential for high-quality 3D rendering. Additionally, we identify areas for future work to further refine and optimize the rendering process.