A Ray Tracing Approach to Diffusion Curves

Abstract

Diffusion curves [OBW * 08] provide a flexible tool to create smooth-shaded images from curves defined with colors. The resulting image is typically computed by solving a Poisson equation that diffuses the curve colors to the interior of the image. In this paper we present a new method for solving diffusion curves by using ray tracing. Our approach is analogous to final gathering in global illumination, where the curves define source radiance whose visible contribution will be integrated at a shading pixel to produce a color using stochastic ray tracing. Compared to previous work, the main benefit of our method is that it provides artists with extended flexibility in achieving desired image effects. Specifically, we introduce generalized curve colors called shaders that allow for the seamless integration of diffusion curves with classic 2D graphics including vector graphics (e.g. gradient fills) and raster graphics (e.g. patterns and textures). We also introduce several extended curve attributes to customize the contribution of each curve. In addition, our method allows any pixel in the image to be independently evaluated, without having to solve the entire image globally (as required by a Poisson-based approach). Finally, we present a GPU-based implementation that generates solution images at interactive rates, enabling dynamic curve editing. Results show that our method can easily produce a variety of desirable image effects.

Gradient Art: Creation and Vectorization

“…Pang et al propose a sorting algorithm that identify the curve segments visible from each vertex. Similarly, Takayama et al [24] use the hardware depth buffer to compute visibility of diffusion surfaces over the vertices of a mesh., while Bowers et al [4] perform ray tracing in a pixel shader to render diffusion curves.…”

“…The main limitation of diffusion curves is the lack of control over the propagation of colors. This is the reason why several extensions have been proposed to improve artistic control using directional diffusion and blockers [3,4], or to produce a smoother color propagation [10]. Jeschke et al [13] also use diffusion curves to control the parameters of procedural textures, while Hnaidi et al [11] create height fields by diffusing height from curves that represent ridges and cliffs.…”

A vectorial solver for free-form vector gradients

“…The artistic control of DCs has been improved by several extensions such as blockers and directional diffusion [Bezerra et al 2010;Bowers et al 2011]. Finch et al [2011] proposed to solve the higher order Bi-Laplace equation to avoid "tent-like" gradients and produce a smoother color interpolation.…”

“…To evaluate visibility, they employ an exhaustive sorting algorithm. An alternative consists in performing ray tracing on the GPU via a pixel shader [Bowers et al 2011]. The approach of Sun et al [2012] avoids the explicit computation of visibility thanks to Green functions, which provide direct evaluation at individual points.…”

Diffusion curves with diffusion coefficients

“…To avoid the need for a computational grid for diffusion curves, Bowers et al [11] recast the generation of diffusion curves as a global illumination problem, and employed a stochastic ray-tracing method to calculate colors. Pang et al [12] triangulated the image plane and interpolated color values on the triangular mesh using mean value coordinates.…”