Eikonal rendering

Abstract

Figure 1: Real-time renderings of complex refractive objects -(left) glass with red wine casting a colorful caustic, 24.8 fps. (middle) Amberlike bunny with black embeddings showing anisotropic scattering and volume caustics in the surrounding smoke and its interior, 13.0 fps. (right) Rounded cube composed of three differently colored and differently refracting kinds of glass showing scattering effects and caustics in its interior, 6.4 fps. AbstractWe present a new method for real-time rendering of sophisticated lighting effects in and around refractive objects. It enables us to realistically display refractive objects with complex material properties, such as arbitrarily varying refractive index, inhomogeneous attenuation, as well as spatially-varying anisotropic scattering and reflectance properties. User-controlled changes of lighting positions only require a few seconds of update time. Our method is based on a set of ordinary differential equations derived from the eikonal equation, the main postulate of geometric optics. This set of equations allows for fast casting of bent light rays with the complexity of a particle tracer. Based on this concept, we also propose an efficient light propagation technique using adaptive wavefront tracing. Efficient GPU implementations for our algorithmic concepts enable us to render a combination of visual effects that were previously not reproducible in real-time.

The State of the Art in Interactive Global Illumination

“…[EAMJ05] and describe a GPU‐friendly beam tracing variant enabling high‐quality volumetric caustics in real‐time. A more generic approach is Eikonal rendering [IZT*07], where light wavefronts are tracked over time in a pre‐computation step. It can account for complex material properties, such as arbitrarily varying refraction index, inhomogeneous attenuation, as well as spatially varying anisotropic scattering and reflectance properties.…”

Generalized projection optimization model for tomographic volumetric additive manufacturing

“…In order to traverse the rays through a gradient-refractive index medium, the propagator needs to solve the kinematic ray equation 35 :…”

“…where 𝒗 ̲ is the velocity of the ray and is parametrized by 𝑠. Alternate parametrization of 𝒙 ̲ and 𝒗 ̲ are time 35 and canonical parameter 32 . The propagator solves the above differential equations with a symplectic Euler integrator 32 :…”

“…In the current implementation, this undersampling issue is only identified and mitigated manually by increasing the ray density. A better approach would be using an adaptive sampling approach 35 to add rays dynamically.…”