Global illumination: Combine accurate lighting simulation and computational efficiency with Ocean™

Global Illumination with Ocean™: Achieving realistic lighting simulations for accurate virtual prototypes

Ocean™ global illumination software, developed by Eclat Digital, uses advanced methods such as bi-directional path tracing and multi-importance sampling to generate highly accurate virtual prototypes. By simulating billions of light paths and their interactions within a scene, Ocean™ ensures that the radiance of each pixel is accurately estimated, resulting in realistic and detailed renderings.

This article is a detailed guide to Ocean™’s technical foundations for global illumination and path tracing techniques and how they are used to generate reliable virtual prototypes suitable for applications requiring accurate appearance.

Reading the following articles is recommended as an introduction to these complex concepts:

Exploring the rendering equation, Monte Carlo integration, and advanced sampling strategies, we also highlight the practical benefits of using Ocean™ for R&D purposes, explaining its ability to enhance realism, improve material representation, and reduce prototyping costs. By integrating state-of-the-art optical simulation techniques, Ocean™ sets a new standard for accuracy and efficiency in virtual prototyping.

Ocean™ Global Illumination solutions for accurate virtual prototyping

The Rendering Equation: Foundation of Realistic Rendering

The goal of rendering is to simulate the incoming light perceived by a virtual instrument, that we call eye. This problem has been addressed with a precise mathematical framework via the rendering equation. The equation consists of several independent contributions (light sources, light-material interactions) and entails a complex integral over space. Unfortunately, solving this equation directly is possible only in simple cases. This is why we use path tracing to tackle this complexity by simulating light rays traveling from light sources, bouncing off and interacting with objects in the scene, and eventually reaching the eye. We track billions of these paths and average their contributions to estimate the incoming radiance at each pixel.

To go further: the rendering equation:

The rendering equation is derived from the law of energy conservation. It mathematically describes the outgoing radiance in direction wo from a point x:

This equation entails two terms: the emitted light from point in direction (yellow term, yellow arrow in Figure X) and the integral over the unit hemisphere Ω (clear blue in Fig. X) of the incident light reaching point from any direction (purple arrows) multiplied by the BRDF describing light-material interactions and an irradiance factor (green) accounting for the weakening due to the rays’ incident angle with respect to the surface’s normal (green arrow). As can be noticed here, radiance is present on both sides of the equation, making this system rarely amenable to analytical resolution and justifying the use of path tracing to resolve it.

Figure 1: Scheme of the different contributions accounted for in the rendering equation to determine the outgoing radiance from point x in direction ωO

Monte Carlo integration: Optimizing rendering for time and quality.

A way around this issue is to employ Monte Carlo integration. These methods use sampling to get an estimate of the integral by evaluating the expression at several points. Their selection and number determine the accuracy and time efficiency of the estimation. For rendering, we consider a collection of ray paths within the scene. Connecting these paths to the eye, we obtain an approximation of the actual radiance reaching the instrument. While powerful, Monte Carlo integration features some drawbacks:

First, it is a rather complex method that can, in some contexts, converge rather slowly, meaning that rendering can be computationally expensive.
Second, it is a probabilistic method, and thus the result is an approximation with inherent noise. These uncorrelated fluctuations can be noticeable in the rendered image, introducing e.g. black dots, fireflies and graininess, if an insufficient number of samples is used to average the results.

The inherent slowness and stochastic nature of Monte Carlo integration have driven extensive research into developing optimized sampling strategies. To achieve great efficiency and accuracy in Ocean™, we leverage such advanced acceleration techniques as bidirectional path tracing and multi-importance sampling.

Bidirectional Path Tracing: Enhancing Light Path Calculation.

For path tracing, we track the change of direction and intensity at each intersection – “bounce” – of a light ray, as it reflects or refracts off a surface in the scene. Bidirectional path tracing is a technique that improves upon standard path tracing by considering light paths from two directions: rays are sent out in the scene from the eye point and from the light sources. We thus create eye paths (Figure 2, left) and light paths (Figure 2, middle), that are formed with reflection rays. Then the key idea is to connect these two sets of reflection rays with shadow rays (Figure. 2, right). Using this combinatorial approach, we thus quickly generate a high number of paths through the scene to obtain its faithful representation.

To build each path, we employ a recursive approach. We start by finding the first intersection point of the sampled ray, originating from either the eye or a light source, with an object. Then, a reflection ray is sampled. At each step, we track the ray intensity as it interacts with the object. We repeat this process recursively until the ray is absorbed or the user-imposed path length is reached.

To go further: the russian roulette technique

At each surface intersection, the light rays interact with the material. Therefore, their intensity gradually decreases along the path. In theory, a light path is infinite. For rendering, it is necessary to determine a path termination condition. In practice, we would like to consider paths as long as possible to achieve the highest accuracy and avoid biasing. In Ocean™, we use the Russian roulette technique to introduce path termination and ensure increased numerical efficiency. The approach consists of randomly absorbing rays at each intersection. For that, we generate at each intersection a random number and verify if its value is larger than the probability of terminating the path.

Reflection and refraction management in rendering

Every time a light ray intersects with a surface of a material that features some degree of transparency, the ray can either be reflected (surface E1 in Figure 2, left) or transmitted (highlighted surface E2 in figure 2, left). Thus, as a ray hits the surface, for sampling the next direction we need to make a choice: should the following sampled ray direction result from reflection or transmission? To deal with this, we can set a probability for the ray to be transmitted. This probability should be selected wisely, such that it tends towards zero for an opaque material – which systematically reflects rays – and approaches one for transparent materials.

To go further: Snell’s law

The bending of a ray upon transmission is described by Snell’s law:

where and are the refractive indexes of each medium, and are the incident and outgoing angle of the ray. When hitting a transparent surface, a fraction of light rays is reflected, while a fraction is transmitted. These contributions must be accounted for to set the ray transmission probability wisely

For efficient rendering, we can generalize this idea and employ importance sampling. The idea of this technique is to choose the next ray direction based on a probability distribution that closely matches the actual optical behavior of the material. For that, we consider each object’s BSDF (bidirectional scattering distribution function), a function that describes how a material scatters light in all directions, including both reflected and transmitted light (Figure 3).

By using importance sampling, we achieve efficient rendering, particularly in scenarios involving complex materials beyond simple diffuse or purely specular surfaces. This strategy, as illustrated in Figure 4 within the context of our bi-directional path tracing, prioritizes the most probable light paths, ultimately improving rendering efficiency and minimizing noise levels in the final image.

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Daylighting simulations with BSDFs

Light and shadow management for realistic scenes:

Once both paths have been sampled, we introduce shadow rays (Figure 2, right): each intersection point along one path is linked to all intersection points along the other path (solid grey lines), and all points along the eye path (including the eye itself) are linked to the light source (dashed grey lines).

The shadow rays determine the lighting contributions which must be added to the estimate: the contribution is only added if the shadow rays do not hit an intervening object. Exploring the direct connections between bounces and light sources permit capturing shadows in the scene faithfully: if such a ray reaches the light source without intersecting any object, this indicates that the point on the surface is directly illuminated by that light source. On the other hand, if the shadow ray intersects another object before reaching the light source, this means that the first object is blocking the light from reaching the surface point. In that case, the point is in shadow from that specific light source and its contribution to the final image will be significantly reduced or eliminated. Thus, in practice for rendering we populate the scene with light paths and add the contribution of these that are not blocked.

To go further: Efficiency of bidirectional path tracing

The previous figure highlights the efficiency of using this approach. In this simple example, by tracing an eye-path of length 3 and a light-path of length 2 we are considering a maximum of 4×3 = 12 paths, as shown in Figure 5.

Figure 5: Counting the maximum number of paths that can be formed by connecting the eye- and light-path intersections

Shading study

ocean sky importer for enhanced predictive rendering

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Mastering Complex Light Sources for Accurate Optical Simulations with Ocean™

Optimizing Light Configuration for Realistic Virtual Prototyping:

To accurately capture a scene, a detailed description of light sources must be introduced in the simulations. Different light sources have distinct emission profiles, and representing these variations plays a crucial role in achieving realistic lighting effects. We can thus use a variety of light distribution functions to model these emission patterns. Importantly, just like with reflection ray sampling, uniformly sampling light rays from a source can be highly inefficient. Indeed, for certain light distribution functions, such as spotlights or directional lights, most of the emitted light rays are concentrated in a specific direction. Uniform sampling would strongly impact computational efficiency by considering directions with very little light emission. We therefore also opt for importance sampling of light sources.

In Ocean™, we even go a step further by employing multi-importance sampling. Again, the aim of this enhanced technique is to focus on light paths with a higher probability of contributing to the final radiance. We highlight the concept in Figure 6 without going into the details of a complex method: sampling of a light source and BSDF independently can result in focusing on paths with low contribution to the scene radiance. Thus, weighing wisely the sampling of each contribution can permit optimizing the sampling.

Virtual lighting setup in Ocean™ for realistic lighting simulation

lighting analysis for automotive interior

Interior car lighting study

The benefits of using Ocean™’s global illumination rendering software

Here are some of the key benefits of using Ocean™’s global illumination capabilities for R&D purposes:

Enhanced Realism for Prototyping:

Global illumination rendering software ensures that the interaction of light with materials is simulated accurately, producing renders that are far more realistic than those generated by traditional rendering methods. This allows researchers to see subtle variations in material properties, such as surface texture, glossiness, and translucency, with a high degree of accuracy.

Precision in Material Representation:

Global illumination rendering software can be used to virtually test different material combinations and lighting conditions. This allows researchers to optimize material properties for specific applications and take informed decisions for design purposes or material selection.

Reduced Prototyping Costs with virtual simulations:

Virtual prototypes rendered with Ocean™ will closely match their real-world counterparts. This level of realism helps in identifying potential issues early in the development process. By reducing the need for physical prototype samples and allowing for faster design iterations and product development cycles, it helps saving time and resources.

Improved Communication with predictive renderings:

Highly realistic renders can be used to effectively communicate design concepts and material properties to stakeholders, even those who are not familiar with 3D modeling or rendering techniques. From predictive in-situ images, to full-scale rendering or immersive visualization techniques, Ocean™ provides multiple formats for different needs.

Advanced Expertise in Optical Simulation: Combining software development and optical engineering for predicitve results:

Eclat Digital’s engineering expertise ensures that our optical simulation software incorporates advanced principles of physics, resulting in rendered images that are not only visually appealing, but more importantly, scientifically accurate. This is especially important for applications that require precise optical performance, such as lenses, lighting systems, and display technologies.

Improve your R&D workflow with Ocean™: Precision and realism through Global Illumination solutions

Ocean™ realistic rendering software incorporates global illumination to enhance your R&D workflow with real-world accuracy in material representation. Eclat Digital’s expertise in both software development and optical engineering ensures that our solutions meet the highest standards of precision and reliability. For industries where material optical behavior under realistic lighting conditions is of importance, global illumination rendering software is a valuable addition to the toolkit.