Figure 1: the angle of incidence and the angle of reflection are equal. Remember that ray-tracing is essentially a technique for computing the visibility between two points. \(A\) and \(B\) can easily be computed using the following two equations: We already know about \(N\) but what about vector \(M\)? The harder and the more reflective the material becomes, such as metals, the higher the IOR, meaning that it reflects more uniformly from each angle, independently from which angle it’s viewed. This is also what the art of shading is all about. There is an option in vray reflection settings for fresnel ior, you can check this on an you can control the strength of reflections at the grazing angle (as the incidence angle approaches 90 degrees away from the camera target (which would be 0 degrees directly in front of the camera). As stated before air has a refraction index close to 1, and for this reason, in CG, we generally ignore it. It is the dot product between \(N\) and \(I\). It's only when very complex transparent surfaces are rendered (such as water splashes) that using a depth much greater than 5 is necessarily for producing images that are similar to the real thing. While the light beams intersects the surface in the same exact point on the surface, the observer will only see the reflection of the ray in the middle (the ray with the orange color). The higher the recursion the longer it will take to render a frame. and ray scene and bias as a side effect of using ray-tracing to compute or simulate these effects. Vec3f Nrefr = N; VRay shaders already have this phenomenon integrated, for example the VRay Mtl shader already has the option “Use Fresnel” activated to respect the realism of materials. else { The fact that the reflected image of the objects in the scene from which these light rays are emitted changes with the view direction, is the reason why we say that reflection is view dependent. Refraction or the bending of light rays explains why objects seen through transparent objects such as glass or water, look deformed. Uncheck override IOR, and return to the top level of your material, there's an IOR setting there. Light is composed of two perpendicular waves which we call parallel and perpendicular polarised light. If the object that the primary ray hit is a mirror like surface, then we compute the reflection direction using the incident view direction (the primary ray direction) and the normal of the surface at the intersection point. Here is a possible implementation of the Fresnel formula: If you plot this function here is what the curves look like: The curve on the left shows the ratio of reflected light in the case of an air-glass transition. All other brand names, product names, or trademarks belong to their respective holders. } An ideal solution is one in which the bias can be computed automatically as opposed to being fixed for the entire scene, or fixed on an object basis. The Fresnel effect which we will talk about later in this chapter can also have an effect on how much light a surface reflects. Vec3f refract(const Vec3f &I, const Vec3f &N, const float &ior) There is another way of computing or finding out when the incident light is totally reflected rather than being refracted. We look at a different part of the object. They are both refractive and reflective. Explaining the origin of these equations and how they can be derived goes far beyond the level of explanation we are willing to give in this lesson. After two reflections, the ray has a depth of 2 and so on. // mix the two In this chapter, we will learn about simulating reflection, refraction (transmission) and the Fresnel effect which defines for transparent materials such as glass and water how much light is reflected vs. how much light is transmitted. The attenuated the reflection to more easily differentiate the plane from the background. kr = (Rs * Rs + Rp * Rp) / 2; How much light they reflect vs the amount they transmit actually depends on the angle of incidence. // we are outside the surface, we want cos(theta) to be positive float cosi = clamp(-1, 1, dotProduct(I, N)); ... Figure 11: compute the refraction ray direction using geometry. Glass spheres as well as pretty much every other transparent surface (water, diamonds, crystal, etc.) This is not totally wrong, as mirror like surfaces generally never reflect 100% of the incident light anyway. case kReflection: In this lesson, we will only deal with the case of clear transparent objects. refractionColor = castRay(refractionRayOrig, refractionDirection, objects, lights, options, depth + 1); float k = 1 - eta * eta * (1 - cosi * cosi); IOR – Specifies the index of refraction to use when calculating the Fresnel term. if (cosi < 0) { cosi = -cosi; } else { std::swap(etai, etat); n= -N; } ... If a ray kept reflecting other reflecting surfaces without ever reflecting anything else, we would then enter some kind of infinite recursive process. I’ve linked to an article below that talks about Fresnel more, but as a general rule, just keep this box checked. Vec3f refractionRayOrig = outside ? break; When we cast a reflection ray from the primary ray, we say that the ray has a depth of 1. In fact, in computer graphics we like to classify materials in two broad categories: the dielectric materials and the conductor materials. Remember the names conductor and dielectric as they are used a lot in shading and computer graphics. We can just set \(F_R\) to 1. The reflection ray can be called a reflection or also sometimes a specular ray (we will explain what the term specular means in more detail in the next chapter). Thus naturally as we look in the distance, the water surface reflects more light. Nrefr = -N; // Total internal reflection bool outside = dir.dotProduct(hitNormal) < 0; This is very similar to what happens when we observe the reflection of the sun by a wavy water surface. In this lesson we will ignore the effect of light attenuation and absorption by a medium. { you can control the look of the final rendered image. But these cases are hopefully generally rare. As in the example of the real glass ball from figure 9, you can see that the image of the background geometry is inverted in the sphere. Though if we look almost directly down on the water surface, a few meters from where we stand, the angle incidence is low and most of the light is actually transmitted.

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