Online Graphics Course Raytracing 1 - Shadows and reflections

In this segment, we're going to consider the core algorithm of raytracing, which includes shadows and reflections: first, shadows. I've drawn my usual diagram with the camera, the virtual viewpoint, the virtual screen, and the objects. I've added a light source. So I shoot a ray from the camera to the cylinder. And now, to find shadows, I have to shoot a ray from there towards the light source. In this case, the shadow ray hits the light source, so it's unblocked, and the object is therefore visible to the light source. Here is another pixel, where my ray from my camera hits the ground. Again, I shoot a ray towards the light source. But this time, it hits the cylinder. Therefore, the ray to the light source is blocked, and the object is in shadow. As simple as that. In standard rasterization in OpenGL, this is not that simple. There is a way to simulate this using what is known as a shadow map. First store the depths from the light source, then store the depths from the eye. However, it is more complicated and it can have many artifacts associated with it. In raytracing, by contrast, you can easily compute shadows. However, there is a little bit of trickery involved in the sense that you have to be able to get around certain numerical issues. Here is what I want to do, to shoot a ray from the surface towards the light source. But because of numerical error -- of course I'm exaggerating in this diagram -- the ray goes below the surface. Now I shoot a ray towards the light source and I incorrectly say to myself it shadows itself. The solution to this is to move a little bit toward the light source before shooting a ray or otherwise allow a small epsilon tolerance where you don't consider intersections. The next component deals with mirror reflections and refractions. Same diagram again. This time I'm going to shoot a ray in the mirror direction. Same thing for refractions, I'll shoot a ray according to Snell's Law. And where that ray hits I will get the color of background, and this will give me my reflection. So raytracing, in a very simple way, is able to handle shadows and reflections. Which brings us to Turner Whitted's recursive raytracing algorithm. Again, the algorithm is extremely simple and fits on a page. For each pixel, you trace the primary eye ray and you find the intersection of that primary eye ray with the scene. Notice the terminology I'm using here. I'm using eye rays for rays from the eye, often called primary rays. Then you trace the secondary ray or the shadow ray to the light sources. You may trace one shadow ray for each light source. The color, if the shadow ray is visible, corresponds to the illumination model in effect. For example the Blinn Phong model and the Lambertian diffuse model. If the ray is blocked there is no direct illumination from the light sources. Next we trace the reflective ray and the color, notice the use of the plus equal to operator. The color is equal to reflectivity of the surface times the color of the reflected ray. Here is where the recursive raytracing comes into play. Because we've said color is equal to color plus reflectivity, times the color of the reflected ray. To determine the color of the reflected ray you have to go back and trace the ray. Recursion is a great tool in computer science. It enables one to easily express concepts that would be very difficult otherwise. But with all recursive algorithms, we must have some guarantee that the algorithm will stop. Reflection rays may be traced forever. Consider especially if you have something that looks like a hall of mirrors. To avoid this problem, we generally set a maximum recursion depth. Like, if you've traced 5 times, you stop. Other things you might imagine doing is set a threshold. Once the product of the reflectivities goes below a threshold, like 0.02, you stop the ray. Similarly, you can handle transmitted rays. If you study advanced rendering, you'll notice that these kinds of processes involve some notion of bias, because you're throwing away energy. And there is a procedure known as Russian Roulette that adds the energy back in a way that is unbiased. However we don't need to deal with it here. So what are the effects needed for realism? We earlier in this lecture talked about them. Soft shadows, reflections from mirror and glossy surfaces, transparencies, water and glass inter-reflection, color bleeding, complex illumination, natural and aerial lights. The portions in white. That is shadows, mirror reflections, transparency have been discussed in this lecture in the context of recursive raytracing, and are supported by recursive raytracing. The yellow parts, which is soft shadows from area light sources, glossy reflections, complex illumination from natural and area lights are not present in this standard recursive raytracing algorithm, or what you'll implement for homework 3. However, they are possible with simple extensions to distribution raytracing. Finally, inter-reflections of color bleeding are hard with raytracing but not impossible. In most renderings now-a-days are based on raytracing or its extension to path tracing. However, this is a place where the radiosity techniques became very popular and those are based on finite element numerical calculations. As far as this course is concerned, we just deal with simple recursive raytracing.