# TU Wien Rendering #2 - Radiometry Recap, Light Attenuation

## Метаданные

- **Канал:** Two Minute Papers
- **YouTube:** https://www.youtube.com/watch?v=fSB4mqnm5lA
- **Дата:** 25.03.2015
- **Длительность:** 11:01
- **Просмотры:** 43,313
- **Источник:** https://ekstraktznaniy.ru/video/15010

## Описание

Course website: https://www.cg.tuwien.ac.at/courses/Rendering/VU.SS2019.html

Before trying to understand the nature of light, we have to have a grip on the basic units our simulation can rely on. What quantity would be adequate for this? Radiant flux? Irradiance? Radiance? And what do these words mean, anyway?

We also briefly discuss how light is attenuated, why it's so hot at noon and why it's getting golder in the afternoon.

About the course:
This course aims to give an overview of basic and state-of-the-art methods of rendering. Offline methods such as ray and path tracing, photon mapping and many other algorithms are introduced and various refinement are explained. 

The basics of the involved physics, such as geometric optics, surface and media interaction with light and camera models are outlined. 

The apparatus of Monte Carlo methods is introduced which is heavily used in several algorithms and its refinement in the form of stratified sampling and the Metropolis-Hastings met

## Транскрипт

### Quick radiometry recap []

okay so let's jump into the thick of it uh what do we measure in a simulation a quick recap from the last lecture this is going to be just a few minutes so first radiant flux this is the total amount of energy passing through a surface per second what does it mean I imagine some shape anywhere in this space and I count the amount of energy that is passing through this shape every second uh what is the unit of it it's uh Watts or je per second this is the same and this is apparently not enough this is not descriptive enough to create light simulations and uh please raise your hand if you know why okay well let's take a look uh so this says that amount of energy passing through a surface measured per second uh so when we measure a high radiant flux value somewhere we don't know if we have measured a lot of energy that passes through a small surface or if we have drawn or imagined the large surface and there's just a bit of energy passing through this is the same amount of radiant flux so this uh metric is ambiguous it's it's not good enough and this is just an image to uh to to imagine what is really happening so what is the solution for the time being let's compute the flux by unit area this we call IR Radiance and this unit area means that we don't imagine any kind of shape we imagine something that is one square met so we normed by square m so I have explicitly said that it's going to be this big and whatever is going through this is what interest to do okay well unfortunately this is still ambiguous and the reason for this is that we haven't uh taken into consideration uh what angle the light comes in and you will hear about this uh in a second so it matters whether you get a lot of energy in a big angle or uh a small amount of energy in a small angle this is uh this is ambiguous so uh let's remedy this by also norming with the angle so we are talking about unit angles so these meters the square meters we also divide by steradians well what does it mean so steradians is basically angle in multiple uh Dimensions because in the textbook there is only one angle to take into consideration if you draw a triangle but if you would like to look at for instance Q it matters that I turn my head to the right direction in this direction but if I would be looking here I wouldn't be seeing it so I need to take care of another Direction so this is what we denote by Radiance so multiple directions uh next question is so this was radians wats normed Pi square m normed by radians uh why is this still not good enough raise your hand if you know the answer well nothing it's fine as it is so there's going to be questions like that so make sure to think it through before because I think last year someone was almost falling out of the chair yeah I know I was like yeah okay this is fine I mean you can build similar uh okay so how do we do the actual light simulation uh what I'm interested in is how much light exits the surface at a given point so I pick a point in space and the direction is going to be the direction of my ey how much is light how much light is coming through uh from there solution is obviously the maxall equations why uh maxal equations tell you how electromagnetic waves behave and light is an electromagnetic wave in a given uh spectrum that is around uh visible light is as you heard in the last lecture about from 400 nanometers to 730 that's more or less the visible spectrum well uh apparently some people are overly excited about the max equations uh myself included well I don't have a cool tattoo like that I reserve this spot for the rendering equation at some point let's see about that so but unfortunately this doesn't work hopefully uh Thomas have said some things about this but uh the basic principle is that if it's really nanometers then uh we would need to have a simulation on the scale of nanometers and that's impossible that's the simple way to put it and the solution is going to be the rendering equation and uh if you would like a tattoo of an equation I would propose definitely having the rendering equation we will see how beautiful it is but at this point we are not ready to digest all of it so uh let's have some Theory before that uh this is the trivial part okay so scalar product is a number so on the left side I have two vectors on the right side I have a number and the scalar product is of A and B vectors is the length of a Time the length of B time the cosine of the angle between the two vectors uh in this course if even if I don't say anything about the length of the vectors A length of one is assumed every almost every single Vector is going to be normalized so if they are normalized then a length and B length is one so this is strictly going to be the angle between the two vectors so the cosines are going to be angles I mean the cosine of the angle okay some

### Terminology [6:25]

notation this is what you're going to see in many of the figures in the literature uh what's going on uh this point of this is X is the point of Interest this is where we compute some uh unit and V is the direction towards the viewer it's flipped on purpose I'm going to fix that in a second so V is a direction towards the viewer okay so if I have this uh projector above me the V Vector would be pointing towards me if the x is there uh n is the surface normal L is the vector pointing towards the light source okay so if I would be at this point then this uh L Vector would be towards for instance that light source uh R is the reflected ray Direction this means that I have a point I have a light source light is coming towards that point and R is where it's going to be reflected so again an example there is the projector this is the point x this is where the light comes from and this is the reflected Direction so this is flipped along the surface normal you will see examples of all of these and Theta i and r are incident and reflected angles uh and because we are going to be Computing scalar products and things with vectors it is important that these vectors that we're talking about are starting from the same point so uh generally in the images you are going to see this X and some vectors that are pointing outwards all the time because these vectors I can use for computations and uh just another uh important thing this is the definition the mathematical definition of R this is how you compute the ex reflected Vector but I think you have done this before uh in uh previous courses I think is it the E is it not the ECG but H unfortunately I don't remember the name but there there's some basic rate racing is there no it is um ECG you need it for the Shader mhm and okay uh but even if you haven't seen it you will see this in code and you will see how this works uh okay

### Light attenuation [8:46]

so let's uh talk about light attenuation and uh with some experiments that's let's be practical uh so the sun shines onto a point of a surface from above of what portion of the output of one Ray will hit the surface well this is something like a diffuse shading so I'm going to compute a do product between L and N L is towards the light Vector n is the surface normal well it seems to me that L and N is the very same thing in this uh scene so this cosine is going to be 0 de so the cosine of Z is one so I'm going I'm not going to have any kind of light in tenation in this case so uh let's take another example so the sun is around here and this is the light vector and you can also see the r just uh as an example that this is where it is reflected so I'm Computing this diffuse shading uh formula again so L do n now there is some angle let's say that this is 45° is uh the cosine of 4 5° is uh 1 / < TK of 2 right so Square is 1. 41 so 1/ 1. 41 that's around 0. 7 so there is some light attenuation if the Sun is located here and what about the extreme case another extreme case where it's almost at a 90° angle well uh the cosine of 90° is zero so this means that there is tons of light attenuation and this is the reason why it is the hottest point of the day is noon when the sun is exactly above us and after that it's just it's usually if you don't take into consideration anything else then it's only going to get colder and this is why it's so cold at night so uh we can neatly model this light attenuation with a simple dot product which is the cosign of these uh vectors