How to make a Photon Mapper : Whitted Ray Tracer

Hello there,

Today, we are going to see how to make the first part of our photon mapper. We are unfortunately not going to talk about photons, but only about normal ray tracing.

This is ugly !!! There is no shadow…

It is utterly wanted, shadows will be draw by photon mapping with opposite flux. We will see that in the next article.

Introduction

In this chapter, we are going to see one implementation for a whitted ray tracer

Direct Lighting

Direct lighting equation could be exprimed by : $\displaystyle{L_o(\mathbf{x}, \vec{\omega_o}) = \sum_{i\in \{Lights\}}f_r(\mathbf{x}, \vec{\omega_i}, \vec{\omega_o})\frac{\phi_{Light}}{\Omega r^2}cos(\theta)}$

The main difficult is to compute the solid angle $\Omega$.
For a simple isotropic spot light, the solid angle could be compute as : $\displaystyle{\Omega=\int_{0}^{angleCutOff}\int_{0}^{2\pi}sin(\theta)d\theta d\phi =-2\pi(cos(angleCutOff)-1)}$

with :

1. $\Omega$ the solid angle.
2. $\phi_{Light}$ the total flux carried by the light.
3. $cos(\theta)$ the attenuation get by projected light area on lighted surface area.
4. angleCutOff $\in [0; pi]$.

Refraction and reflection

Both are drawn by normal ray tracing.

Architecture

Now, we are going to see how our ray tracer works :

Shapes :

Shapes are bases of renderer. Without any shapes, you can’t have any render. We can have many differents shape, so, we can use one object approach for our shapes.

Materials

For each shapes, we obviously have a particular material. The material have to give us a brdf and can reflect radiance.

Storage Shapes

To have a better ray tracing algorithm, we could use a spatial structure like Kd-tree or other like one :

Algorithm

The main algorithm part is on the materials side. Below, a piece of code where I compute the reflected radiance for a lambertian material and a mirror. You could see that material part has access to other shape via the global variable world.

Lights

Lighting is a useful feature in a render. It’s thanks to lights that you can see the relief. A light carry a flux. Irradiance is the flux received by a surface.

So, our interface is :

Below a piece of code about computing irradiance :

The next time, we will see how to integrate a photon mapper to our photon mapper. If you want to have the complete code, you could get it here :
GitHub

Bye my friends :).