# 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.


#ifndef SHAPE_HPP
#define SHAPE_HPP

#include "ray.hpp"
#include "material.hpp"

/**
* @brief      This class provides an interface to manage differents shape
*/
class AbstractShape {
public:
AbstractShape() = default;
AbstractShape(std::unique_ptr &&material);

/**
* @brief      Return the distance between shape and ray emetter
*
* @param      ray
*
* @return     Negative value if not found. Distance between object and ray emetter
*/
virtual float intersect(Ray const &ray) const = 0;
virtual glm::vec3 getNormal(glm::vec3 const &position) const = 0;

/**
* @brief      Return the radiance returned by the material owned
*
* @param      ray
*
*/

virtual ~AbstractShape() = default;

private:
std::unique_ptr mMaterial = std::make_unique(glm::vec3(1.0, 1.0, 1.0), 1.0);
};


### Materials

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


/**
* @brief      This class describes a material
*/
class AbstractMaterial {
public:
AbstractMaterial(float albedo);

/**
* @brief      Get the reflected radiance
*
* @param      ray
* @param      shape  Useful to get normal, UV for texture???
*
* @return     { description_of_the_return_value }
*/
virtual glm::vec3 getReflectedRadiance(Ray const &ray, AbstractShape const &shape) = 0;

virtual void bouncePhoton(Photon const &photon, AbstractShape const &shape) = 0;

virtual ~AbstractMaterial() = default;

float albedo;
protected:
/**
* @brief      Get the Bidirectionnal Reflectance Distribution Function
*
* @param      ingoing
* @param      outgoing
* @param      normal
*
* @return     the brdf
*/
virtual float brdf(glm::vec3 const &ingoing, glm::vec3 const &outgoing, glm::vec3 const &normal) = 0;
};


### Storage Shapes

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


/**
* @brief      This class provide a structure to store shapes
*/
class AbstractShapeStorage {
public:
/**
* @brief      Add a shape in structure
*
* @param      shape
*/
virtual void addShape(std::shared_ptr const &shape) = 0;

/**
* @brief      Get the nearest shape
*
* @param      ray
*
* @return     a tuple with shape and distance. Shape could be null if no shape found
*/
virtual std::tuple<std::shared_ptr, float> findNearest(Ray const &ray) = 0;

~AbstractShapeStorage() = default;
};


### 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.


float LambertianMaterial::brdf(const glm::vec3 &, const glm::vec3 &, glm::vec3 const &) {
return albedo / M_PI;
}

vec3 UniformLambertianMaterial::getReflectedRadiance(Ray const &ray, AbstractShape const &shape) {
float f = brdf(vec3(), vec3(), vec3());

return color * f * (directLighting);
}

float MirrorMaterial::brdf(const vec3&, const vec3&, const vec3&) {
return albedo;
}

vec3 MirrorMaterial::getReflectedRadiance(const Ray &ray, const AbstractShape &shape) {
if(ray.recursionDeep >= MAX_BOUNCES)
return vec3();

Ray reflectedRay = getReflectedRay(ray, shape.getNormal(ray.origin + ray.direction * ray.distMax));
auto nearest = World::world.findNearest(reflectedRay);

if(get(nearest) != nullptr) {
reflectedRay.distMax = get(nearest);
return brdf(vec3(), vec3(), vec3()) * get(nearest)->getReflectedRadiance(reflectedRay);
}

return vec3();
}


### 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 :


/**
* @brief      Interface for a light
*/
class AbstractLight {
public:
AbstractLight(glm::vec3 const &flux);

/**
*
* @param      position  surface's position
* @param      normal    surface's normal
*
*/
virtual glm::vec3 getIrradiance(glm::vec3 const &position, glm::vec3 const &normal) = 0;

virtual void emitPhotons(std::size_t number) = 0;

virtual ~AbstractLight() = default;

protected:
glm::vec3 mTotalFlux;
};



vec3 SpotLight::getIrradiance(const vec3 &position, const vec3 &normal) {
vec3 posToLight = mPosition - position;
vec3 posToLightNormalized = normalize(posToLight);

if(dot(-posToLightNormalized, mDirection) > mCosCutoff) {
float solidAngle = - 2.f * M_PI * (mCosCutoff - 1);
return lambertCosineLaw(posToLightNormalized, normal) * mTotalFlux /
(solidAngle * dot(posToLight, posToLight));
}

return vec3();
}


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 :).