Rendering equation

$$\scriptsize{L_o(X, \vec{\omega_o}) = L_e(X, \vec{\omega_o}) + \int_S L_i(X, \vec{\omega_i}) f_{X,\vec{n}}(\vec{\omega_i}, \vec{\omega_o}) |\vec{\omega_i} \cdot \vec{n} | d{\omega_i}}$$

where $X$ is a position on the object or surface,

$\vec{\omega_o}$ is a direction toward the eye or camera,

$L_o(X, \vec{\omega_o})$ is all outgoing light from the position,

$L_e(X, \vec{\omega_o})$ is emitted light [1]

Rendering equation

$$\scriptsize{L_o(X, \vec{\omega_o}) = L_e(X, \vec{\omega_o}) + \int_S L_i(X, \vec{\omega_i}) f_{X,\vec{n}}(\vec{\omega_i}, \vec{\omega_o}) |\vec{\omega_i} \cdot \vec{n} | d{\omega_i}}$$

where $\vec{n}$ is normal to surface at $X$ position,

$S$ is a unit hemisphere among $\vec{n}$ with center in $X$,

$L_i(X, \vec{\omega_i})$ is a light coming from $\vec{\omega_i}$ direction,

$f_{X,\vec{n}}(\vec{\omega_i}, \vec{\omega_o})$ is the bidirectional reflectance distribution function (BRDF) [1]

Lambertian shading

$$L_d = k_dI\max(0, \vec{n}\cdot\vec{l})$$

where $L_d$ - diffusely reflected light,

$k_d$ - material’s diffuse coefficient,

$\vec{n}$ - surface normal,

$\vec{l}$ - direction toward the light [4]

Lab: 2.03 Lambertian shading

Principles, laws, and variables

Principles: create an image in the most effective way, immersive experience principle

Laws: rendering quation, Lambertian shading law

Variables: diffuse color, light color, num of lights

Lab: 2.03 Lambertian shading

Experiment goal

• Implement Lambertian shading
• Compare results with previous ones in terms of a perception

Lab: 2.03 Lambertian shading

Coding task

1. Add light information to lights array of ray_tracing_renderer
2. Adjust closest_hit_shader of raytracer to implement Lambertian shading model

TODO: Lab: 2.03 Lambertian shading

Lab: 2.03 Lambertian shading

Data gathering

Collect images before and after the experiment

Lab: 2.03 Lambertian shading

Result discussion

• How did a perseption of the image changed with Lambertian shading?
• How could a performance changed with increasing num of light sources?
• Updated principles, laws, and variables

Shadow rays idea

Before adding the light source to the final point on the point $X$, we should cast a ray from the point $X$ towards the light source. If any object occludes the shadow ray, the point $X$ is on shadow and the light should not be added the light source

Shadow rays tips

• Intersection with any geometry farther than light source doesn’t occlude the light source. To skip such object cast the ray with $t_{max}$ less than distance from $X$ to the light source
• To avoid self-intersection with the triangle owning $X$, use $t_{min}$ more than 0
• One intersection is enough to find an occlusion - use an AnyHit shader

Lab: 2.04 Shadow rays

Principles, laws, and variables

Principles: create an image in the most effective way, immersive experience principle

Laws: rendering quation, Lambertian shading law

Variables: num of rays, num of triangles

Lab: 2.04 Shadow rays

Experiment goal

• Implement a shadow rays technique
• Compare current images with previous ones in terms of a perception
• Evaluate performance changes

Lab: 2.04 Shadow rays

Coding task

1. Adjust trace_ray method of raytracer to use any_hit_shader
2. Initialize shadow_raytracer in ray_tracing_renderer
3. Define any_hit_shader and miss_shader for shadow_raytracer
4. Adjust closest_hit_shader of raytracer to cast shadows rays and to ignore occluded lights

TODO: Lab: 2.04 Shadow rays

Lab: 2.04 Shadow rays

Data gathering

• Collect images before and after the experiment
• Collect performance data

Lab: 2.04 Shadow rays

Result discussion

• How did a perseption of the image changed with shadow rays?
• How did a performance changed?
• Updated principles, laws, and variables

References