Ray Tracing Graphics: Exploring Photorealistic Rendering in Computer Vision

By Fouad Sabry

What is Ray Tracing Graphics

In 3D computer graphics, ray tracing is a technique for modeling light transport for use in a wide variety of rendering algorithms for generating digital images.

How you will benefit

(I) Insights, and validations about the following topics:

Chapter 1: Ray tracing (graphics)

Chapter 2: Rendering (computer graphics)

Chapter 3: Global illumination

Chapter 4: Radiosity (computer graphics)

Chapter 5: Photon mapping

Chapter 6: Ray casting

Chapter 7: Specular reflection

Chapter 8: Geometrical optics

Chapter 9: Graphics pipeline

Chapter 10: Rendering equation

(II) Answering the public top questions about ray tracing graphics.

(III) Real world examples for the usage of ray tracing graphics in many fields.

Who this book is for

Professionals, undergraduate and graduate students, enthusiasts, hobbyists, and those who want to go beyond basic knowledge or information for any kind of Ray Tracing Graphics.

• Language: English
• Publisher: One Billion Knowledgeable
• Release date: May 14, 2024

Book preview

Chapter 1: Ray tracing (graphics)

In 3D computer graphics, ray tracing is a technique for simulating light transport that may be applied to a wide range of rendering techniques for generating digital images.

Ray tracing-based rendering techniques, such as ray casting, recursive ray tracing, distribution ray tracing, photon mapping, and route tracing, are often slower and more accurate than scanline rendering methods.

Since 2019, hardware acceleration for real-time ray tracing has become standard on new commercial graphics cards, and graphics APIs have followed suit, enabling developers to use hybrid ray tracing and rasterization-based rendering in games and other real-time applications with a smaller impact on frame render times.

Ray tracing is capable of replicating a range of optical phenomena. In fact, ray tracing may imitate any physical wave or particle phenomenon with approximately linear motion.

Ray tracing-based rendering approaches that sample light over a domain cause image noise artifacts that can be mitigated by tracing a very high number of rays or by employing denoising algorithms.

The idea of ray tracing comes from as early as the 16th century when it was described by Albrecht Dürer, who is credited with its development?.

Dürer described multiple techniques for projecting 3D scenes onto an image plane.

Some of these project certain geometry onto the image location, As is done currently with rasterization.

Others define visual geometry along a particular beam, Similarly to ray tracing.

Appel utilized ray tracing to determine main visibility (determining the closest surface to the camera at each image point), then traced secondary rays from each darkened point to the light source to assess whether the point was in shadow or not.

Later, in 1971, MAGI's Goldstein and Nagel (Mathematical Applications Group, Inc.)

1976 saw another early case of ray casting, Scott Roth made a flip book animation in Bob Sproull's Caltech computer graphics class.

The scanned pages are displayed on the right as a video.

The computer software of Roth recorded an edge point at a pixel location if the ray intersected a different bounding plane than its neighbors.

Of course, A ray may cross numerous planes in space, However, just the closest surface point to the camera was visible.

The edges are jagged because the computational capabilities of the time-sharing DEC PDP-10 allowed for only a coarse resolution.

The terminal was a Tektronix storage-tube display for text and graphics.

Attached to the display was a printer that printed an image of the display onto thermal paper on a roll.

Roth expanded the structure, presented ray casting in the context of computer graphics and solid modeling, Later, he published his work while working at GM Research Labs.

1979, while working as an engineer at Bell Labs.

Whitted's deeply recursive ray tracing technique reframed rendering as a function of light transport rather than surface visibility determination.

His publication stimulated a succession of future research, including distributed ray tracing and unbiased path tracing, It gives the rendering equation framework that has enabled computer generated graphics to be realistic.

Decades ago, additional lighting was used to simulate global illumination in films utilizing computer-generated images. Eventually, ray tracing-based rendering modified this by enabling physically-based light transport. Monster House (2006) and Cloudy with a Chance of Meatballs (2009) are examples of early feature films totally rendered utilizing path tracing (2009), Optical ray tracing is a technique for generating more photorealistic visuals in 3D computer graphics environments than ray casting or scanline rendering. It operates by following a route from a fictitious eye through each pixel on a virtual screen and computing the color of the thing viewed through it.

Scenes in ray tracing are mathematically described by a programmer or an artist (normally using intermediary tools). Scenes may also include data from collected photos and models, such as digital photography.

Each ray must typically be verified for intersection with a subset of the scene's objects. Once the closest item has been discovered, the algorithm will estimate the incoming light at the intersection point, check the material qualities of the object, and integrate this information to determine the pixel's final color. Certain illumination algorithms and reflecting or translucent materials may need the recasting of additional rays into the scene.

Sending rays away from the camera, rather than into it (like light does in reality), is many orders of magnitude more efficient. Since the vast majority of light beams from a particular light source do not reach the viewer's sight, a forward simulation could waste a great deal of compute on light routes that are never recorded.

Consequently, the ray tracing shortcut is to assume that a particular ray intersects the view frame. The pixel's value is updated when the ray reaches either a maximum number of reflections or a specific distance without intersecting anything.

Based on information we have (in calculation we use vector normalization and cross product):

{\displaystyle E\in \mathbb {R^{3}} } eye position

{\displaystyle T\in \mathbb {R^{3}} } target position

{\displaystyle \theta \in [0,\pi ]} field of view - for humans, we can assume {\displaystyle \approx \pi /2{\text{ rad}}=90^{\circ }}

{\displaystyle m,k\in \mathbb {N} } numbers of square pixels on viewport vertical and horizontal direction

{\displaystyle i,j\in \mathbb {N} ,1\leq i\leq k\land 1\leq j\leq m}

numbers of actual pixel

{\displaystyle {\vec {v}}\in \mathbb {R^{3}} } vertical vector which indicates where is up and down, usually {\displaystyle {\vec {v}}=[0,1,0]} (not visible on picture) - roll component which determine viewport rotation around point C (where the axis of rotation is the ET section)

Viewport schema witch pixels, eye E and target T, viewport center C

The idea is to find the position of each viewport pixel center P_{ij} which allows us to find the line going from eye E through that pixel and finally get the ray described by point E and vector {\displaystyle {\vec {R}}_{ij}=P_{ij}-E} (or its normalisation {\displaystyle {\vec {r}}_{ij}} ).

First we need to find the coordinates of the bottom left viewport pixel {\displaystyle P_{1m}} and find the next pixel by making a shift along directions parallel to viewport (vectors {\displaystyle {\vec {b}}_{n}} i {\displaystyle {\vec {v}}_{n}} ) multiplied by the size of the pixel.

Below we introduce formulas which include distance d between the eye and the viewport.

However, this value will be reduced during ray normalization {\displaystyle {\vec {r}}_{ij}} (so you might as well accept that d=1 and remove it from calculations).

Pre-calculations: let's find and normalise vector {\displaystyle {\vec {t}}} and vectors {\displaystyle {\vec {b}},{\vec {v}}} which are parallel to the viewport (all depicted on above picture)

{\displaystyle {\vec {t}}=T-E,\qquad {\vec {b}}={\vec {t}}\times {\vec {v}}}{\displaystyle {\vec {t}}_{n}={\frac {\vec {t}}{||{\vec {t}}||}},\qquad {\vec {b}}_{n}={\frac {\vec {b}}{||{\vec {b}}||}},\qquad {\vec {v}}_{n}={\vec {t}}_{n}\times {\vec {b}}_{n}}

note that viewport center {\displaystyle C=E+{\vec {t}}_{n}d} , next we calculate viewport sizes {\displaystyle h_{x},h_{y}} divided by 2 including inverse aspect ratio {\displaystyle {\frac {m-1}{k-1}}}

{\displaystyle g_{x}={\frac {h_{x}}{2}}=d\tan {\frac {\theta }{2}},\qquad g_{y}={\frac {h_{y}}{2}}=g_{x}{\frac {m-1}{k-1}}}

and then we calculate next-pixel shifting vectors {\displaystyle q_{x},q_{y}} along directions parallel to viewport ( {\displaystyle {\vec {b}},{\vec {v}}} ), and left bottom pixel center {\displaystyle p_{1m}}

{\displaystyle {\vec {q}}_{x}={\frac {2g_{x}}{k-1}}{\vec {b}}_{n},\qquad {\vec {q}}_{y}={\frac {2g_{y}}{m-1}}{\vec {v}}_{n},\qquad {\vec {p}}_{1m}={\vec {t}}_{n}d-g_{x}{\vec {b}}_{n}-g_{y}{\vec {v}}_{n}}

Calculations: note {\displaystyle P_{ij}=E+{\vec {p}}_{ij}} and ray {\displaystyle {\vec {R}}_{ij}=P_{ij}-E={\vec {p}}_{ij}} so

{\displaystyle {\vec {p}}_{ij}={\vec {p}}_{1m}+{\vec {q}}_{x}(i-1)+{\vec {q}}_{y}(j-1)}{\displaystyle {\vec {r}}_{ij}={\frac {{\vec {R}}_{ij}}{||{\vec {R}}_{ij}||}}={\frac {{\vec {p}}_{ij}}{||{\vec {p}}_{ij}||}}}

This JavaScript project evaluated the above formula (works in browser).

In nature, a light source releases a ray of light that finally reaches a surface that blocks its path. This ray can be compared to a stream of photons flowing along the same route. In an ideal vacuum, this ray will be straight (ignoring relativistic effects). This light ray could undergo any combination of absorption, reflection, refraction, and fluorescence. A surface may absorb a portion of the light ray, causing a reduction in the intensity of the reflected and/or refracted light. Additionally, it may reflect all or a portion of the light ray in one or more directions. If the surface is transparent or translucent, it refracts a component of the light beam while absorbing some (or all) of the spectrum (and possibly altering the color). Infrequently, a surface may absorb a portion of the light and fluorescently re-emit it at a longer wavelength hue and in a random direction, although this is so uncommon that it can be ignored in the majority of rendering applications. All of the entering light must be accounted for by absorption, reflection, refraction, and fluorescence, and nothing more. A surface cannot, for example, reflect 66 percent of an incoming light beam and refract 50 percent, because the