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GABRIEL GAMBETTA
Hello! I’m Gabriel Gambetta. I’m a senior software engineer at Google Zürich; the author of Computer Graphics from Scratch; and an aspiring writer, filmmaker and actor. In the past I worked at Improbable in London for a few years. It was a seed-stage, 30-person startup when I joined; by the time I left, it was an unicorn with 500+people.
COMPUTER GRAPHICS FROM SCRATCH Computer Graphics from Scratch. Computer Graphics from Scratch demystifies the algorithms used in modern graphics software with basic programming and high school math. PERSPECTIVE PROJECTION The Projection Equation. Let’s put all this together. Given a point P in the scene and a standard camera and viewport setup, we can compute the projection of P on the viewport, which we call P ′, as follows: P ′ x = Px ⋅ d Pz. P ′ y = Py ⋅ d Pz. P ′ z = d. P ′ is on the viewport, but it’s still a point in 3D space.LINEAR ALGEBRA
Algebraically, you multiply the coordinates individually and add them: →V, →W = (Vx, Vy, Vz), (Wx, Wy, Wz) = Vx ⋅ Wx + Vy ⋅ Wy + Vz ⋅ Wz. Geometrically, the dot product of →V and →W is related to their lengths and to the angle α between them. The exact formulaneatly ties
LIGHT - COMPUTER GRAPHICS FROM SCRATCH - GABRIEL GAMBETTA Let’s define the vector →L as the direction from a point in the scene, P, to the light, Q. We can calculate this vector, called the light vector, as Q − P. Note that since Q is fixed but P can be any point in the scene, →L is different for every point in the scene, as you can see in Figure 3-1. Figure 3-1: A point light at Q. INTRODUCTORY CONCEPTS Introductory Concepts. A raytracer and a rasterizer take very different approaches to rendering a 3D scene onto a 2D screen. However, there are a few fundamental concepts that are common to both approaches. In this chapter, we’ll explore the canvas, the abstract surface on which we’ll render our images; the coordinate systemwe’ll use to
FILLED TRIANGLES
Figure 7-2: Drawing a filled triangle using horizontal segments. The following is a very rough first approximation of what we want to do: for each horizontal line y between the triangle's top and bottom compute x_left and x_right for this y DrawLine (x_left, y, x_right, y) Let’s start with “between the triangle’s top and bottom.”. SHADOWS AND REFLECTIONS Shadows and Reflections. Our quest to render the scene in progressively more realistic ways continues. In the previous chapter, we modeled the way rays of light interact with surfaces. In this chapter, we’ll model two aspects of the way light interacts with the scene: objects casting shadows and objects reflecting on otherobjects.
BASIC RAYTRACING
Basic Raytracing. In this chapter, we’ll introduce raytracing, the first major algorithm we’ll cover. We start by motivating the algorithm and laying out some basic pseudocode. Then we look at how to represent rays of light and objects in a scene. Finally, we derive a way to compute which rays of light make up the visible image of eachof
FAST-PACED MULTIPLAYER: SAMPLE CODE AND LIVE DEMO Fast-Paced Multiplayer: Sample Code and Live Demo. This is a sample implementation of a client-server architecture demonstrating the main concepts explained in my Fast-Paced Multiplayer series of articles. It won’t make much sense unless you’ve read the articles first. The code is pure JavaScript and it’s fully contained in this page.GABRIEL GAMBETTA
Hello! I’m Gabriel Gambetta. I’m a senior software engineer at Google Zürich; the author of Computer Graphics from Scratch; and an aspiring writer, filmmaker and actor. In the past I worked at Improbable in London for a few years. It was a seed-stage, 30-person startup when I joined; by the time I left, it was an unicorn with 500+people.
COMPUTER GRAPHICS FROM SCRATCH Computer Graphics from Scratch. Computer Graphics from Scratch demystifies the algorithms used in modern graphics software with basic programming and high school math. PERSPECTIVE PROJECTION The Projection Equation. Let’s put all this together. Given a point P in the scene and a standard camera and viewport setup, we can compute the projection of P on the viewport, which we call P ′, as follows: P ′ x = Px ⋅ d Pz. P ′ y = Py ⋅ d Pz. P ′ z = d. P ′ is on the viewport, but it’s still a point in 3D space.LINEAR ALGEBRA
Algebraically, you multiply the coordinates individually and add them: →V, →W = (Vx, Vy, Vz), (Wx, Wy, Wz) = Vx ⋅ Wx + Vy ⋅ Wy + Vz ⋅ Wz. Geometrically, the dot product of →V and →W is related to their lengths and to the angle α between them. The exact formulaneatly ties
LIGHT - COMPUTER GRAPHICS FROM SCRATCH - GABRIEL GAMBETTA Let’s define the vector →L as the direction from a point in the scene, P, to the light, Q. We can calculate this vector, called the light vector, as Q − P. Note that since Q is fixed but P can be any point in the scene, →L is different for every point in the scene, as you can see in Figure 3-1. Figure 3-1: A point light at Q. INTRODUCTORY CONCEPTS Introductory Concepts. A raytracer and a rasterizer take very different approaches to rendering a 3D scene onto a 2D screen. However, there are a few fundamental concepts that are common to both approaches. In this chapter, we’ll explore the canvas, the abstract surface on which we’ll render our images; the coordinate systemwe’ll use to
FILLED TRIANGLES
Figure 7-2: Drawing a filled triangle using horizontal segments. The following is a very rough first approximation of what we want to do: for each horizontal line y between the triangle's top and bottom compute x_left and x_right for this y DrawLine (x_left, y, x_right, y) Let’s start with “between the triangle’s top and bottom.”. SHADOWS AND REFLECTIONS Shadows and Reflections. Our quest to render the scene in progressively more realistic ways continues. In the previous chapter, we modeled the way rays of light interact with surfaces. In this chapter, we’ll model two aspects of the way light interacts with the scene: objects casting shadows and objects reflecting on otherobjects.
BASIC RAYTRACING
Basic Raytracing. In this chapter, we’ll introduce raytracing, the first major algorithm we’ll cover. We start by motivating the algorithm and laying out some basic pseudocode. Then we look at how to represent rays of light and objects in a scene. Finally, we derive a way to compute which rays of light make up the visible image of eachof
FAST-PACED MULTIPLAYER: SAMPLE CODE AND LIVE DEMO Fast-Paced Multiplayer: Sample Code and Live Demo. This is a sample implementation of a client-server architecture demonstrating the main concepts explained in my Fast-Paced Multiplayer series of articles. It won’t make much sense unless you’ve read the articles first. The code is pure JavaScript and it’s fully contained in this page.INTRODUCTION
Introduction. Computer graphics is a fascinating topic. How do you go from a few algorithms and some geometric data to the special effects for movies like Star Wars and The Avengers, animated movies like Toy Story and Frozen, or the graphics of popular video games like Fortnite or Call of Duty?. Computer graphics is also a frighteningly broad topic: from rendering 3D scenes to creating image TEXTURES - COMPUTER GRAPHICS FROM SCRATCH - GABRIEL GAMBETTA First, we need an image to paint on our triangles; in this context, we call this image a texture. Figure 14-1 shows a wooden crate texture. Figure 14-1: Wooden crate texture (by Filter Forge— Attribution 2.0 Generic (CC BY 2.0) license) Next, we need to specify how this texture is applied to the model. INTRODUCTORY CONCEPTS Introductory Concepts. A raytracer and a rasterizer take very different approaches to rendering a 3D scene onto a 2D screen. However, there are a few fundamental concepts that are common to both approaches. In this chapter, we’ll explore the canvas, the abstract surface on which we’ll render our images; the coordinate systemwe’ll use to
LINES - COMPUTER GRAPHICS FROM SCRATCH - GABRIEL GAMBETTA Lines. In Part I of this book, we studied raytracing extensively and developed a raytracer that could render our test scene with accurate lighting, material properties, shadows, and reflection using relatively simple algorithms and math. This simplicity comes at a cost: performance. While non-real-time performance is fine for certain ENTITY INTERPOLATION This way you’re always showing the user actual movement data, except you’re showing it 100 ms “late”. Client 2 renders Client 1 “in the past”, interpolating last known positions. The position data you use to interpolate from t = 900 to t = 1000 depends on the game. Interpolation usually works well enough. If it doesn’t, you can CLIENT-SIDE PREDICTION AND SERVER RECONCILIATION This isn’t terribly difficult to work around, though. First, the client adds a sequence number to each request; in our example, the first key press is request #1, and the second key press is request #2. Then, when the server replies, it includes the sequence number of the last input it processed: Client-side prediction + serverreconciliation.
LAG COMPENSATION
Lag Compensation. So you’re aiming perfectly at the target’s head with your sniper rifle. You shoot - it’s a shot you can’t miss. But you miss. Why does this happen? Because of the client-server architecture explained before, you were aiming at where the enemy’s head was 100ms before you shot - EXTENDING THE RASTERIZER These are often called hard shadows. Our rasterizer renders the scene in a single pass; it goes over every triangle in the scene and renders it on the canvas, computing the full illumination equation every time (on a per-triangle, per-vertex, or per-pixel basis, depending on theshading algorithm).
DESCRIBING AND RENDERING A SCENE Describing and Rendering a Scene. In the last few chapters, we’ve developed algorithms to draw 2D triangles on the canvas given their 2D coordinates, and we’ve explored the math required to transform the 3D coordinates of points in the scene to the 2D coordinates of pointson the canvas.
EXTENDING THE RAYTRACER Extending the Raytracer. We’ll conclude the first part of the book with a quick discussion of several interesting topics that we haven’t yet covered: placing the camera anywhere in the scene, performance optimizations, primitives other than spheres, modeling objects using constructive solid geometry, supporting transparent surfaces, and supersampling.GABRIEL GAMBETTA
Hello! I’m Gabriel Gambetta. I’m a senior software engineer at Google Zürich; the author of Computer Graphics from Scratch; and an aspiring writer, filmmaker and actor. In the past I worked at Improbable in London for a few years. It was a seed-stage, 30-person startup when I joined; by the time I left, it was an unicorn with 500+people.
COMPUTER GRAPHICS FROM SCRATCH Computer Graphics from Scratch. Computer Graphics from Scratch demystifies the algorithms used in modern graphics software with basic programming and high school math. ENTITY INTERPOLATION This way you’re always showing the user actual movement data, except you’re showing it 100 ms “late”. Client 2 renders Client 1 “in the past”, interpolating last known positions. The position data you use to interpolate from t = 900 to t = 1000 depends on the game. Interpolation usually works well enough. If it doesn’t, you can LINES - COMPUTER GRAPHICS FROM SCRATCH - GABRIEL GAMBETTA Lines. In Part I of this book, we studied raytracing extensively and developed a raytracer that could render our test scene with accurate lighting, material properties, shadows, and reflection using relatively simple algorithms and math. This simplicity comes at a cost: performance. While non-real-time performance is fine for certain FAST-PACED MULTIPLAYER: SAMPLE CODE AND LIVE DEMO Fast-Paced Multiplayer: Sample Code and Live Demo. This is a sample implementation of a client-server architecture demonstrating the main concepts explained in my Fast-Paced Multiplayer series of articles. It won’t make much sense unless you’ve read the articles first. The code is pure JavaScript and it’s fully contained in this page.LINEAR ALGEBRA
Algebraically, you multiply the coordinates individually and add them: →V, →W = (Vx, Vy, Vz), (Wx, Wy, Wz) = Vx ⋅ Wx + Vy ⋅ Wy + Vz ⋅ Wz. Geometrically, the dot product of →V and →W is related to their lengths and to the angle α between them. The exact formulaneatly ties
FILLED TRIANGLES
Figure 7-2: Drawing a filled triangle using horizontal segments. The following is a very rough first approximation of what we want to do: for each horizontal line y between the triangle's top and bottom compute x_left and x_right for this y DrawLine (x_left, y, x_right, y) Let’s start with “between the triangle’s top and bottom.”. CLIENT-SIDE PREDICTION AND SERVER RECONCILIATION This isn’t terribly difficult to work around, though. First, the client adds a sequence number to each request; in our example, the first key press is request #1, and the second key press is request #2. Then, when the server replies, it includes the sequence number of the last input it processed: Client-side prediction + serverreconciliation.
BASIC RAYTRACING
Basic Raytracing. In this chapter, we’ll introduce raytracing, the first major algorithm we’ll cover. We start by motivating the algorithm and laying out some basic pseudocode. Then we look at how to represent rays of light and objects in a scene. Finally, we derive a way to compute which rays of light make up the visible image of eachof
PERSPECTIVE PROJECTION The Projection Equation. Let’s put all this together. Given a point P in the scene and a standard camera and viewport setup, we can compute the projection of P on the viewport, which we call P ′, as follows: P ′ x = Px ⋅ d Pz. P ′ y = Py ⋅ d Pz. P ′ z = d. P ′ is on the viewport, but it’s still a point in 3D space.GABRIEL GAMBETTA
Hello! I’m Gabriel Gambetta. I’m a senior software engineer at Google Zürich; the author of Computer Graphics from Scratch; and an aspiring writer, filmmaker and actor. In the past I worked at Improbable in London for a few years. It was a seed-stage, 30-person startup when I joined; by the time I left, it was an unicorn with 500+people.
COMPUTER GRAPHICS FROM SCRATCH Computer Graphics from Scratch. Computer Graphics from Scratch demystifies the algorithms used in modern graphics software with basic programming and high school math. ENTITY INTERPOLATION This way you’re always showing the user actual movement data, except you’re showing it 100 ms “late”. Client 2 renders Client 1 “in the past”, interpolating last known positions. The position data you use to interpolate from t = 900 to t = 1000 depends on the game. Interpolation usually works well enough. If it doesn’t, you can LINES - COMPUTER GRAPHICS FROM SCRATCH - GABRIEL GAMBETTA Lines. In Part I of this book, we studied raytracing extensively and developed a raytracer that could render our test scene with accurate lighting, material properties, shadows, and reflection using relatively simple algorithms and math. This simplicity comes at a cost: performance. While non-real-time performance is fine for certain FAST-PACED MULTIPLAYER: SAMPLE CODE AND LIVE DEMO Fast-Paced Multiplayer: Sample Code and Live Demo. This is a sample implementation of a client-server architecture demonstrating the main concepts explained in my Fast-Paced Multiplayer series of articles. It won’t make much sense unless you’ve read the articles first. The code is pure JavaScript and it’s fully contained in this page.LINEAR ALGEBRA
Algebraically, you multiply the coordinates individually and add them: →V, →W = (Vx, Vy, Vz), (Wx, Wy, Wz) = Vx ⋅ Wx + Vy ⋅ Wy + Vz ⋅ Wz. Geometrically, the dot product of →V and →W is related to their lengths and to the angle α between them. The exact formulaneatly ties
FILLED TRIANGLES
Figure 7-2: Drawing a filled triangle using horizontal segments. The following is a very rough first approximation of what we want to do: for each horizontal line y between the triangle's top and bottom compute x_left and x_right for this y DrawLine (x_left, y, x_right, y) Let’s start with “between the triangle’s top and bottom.”. CLIENT-SIDE PREDICTION AND SERVER RECONCILIATION This isn’t terribly difficult to work around, though. First, the client adds a sequence number to each request; in our example, the first key press is request #1, and the second key press is request #2. Then, when the server replies, it includes the sequence number of the last input it processed: Client-side prediction + serverreconciliation.
BASIC RAYTRACING
Basic Raytracing. In this chapter, we’ll introduce raytracing, the first major algorithm we’ll cover. We start by motivating the algorithm and laying out some basic pseudocode. Then we look at how to represent rays of light and objects in a scene. Finally, we derive a way to compute which rays of light make up the visible image of eachof
PERSPECTIVE PROJECTION The Projection Equation. Let’s put all this together. Given a point P in the scene and a standard camera and viewport setup, we can compute the projection of P on the viewport, which we call P ′, as follows: P ′ x = Px ⋅ d Pz. P ′ y = Py ⋅ d Pz. P ′ z = d. P ′ is on the viewport, but it’s still a point in 3D space. EMULATOR-BACKED REMAKES The only way to reach a really high level of accuracy is to actually disassemble the original code and replicate the logic. Use an emulator. There’s always DOSBox, and specific solutions for certain games, such as ScummVM. This works, but let’s be honest, most gameshaven’t aged well
GENERIC SEARCH ALGORITHM Introduction. Pathfinding is one of these topics that usualy baffles game developers. The A* algorithm in particular is poorly understood, and the general belief seems to be that it’s arcane magic.. The objective of this series of articles is to explain pathfinding in general and A* in particular in a very clear and accessible way, and put an end to the misconception that it’s a difficult CLIENT-SIDE PREDICTION AND SERVER RECONCILIATION This isn’t terribly difficult to work around, though. First, the client adds a sequence number to each request; in our example, the first key press is request #1, and the second key press is request #2. Then, when the server replies, it includes the sequence number of the last input it processed: Client-side prediction + serverreconciliation.
INTRODUCTION
Introduction. Computer graphics is a fascinating topic. How do you go from a few algorithms and some geometric data to the special effects for movies like Star Wars and The Avengers, animated movies like Toy Story and Frozen, or the graphics of popular video games like Fortnite or Call of Duty?. Computer graphics is also a frighteningly broad topic: from rendering 3D scenes to creating image HOW I WROTE AND PUBLISHED MY NOVEL USING ONLY OPEN SOURCE How I wrote and published my novel using only open source tools From Markdown to paperback and Kindle without proprietary software. I’ve recently published my first novel The Golden Seed on Kindle and paperback through Amazon, achieving very professional results. Along the way, I created a process and a couple of tools based exclusively on open source software.LAG COMPENSATION
Lag Compensation. So you’re aiming perfectly at the target’s head with your sniper rifle. You shoot - it’s a shot you can’t miss. But you miss. Why does this happen? Because of the client-server architecture explained before, you were aiming at where the enemy’s head was 100ms before you shot - INTRODUCTORY CONCEPTS Introductory Concepts. A raytracer and a rasterizer take very different approaches to rendering a 3D scene onto a 2D screen. However, there are a few fundamental concepts that are common to both approaches. In this chapter, we’ll explore the canvas, the abstract surface on which we’ll render our images; the coordinate systemwe’ll use to
HOW I WROTE MY FIRST NOVEL DURING MY DAILY COMMUTE So I took the obvious next step: I added a new column named _“my novel”_and set out to fill in the blanks. Although it ended up looking quite different, this column was the basis for what later became my first novel, The Golden Seed. Four more years would pass before I had the first copy of the novel in my hands. HIDDEN SURFACE REMOVAL The edge case \(\langle \vec{N}, \vec{V} \rangle = 0\) corresponds to the case where we’re looking at the edge of a triangle head on—that is, when the camera and the triangle are coplanar. We can classify this triangle either way without affecting the result much, so we choose to classify it as back-facing to avoid dealing with degenerate triangles. EXTENDING THE RAYTRACER Extending the Raytracer. We’ll conclude the first part of the book with a quick discussion of several interesting topics that we haven’t yet covered: placing the camera anywhere in the scene, performance optimizations, primitives other than spheres, modeling objects using constructive solid geometry, supporting transparent surfaces, and supersampling. HELLO! I’M GABRIEL GAMBETTA. I’m a senior software engineer, actor, writer and filmmaker. This website is mostly about tech; I have a separate websiteabout acting.
As a software engineer, I’ve worked at Google Zürich, and at Improbable in London; before all this, I ran a small indie game dev studio for almost a decade. I also taught Computer Graphics at my university; I’ve written a textbook based on my lectures. I post semi-regularly on Facebookand Twitter
. I can also be found in LinkedInand IMDB
. The easiest way to say “hi”is via email.
Here are some things I’ve made and written over the years.TECH
*
FAST-PACED MULTIPLAYER : A series of articles about CLIENT-SIDE PREDICTION, and the architecture of fast-paced client-server multiplayer games. This series has become one of the main references on the topic found on the Internet. * Client-Server Game Architecture Client-Side Prediction and Server ReconciliationEntity
Interpolation · Lag CompensationLive Demo
*
COMPUTER GRAPHICS FROM SCRATCH : A raytracing and rasterization textbook, based on the lectures I gave during my teaching years.*
PATHFINDING DEMYSTIFIED : A series of articles about pathfinding in general and the A* algorithm in particular. * Generic Search · Search StrategiesA* Demystified
Practical A*
*
EMULATOR-BACKED REMAKES : A proof of concept of a revolutionary way to make remakes of old games.*
TINY RAYTRACER : A ray tracer with lighting, shadows and reflections written in 1000 bytes of JavaScript.*
LIBZ80 : An emulator of the Z80 processor (C library).*
MYSTERY STUDIO : The game development startup I founded and ran from 2002 to 2011.WRITING
*
THE GOLDEN LEGACY : an action/thriller novel. _“The Da Vinci Code meets Jason Bourne”_. Available on Kindleand paperback
.
*
Read the FIRST 24 CHAPTERS online.*
Some thoughts about THE CREATIVE PROCESS and THE TECHNICAL ASPECTS OF PUBLISHING .*
LA SEMILLA DORADA (Spanish version)*
THE TESLA LOOP
: an
action/sci-fi feature-length screenplay (of the time travel variety).*
OVERTURE : an
action/sci-fi feature-length screenplay (of the alien invasionvariety).
*
UNTITLED TRAVEL BOOK: Emails and pictures from a 6-month trip around Asia and Europe in made in 2008, in a van and with a tiny budget(coming soon).
*
SHORT STORIES I wrote as a teenager.MISC
* ABOUT ME : My story so far. STAY IN TOUCH! Your email: Please enter a valid email address. ------------------------- Gabriel Gambetta 2019Details
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