From 240058ad60c9b7a49b4d71642aa1b1958ca6f09f Mon Sep 17 00:00:00 2001 From: Andrew Date: Tue, 24 Sep 2024 19:51:13 +0100 Subject: [PATCH] [CT404]: Add Week 2 lecture notes + slides --- .../notes/CT404-Notes.pdf | Bin 709301 -> 798360 bytes .../notes/CT404-Notes.tex | 456 ++++++++++++++++++ .../notes/images/viewing_frustum.png | Bin 0 -> 34319 bytes .../24_02_Intro_3D_Graphics_Threejs.pdf | Bin 0 -> 1380610 bytes 4 files changed, 456 insertions(+) create mode 100644 year4/semester1/CT404: Graphics & Image Processing/notes/images/viewing_frustum.png create mode 100644 year4/semester1/CT404: Graphics & Image Processing/slides/24_02_Intro_3D_Graphics_Threejs.pdf diff --git a/year4/semester1/CT404: Graphics & Image Processing/notes/CT404-Notes.pdf b/year4/semester1/CT404: Graphics & Image Processing/notes/CT404-Notes.pdf index 8d70ddd60f11c7696fbe6c541233d533b4dfbabc..82f16476bf9a1d17eaaa21a155a895bd63e74004 100644 GIT binary patch delta 190464 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b/year4/semester1/CT404: Graphics & Image Processing/notes/CT404-Notes.tex @@ -16,6 +16,8 @@ \usepackage[a4paper,left=2cm,right=2cm,top=\dimexpr15mm+1.5\baselineskip,bottom=2cm]{geometry} \setlength{\parindent}{0pt} +\usepackage{ulem} +\usepackage{gensymb} \usepackage{fancyhdr} % Headers and footers \fancyhead[R]{\normalfont \leftmark} \fancyhead[L]{} @@ -586,5 +588,459 @@ Colours can be specified by name (\mintinline{javascript}{red}), by a string of \caption{Rendering of the Above JavaScript Code} \end{figure} +\section{3D Co-Ordinate Systems} +In a 3D co-ordinate system, a point $P$ is referred to by three real numbers (co-ordinates): $(x,y,z)$. +The directions of $x$, $y$, \& $z$ are not universally defined but normally follow the \textbf{right-hand rule} +for axes systems. +In this case, $z$ defined the co-ordinate's distance ``out of'' the monitor and negative $z$ values go ``into'' +the monitor. + +\subsection{Nested Co-Ordinate Systems} +A \textbf{nested co-ordinate system} is defined as a translation relative to the world co-ordinate system. +For example, $-3.0$ units along the $x$ axis, $2.0$ units along the $y$ axis, and $2.0$ units along the $z$ axis. + +\subsection{3D Transformations} +\subsubsection{Translation} +To translate a 3D point, modify each dimension separately: +$$ +x' = x + a_1 +$$ +$$ +y' = y + a_2 +$$ +$$ +z' = z + a_3 +$$ + +$$ +\begin{bmatrix} + x' & y' & z' & 1 +\end{bmatrix} += +\begin{bmatrix} + x & y & z & 1 +\end{bmatrix} +\begin{bmatrix} + 1 & 0 & 0 & 0 \\ + 0 & 1 & 0 & 0 \\ + 0 & 0 & 1 & 0 \\ + a_1 & a_2 & a_3 & 1 +\end{bmatrix} +$$ + +\subsubsection{Rotation About Principal Axes} +A \textbf{principal axis} is an imaginary line through the ``center of mass'' of a body around which the body +rotates. +\begin{itemize} + \item Rotation around the $x$-axis is referred to as \textbf{pitch}. + \item Rotation around the $y$-axis is referred to as \textbf{yaw}. + \item Rotation around the $z$-axis is referred to as \textbf{roll}. +\end{itemize} + +\textbf{Rotation matrices} define rotations by angle $\alpha$ about the principal axes. +$$ +R_x = +\begin{bmatrix} + 1 & 0 & 0 \\ + 0 & \cos \alpha & \sin \alpha \\ + 0 & - \sin \alpha & \cos \alpha +\end{bmatrix} +$$ + +To get new co-ordinates after rotation, multiply the point $\begin{bmatrix} x & y & z \end{bmatrix}$ by the +rotation matrix: +$$ +\begin{bmatrix} + x' & y' & z' +\end{bmatrix} += +\begin{bmatrix} + x & y & z +\end{bmatrix} +R_x +$$ + +For example, as a point rotates about the $x$-axis, its $x$ component remains unchanged. + +\subsubsection{Rotation About Arbitrary Axes} +You can rotate about any axis, not just the principal axes. +You specify a 3D point, and the axis of rotation is defined as the line that joins the origin to this point +(e.g., a toy spinning top will rotate about the $y$-axis, defined as $(0, 1, 0)$). +You must also specify the amount to rotate by, this is measured in radians (e.g., $2\pi$ radians is $360\degree$). + +\section{Graphics APIs} +\textbf{Low-level} graphics APIs are libraries of graphics functions that can be accessed from a standard +programming language. +They are typically procedural rather than descriptive, i.e. the programmer calls the graphics functions which +carry out operations immediately. +The programmer also has to write all other application code: interface, etc. +Procedural programming languages are typically faster than descriptive programming languages. +Examples include OpenGL, DirectX, Vulkan, Java Media APIs. +Examples that run in the browser include Canvas2D, WebGL, SVG. +\\\\ +\textbf{High-level} graphics APIs are ones in which the programmer describes the required graphics, animations, +interactivity, etc. and doesn't need to deal with how this will be displayed \& updated. +They are typically descriptive rather than procedural and so are generally slower \& less flexible because it is +generally interpreted and rather general-purpose rather than task-specific. +Examples include VRML/X3D. + +\subsection{Three.js} +\textbf{WebGL (Web Graphics Library)} is a JavaScript API for rendering interactive 2D \& 3D graphics within any +compatible web browser without the use of plug-ins. +WebGL s fully integrated with other web standards, allowing GPU-accelerated usage of physics \& image processing +and effects as part of the web page canvas. +\\\\ +\textbf{Three.js} is a cross-browser JavaScript library and API used to create \& display animated 4D computer +graphics in a web browser. +Three.js uses WebGL. + +\begin{code} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + + + + +\end{minted} +\caption{``Hello World'' in Three.js} +\end{code} + +In Three.js, a visible object is represented as a \textbf{mesh} and is constructed from a \textit{geometry} \& a +\textit{material}. + +\subsubsection{3D Primitives} +Three.js provides a range of primitive geometry as well as the functionality to implement more complex geometry at a lower +level. +See \url{https://threejs.org/manual/?q=prim#en/primitives}. + +\begin{code} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + + + + +\end{minted} +\caption{Code Illustrating Some Primitives Provided by Three.js} +\end{code} + +\subsubsection{Cameras} +3D graphics API cameras allow you to define: +\begin{itemize} + \item The camera location $(x,y,z)$. + \item The camera orientation (\sout{straight, gay} $x$ rotation, $y$ rotation, $z$ rotation). + \item The \textbf{viewing frustum} (the Field of View (FoV) \& clipping planes). + \begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{images/viewing_frustum.png} + \caption{The Viewing Frustum} + \end{figure} +\end{itemize} + +In Three.js, the FoV can be set differently in the vertical and horizontal directions via the first \& second arguments +to the constructor can be set differently in the vertical and horizontal directions via the first \& second arguments +to the constructor \mintinline{javascript}{(fov, aspect)}. +Generally speaking, the aspect ratio should match that of the canvas width \& height to avoid the scene appearing to be +stretched. + +\subsubsection{Lighting} +Six different types of lights are available in both Three.js \& WebGL: +\begin{itemize} + \item \textbf{Point lights:} rays emanate in all directions from a 3D point source (e.g., a lightbulb). + \item \textbf{Directional lights:} rays emanate in one direction only from infinitely far away + (similar effect rays from the Sun, i.e. very far away). + \item \textbf{Spotlights:} project a cone of light from a 3D point source aimed at a specific target point. + \item \textbf{Ambient lights:} simulate in a simplified way the lighting of an entire scene due to complex + light/surface interactions -- lights up everything in the scene regardless of position or occlusion. + \item \textbf{Hemisphere lights:} ambient lights that affect the ``ceiling'' or ``floor'' hemisphere of objects + rather than affecting them in their entirety. + \item \textbf{RectAreaLights:} emit rectangular areas of light (e.g., fluorescent light strip). +\end{itemize} + +\begin{code} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + + + +\end{minted} +\caption{Rotation Around a Local Origin in Three.js} +\end{code} + +\subsubsection{Nested Co-Ordinates} +\textbf{Nested co-ordinates} help manage complexity as well as promote reusability \& simplify the transformations of +objects composed of multiple primitive shapes. +In Three.js, 3D objects have a \mintinline{javascript}{children} array; +a child can be added to an object using the method \mintinline{javascript}{.add(childObject)}, i.e. nesting the child +object's transform within the parent object. +Objects have a parent in the scene graph so when you set their transforms (translation, rotation) it's relative to that +parent's local co-ordinate system. + + +\begin{code} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + + + + +\end{minted} +\caption{Partial Desk Lamp with Nested Objects} +\end{code} + +The above code creates a correctly set-up hierarchy of nested objects, allowing us to: +\begin{itemize} + \item Translate the base while the two arms remain in the correct relative position. + \item Rotate the first arm while keeping the second arm in the correct position. +\end{itemize} + +\subsubsection{Geometry Beyond Primitives} +In Three.js, the term ``low-level geometry'' is used to refer to geometry objects consisting of vertices, faces, \& +normal. + + + + + + + + \end{document} diff --git a/year4/semester1/CT404: Graphics & Image Processing/notes/images/viewing_frustum.png b/year4/semester1/CT404: Graphics & Image Processing/notes/images/viewing_frustum.png new file mode 100644 index 0000000000000000000000000000000000000000..130731cd0e8977dbef8af91ed11d85549829dc5b GIT binary patch literal 34319 zcmb5WbyQYu_brTKq5_JdAR!`1HzKJb1|T3QAR!$}cU#z?NUMN?C`d_nsDvPblypd! 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