From 62ba765ddc2ea9e2c68934149f2f5c1a4311fdd1 Mon Sep 17 00:00:00 2001 From: Andrew Date: Mon, 16 Sep 2024 19:24:20 +0100 Subject: [PATCH] [CT404]: Add Week 1 lecture notes --- .../notes/CT404-Notes.pdf | Bin 25622 -> 709301 bytes .../notes/CT404-Notes.tex | 489 ++++++++++++++++++ .../notes/images/2d_arbitrary_rotation.png | Bin 0 -> 27797 bytes .../notes/images/2d_object_rotation.png | Bin 0 -> 64361 bytes .../notes/images/2d_point_rotation.png | Bin 0 -> 23865 bytes .../notes/images/2d_translation.png | Bin 0 -> 18194 bytes .../notes/images/canvas2d_drawimage.png | Bin 0 -> 9327 bytes .../notes/images/canvas2d_fill_stroke.png | Bin 0 -> 12662 bytes .../canvas2d_order_of_transformations.png | Bin 0 -> 12959 bytes .../notes/images/canvas2d_primitives.png | Bin 0 -> 6587 bytes .../images/canvas2d_programmatic_graphics.png | Bin 0 -> 40221 bytes .../notes/images/canvas2d_scaling.png | Bin 0 -> 1645 bytes .../notes/images/canvas2d_translations.png | Bin 0 -> 4270 bytes .../images/canvas_rendering_contexts.png | Bin 0 -> 685 bytes .../notes/images/cover.png | Bin 0 -> 15590 bytes .../notes/images/order_of_transformations.png | Bin 0 -> 123289 bytes .../images/real_time_graphics_pipeline.png | Bin 0 -> 258163 bytes 17 files changed, 489 insertions(+) create mode 100644 year4/semester1/CT404: Graphics & Image Processing/notes/images/2d_arbitrary_rotation.png create mode 100644 year4/semester1/CT404: Graphics & Image Processing/notes/images/2d_object_rotation.png create mode 100644 year4/semester1/CT404: Graphics & Image Processing/notes/images/2d_point_rotation.png create mode 100644 year4/semester1/CT404: Graphics & Image Processing/notes/images/2d_translation.png create mode 100644 year4/semester1/CT404: Graphics & Image Processing/notes/images/canvas2d_drawimage.png create mode 100644 year4/semester1/CT404: Graphics & Image Processing/notes/images/canvas2d_fill_stroke.png create mode 100644 year4/semester1/CT404: Graphics & Image 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aIQbBq9660bjK;>v#>S39MJ1smiSi#;4*{eA diff --git a/year4/semester1/CT404: Graphics & Image Processing/notes/CT404-Notes.tex b/year4/semester1/CT404: Graphics & Image Processing/notes/CT404-Notes.tex index a62281b5..ba889f07 100644 --- a/year4/semester1/CT404: Graphics & Image Processing/notes/CT404-Notes.tex +++ b/year4/semester1/CT404: Graphics & Image Processing/notes/CT404-Notes.tex @@ -28,6 +28,8 @@ \usepackage[final, colorlinks = false, urlcolor = linkblue]{hyperref} % \newcommand{\secref}[1]{\textbf{§~\nameref{#1}}} \newcommand{\secref}[1]{\textbf{§\ref{#1}~\nameref{#1}}} +\usepackage{multicol} +\usepackage{amsmath} \usepackage{changepage} % adjust margins on the fly @@ -67,6 +69,8 @@ \hrule \vfill + \centering + \includegraphics[width=\textwidth]{images/cover.png} \vfill \hrule @@ -97,5 +101,490 @@ \pagenumbering{arabic} \section{Introduction} +Textbooks: +\begin{itemize} + \item Main textbook: \textit{Image Processing and Analysis} -- Stan Birchfield (ISBN: 978-1285179520). + \item \textit{Introduction to Computer Graphics} -- David J. Eck. (Available online at \url{https://math.hws.edu/graphicsbook/}). + \item \textit{Computer Graphics: Principles and Practice} -- John F. Hughes et al. (ISBN: 0-321-39952-8). + \item \textit{Computer Vision: Algorithms and Applications} -- Richard Szeliski (ISBN: 978-3-030-34371-2). +\end{itemize} + +\textbf{Computer graphics} is the processing \& displaying of images of objects that exist conceptually rather than +physically with emphasis on the generation of an image from a model of the objects, illumination, etc. and the +real-time rendering of images. +Ideas from 2D graphics extend to 3D graphics. +\\\\ +\textbf{Digital Image processing/analysis} is the processing \& display of images of real objects, with an emphasis +on the modification and/or analysis of the image in order to automatically or semi-automatically extract useful +information. +Image processing leads to more advanced feature extraction \& pattern recognition techniques for image analysis \& +understanding. + +\subsection{Grading} +\begin{itemize} + \item Assignments: 30\%. + \item Final Exam: 70\%. +\end{itemize} + +\subsubsection{Reflection on Exams} +``A lot of people give far too little detail in these questions, and/or don't address the discussion +parts -- they just give some high-level definitions and consider it done -- which isn't enough for +final year undergrad, and isn't answering the question. +More is expected in answers than just repeating what's in my slides. +The top performers demonstrate a higher level of understanding and synthesis as well as more +detail about techniques and discussion of what they do on a technical level and how they fit +together'' + +\subsection{Lecturer Contact Information} +\begin{multicols}{2} + \begin{itemize} + \item Dr. Nazre Batool. + \item \href{mailto://nazre.batool@universityofgalway.ie}{\texttt{nazre.batool@universityofgalway.ie}} + \item Office Hours: Thursdays 16:00 -- 17:00, CSB-2009. + + \item Dr. Waqar Shahid Qureshi. + \item \href{mailto://waqarshahid.qureshi@universityofgalway.ie}{\texttt{waqarshahid.qureshi@universityofgalway.ie}}. + \item Office Hours: Thursdays 16:00 -- 17:00, CSB-3001. + \end{itemize} +\end{multicols} + +\section{Introduction to 2D Graphics} +\subsection{Digital Images -- Bitmaps} +\textbf{Bitmaps} are grid-based arrays of colour or brightness (greyscale) information. +\textbf{Pixels} (\textit{picture elements}) are the cells of a bitmap. +The \textbf{depth} of a bitmap is the number of bits-per-pixel (bpp). + +\subsection{Colour Encoding Schemes} +Colour is most commonly represented using the \textbf{RGB (Red, Green, Blue)} scheme, typically using 24-bit colour +with one 8-bit number representing the level of each colour channel in that pixel. +\\\\ +Alternatively, images can also be represented in \textbf{greyscale} wherein pixels are represented with one +(typically 8-bit) brightness value (or scale of grey) . + +\subsection{The Real-Time Graphics Pipeline} +\begin{figure}[H] + \centering + \includegraphics[width=\textwidth]{images/real_time_graphics_pipeline.png} + \caption{The Real-Time Graphics Pipeline} +\end{figure} + +\subsection{Graphics Software} +The \textbf{Graphics Processing Unit (GPU)} of a computer is a hardware unit designed for digital image processing \& to +accelerate computer graphics that is included in modern computers to complement the CPU. +They have internal, rapid-access GPU memory and parallel processors for vertices \& fragments to speed up graphics +renderings. +\\\\ +\textbf{OpenGL} is a 2D \& 3D graphics API that has existed since 1992 that is supported by the graphics hardware in most +computing devices today. +\textbf{WebGL} is a web-based implementation of OpenGL for use within web browsers. +OpenGL ES for Embedded Systems such as tablets \& mobile phones also exists. +\\\\ +OpenGL was originally a client/server system with the CPU+Application acting as a client sending commands \& data to the GPU +acting as a server. +This was later replaced by a programmable graphics interface (OpenGL 3.0) to write GPU programs (shaders) to be run by the +GPU directly. +It is being replaced by newer APIs such as Vulkan, Metal, \& Direct3D and WebGL is being replaced by WebGPU. + +\subsection{Graphics Formats} +\textbf{Vector graphics} are images described in terms of co-ordinate drawing operations, e.g. AutoCAD, PowerPoint, Flash, +SVG. +\textbf{SVG (Scalable Vector Graphics)} is an image specified by vectors which are scalable without losing any quality. +\\\\ +\textbf{Raster graphics} are images described as pixel-based bitmaps. +File formats such as GIF, PNG, JPEG represent the image by storing colour values for each pixel. + +\section{2D Vector Graphics} +\textbf{2D vector graphics} describe drawings as a series of instructions related to a 2-dimensional co-ordinate system. +Any point in this co-ordinate system can be specified using two numbers $(x, y)$: +\begin{itemize} + \item The horizontal component $x$, measuring the distance from the left-hand edge of the screen or window. + \item The vertical component $y$, measuring the distance from the bottom of the screen or window (or sometimes from the + top). +\end{itemize} + +\subsection{Transformations} +\subsubsection{2D Translation} +The \textbf{translation} of a point in 2 dimensions is the movement of a point $(x,y)$ to some other point $(x', y')$. +$$ +x' = x + a +$$ +$$ +y' = y + b +$$ + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{images/2d_translation.png} + \caption{2D Translation of a Point} +\end{figure} + +\subsubsection{2D Rotation of a \textit{Point}} +The simplest rotation of a point around the origin is given by: +$$ +x' = x \cos \theta - y \sin \theta +$$ +$$ +y' = x \cos \theta + y \sin \theta +$$ + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{images/2d_point_rotation.png} + \caption{2D Rotation of a Point} +\end{figure} + +\subsubsection{2D Rotation of an \textit{Object}} +In vector graphics, \textbf{objects} are defined as series of drawing operations (e.g., straight lines) performed on a set +of vertices. +To rotate a line or more complex object, we simply apply the equations to rotate a point to the $(x,y)$ co-ordinates of each +vertex. + +\begin{figure}[H] + \centering + \includegraphics[width=0.7\textwidth]{images/2d_object_rotation.png} + \caption{2D Rotation of an Object} +\end{figure} + +\subsubsection{Arbitrary 2D Rotation} +In order to rotate around an arbitrary point $(a,b)$, we perform translation, then rotation, then reverse the translation. +$$ +x' = a + (x - a) \cos \theta - (y - b) \sin \theta +$$ +$$ +y' = a + (x - a) \cos \theta + (y - b) \sin \theta +$$ + +\begin{figure}[H] + \centering + \includegraphics[width=0.5\textwidth]{images/2d_arbitrary_rotation.png} + \caption{Arbitrary 2D Rotation} +\end{figure} + +\subsubsection{Matrix Notation} +\textbf{Matrix notation} is commonly used for vector graphics as more complex operations are often easier in matrix format +and because several operations can be combined easily into one matrix using matrix algebra. + +Rotation about $(0,0)$: +$$ +\begin{bmatrix} + x' & y' +\end{bmatrix} += +\begin{bmatrix} + x & y +\end{bmatrix} +\begin{bmatrix} + \cos \theta & \sin \theta \\ +-\sin \theta & \cos \theta +\end{bmatrix} +$$ + +Translation: +$$ +\begin{bmatrix} + x' & y' 1 +\end{bmatrix} += +\begin{bmatrix} + x & y & 1 +\end{bmatrix} +\begin{bmatrix} + 1 & 0 & 0 \\ + 0 & 1 & 0 \\ + a & 0 & 1 +\end{bmatrix} +$$ + +\subsubsection{Scaling} +\textbf{Scaling} of an object is achieved by considering each of its vertices in turn, multiplying said vertex's $x$ \& $y$ +values by the scaling factor. +A scaling factor of 2 will double the size of the object, while a scaling factor of 0.5 will halve it. +It is possible to have different scaling factors for $x$ \& $y$, resulting in a \textbf{stretch}: +$$ +x' = x \times s +$$ +$$ +y' = y \times t +$$ + +If the object is not centred on the origin, then scaling it will also effect a translation. + +\subsubsection{Order of Transformations} +\begin{figure}[H] + \centering + \includegraphics[width=0.8\textwidth]{images/order_of_transformations.png} + \caption{Order of Transformations} +\end{figure} + +\section{2D Raster Graphics} +The raster approach to 2D graphics considers digital images to be grid-based arrays of pixels and operates on the +images at the pixel level. + +\subsection{Introduction to HTML5/Canvas} +\textbf{HTML} or HyperText Markup Language is a page-description language used primarily for website. +\textbf{HTML5} brings major updates \& improvements to the power of client-side web development. +\\\\ +A \textbf{canvas} is a 2D raster graphics component in HTML5. +There is also a \textbf{canvas with 3D} (WebGL) which is a 3D graphics component that is more likely to be +hardware-accelerated but is also more complex. + +\subsubsection{Canvas: Rendering Contexts} +\mintinline{html}{} creates a fixed-size drawing surface that exposes one or more \textbf{rendering contexts}. +The \mintinline{javascript}{getContext()} method returns an object with tools (methods) for drawing. + +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + +\end{minted} + +\begin{figure}[H] + \centering + \includegraphics[width=0.2\textwidth]{images/canvas_rendering_contexts.png} + \caption{Rendering of the Above HTML Code} +\end{figure} + +\subsubsection{Canvas2D: Primitives} +Canvas2D only supports one primitive shape: rectangles. +All other shapes must be created by combining one or more \textit{paths}. +Fortunately, there are a collection of path-drawing functions which make it possible to compose complex shapes. + +\begin{minted}[linenos, breaklines, frame=single]{javascript} +function draw(){ + var canvas = document.getElementById('canvas'); + var ctx = canvas.getContext('2d'); + ctx.fillRect(125,25,100,100); + ctx.clearRect(145,45,60,60); + ctx.strokeRect(150,50,50,50); + ctx.beginPath(); + ctx.arc(75,75,50,0,Math.PI*2,true); // Outer circle + ctx.moveTo(110,75); + ctx.arc(75,75,35,0,Math.PI,false); // Mouth (clockwise) + ctx.moveTo(65,65); + ctx.arc(60,65,5,0,Math.PI*2,true); // Left eye + ctx.moveTo(95,65); + ctx.arc(90,65,5,0,Math.PI*2,true); // Right eye + ctx.stroke(); // renders the Path that has been built up.. +} +\end{minted} + +\begin{figure}[H] + \centering + \includegraphics[width=0.3\textwidth]{images/canvas2d_primitives.png} + \caption{Rendering of the Above JavaScript Code} +\end{figure} + +\subsubsection{Canvas2D: \mintinline{javascript}{drawImage()}} +The example below uses an external image as the backdrop of a small line graph: +\begin{minted}[linenos, breaklines, frame=single]{javascript} +function draw() { + var ctx = document.getElementById('canvas').getContext('2d'); + var img = new Image(); + img.src = 'backdrop.png'; + img.onload = function(){ + ctx.drawImage(img,0,0); + ctx.beginPath(); + ctx.moveTo(30,96); + ctx.lineTo(70,66); + ctx.lineTo(103,76); + ctx.lineTo(170,15); + ctx.stroke(); + } +} +\end{minted} + +\begin{figure}[H] + \centering + \includegraphics[width=0.3\textwidth]{images/canvas2d_drawimage.png} + \caption{Rendering of the Above JavaScript Code} +\end{figure} + +\subsubsection{Canvas2D: Fill \& Stroke Colours} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + +\end{minted} + +Colours can be specified by name (\mintinline{javascript}{red}), by a string of the form +\mintinline{javascript}{rgb(r,g,b)}, or by hexadecimal colour codes \mintinline[escapeinside=||]{javascript}{|#|RRGGBB}. + +\begin{figure}[H] + \centering + \includegraphics[width=0.3\textwidth]{images/canvas2d_fill_stroke.png} + \caption{Rendering of the Above JavaScript Code} +\end{figure} + +\subsubsection{Canvas2D: Translations} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + +\end{minted} + +\begin{figure}[H] + \centering + \includegraphics[width=0.3\textwidth]{images/canvas2d_translations.png} + \caption{Rendering of the Above JavaScript Code} +\end{figure} + +\subsubsection{Canvas2D: Order of Transformations} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + +\end{minted} + +\begin{figure}[H] + \centering + \includegraphics[width=0.2\textwidth]{images/canvas2d_order_of_transformations.png} + \caption{Rendering of the Above JavaScript Code} +\end{figure} + +\subsubsection{Scaling} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + +\end{minted} + +\begin{figure}[H] + \centering + \includegraphics[width=0.2\textwidth]{images/canvas2d_scaling.png} + \caption{Rendering of the Above JavaScript Code} +\end{figure} + +\subsubsection{Canvas2D: Programmatic Graphics} +\begin{minted}[linenos, breaklines, frame=single]{html} + + + + + + + + +\end{minted} + +\begin{figure}[H] + \centering + \includegraphics[width=0.2\textwidth]{images/canvas2d_programmatic_graphics.png} + \caption{Rendering of the Above JavaScript Code} +\end{figure} + \end{document} diff --git a/year4/semester1/CT404: Graphics & Image 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