2D graphics

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Introduction to 2D Graphics
Using OpenGL
2D Graphics using OpenGL

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Why Learn About OpenGL?
• A well-known industry standard for real-time 2D and 3D computer graphics
• Available on most platforms
• Desktop operating systems, mobile devices (OpenGL ES), browsers (WebGL)
• Older (OpenGL 1.0) API provides features for rapid prototyping; newer API
(OpenGL 2.0 and newer) provides more flexibility and control
• Many old features available in new API as “deprecated” functionality
• This year for the first time we will use the new API exclusively

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Why Learn 2D first?
• A good stepping stone towards 3D – many issues much easier to
understand in 2D
• no need to simulate lights, cameras, the physics of light interacting with
objects, etc.
• intro to modeling vs. rendering and other notions
• get used to rapid prototyping in OpenGL, both of designs and concepts
• 2D is still really important and the most common use of computer
graphics, e.g. in UI/UX, documents, browsers

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Graphics Platforms (1/4)
• Applications that only write pixels are rare
• Application Model (AM) is the data being represented by a rendered image
• manipulated by user interaction with the application
• Graphics Platform is intermediary between App and platform
• rendering and interaction handling

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• Graphics Platform runs in conjunction with window manager
• Determines what section of the screen is allocated to the application
• Handles “chrome” (title bar, resize handles); client area is controlled by application

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• Typically, AM uses client area for:
• user interface to collect input to the AM
• display some representation of AM in the viewport
• This is usually called the scene, in the context of both 2D and 3D applications
• Scene is rendered by the scene generator, which is typically separate from the UI
generator, which renders rest of UI

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• Early raster graphics packages/libraries/platforms
• RamTek library 1981, Apple QuickDraw 1984
• Microsoft's Graphics Display Interface (GDI 1990, now GDI+), Java.awt.Graphics2D
• Earliest packages usually had these characteristics:
• geometric primitives/shapes, appearance attributes specified in attribute bundles
(a.k.a. ”graphical contexts”/”brushes”),
• applied modally rather than in a parameter list for each primitive (too many parameters for that)
• integer coordinates map directly to screen pixels on output device
• immediate mode (no record kept of display commands)
• no built-in functions for applying transforms to primitives
• no built-in support for component hierarchy (no composite shapes)
• Early packages were little more than assembly languages for display device

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Problems with Early Graphics Platforms (1/3)
Geometric Scalability
• Integer coordinates mapped to display pixels affects apparent size of
image: large on low-res display & small on high-res display
• Application needs flexible internal coordinate representation
• floating point is essential
• float to fixed conversion required; actually a general mapping

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Display updates
• To perform operations on objects in scene, application must keep list of all
primitives and their attributes (along with application-specific data)
• Some updates are transitory “feedback animations,” only a display change
• Consider an interior-design layout application
• when user picks up an object and drags to new location, object follows cursor movement
• interim movements do not relate to data changes in application model, purely visual changes
• application model only updated when user drops object (releases mouse button)
• in immediate mode, application must re-specify entire scene each time cursor moves
• Alternatively, use a retained mode platform, which will store an internal
representation of all objects in scene
• called a display model to distinguish it from application model

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Interaction
• Consider a simple clock example:
• User clicks minute hand, location must be mapped to relevant
application object; called pick correlation
• Developer responsible for pick correlation (usually some kind of "point-
in-bounding box rectangle" test based on pick coordinates)
• find top-most object at clicked location
• may need to find entire composite object hierarchy from lowest-level primitive
to highest level composite
• e.g., triangle -> hand -> clock
• Solution: retained mode can do pick correlation, as it has a
representation of scene

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Modern Graphics Platforms (1/2)
• Device-independent floating point coordinate system
• packages convert “application-space" to "device-space" coordinates
• Specification of hierarchy
• support building scenes as hierarchy of objects, using transforms (scale, rotate,
translate) to place children into parents' coordinate systems
• support manipulating composites as coherent objects
• Smart Objects (Widgets, etc.)
• graphic objects have innate behaviors and interaction responses
• e.g., button that automatically highlights itself when cursor is over it

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Modern Graphics Platforms (2/2)

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Immediate Mode Vs Retained Mode
Immediate Mode (OpenGL, DirectX)
• Application model: stores both geometric information and non-geometric
information in Application Database.
• Platform keeps no record of primitives that compose scene

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Immediate Mode Vs Retained Mode
Retained Mode (WPF, SVG, most game engines)
• Application model in app and Display model in platform
• Display model contains information that defines geometry to be viewed
• Display model is a geometric subset of Application model (typically a scene graph)
• Simple drawing application does not need Application model (e.g., clock example)
• No right answer on which to use – context-dependent tradeoffs (see Chapter 16)

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OpenGL (1/3)
• Immediate-mode graphics API
• No display model, application must direct
OpenGL to draw primitives
• Implemented in C, also works in C++
• Bindings available for many other programming languages
• Cross-platform
• Also available on mobile (OpenGL ES*) and in the browser (WebGL)
• Different platforms provide ‘glue’ code for initializing OpenGL within the desktop
manager (e.g. GLX, WGL)
• Labs and projects use Qt library to abstract this away
* - ES: “Embedded Systems”

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OpenGL (2/3)
• Created by Silicon Graphics Inc. (SGI, http://sgi.com) in 1992, now managed by the non-
profit Khronos Group (http://khronos.org)
• Originally aimed to allow any OpenGL program to run on a variety of graphics hardware
devices
• Invented when “fixed-function” hardware was the norm
• Techniques were implemented in the hardware; OpenGL calls sent commands to the hardware to
activate / configure different features
• Now supports programmable hardware
• Modern graphics cards are miniature, highly parallel computers themselves, with many-core GPUs, on-
board RAM, etc.
• GPUs are a large collection of highly parallel high speed arithmetic units; several thousand cores!
• GPUs run simple programs (called “shaders”): take in vertices and other data and output a color value
for an individual pixel.
• GLSL, (O)GL Shader Language, is C-like language, control arithmetic pipelines
• Implement new features in shaders instead of waiting for hardware vendors to support them in h/w
• Your final project (typically a team project) will involve writing your choice of shaders

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OpenGL (3/3)
• Fixed-function API provides features that make it easier to prototype
• e.g., the OGL library implements much of the linear algebra needed to move
objects on the screen
• GL utility library (“GLU”) provides additional high-level utilities
• Programmable API implements most of the fixed-function API for
backwards compatibility, but uses shaders for implementation
• Only true for desktop; must use shaders exclusively to program with OpenGL
ES 2.0+ or WebGL
• We will use GLM (OpenGL Mathematics) to do our linear algebra instead of
using the Fixed-function API

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Shaders
• In future labs and your final project you will write your own shaders, but for
now we will provide shaders for you.
• Various types of input to shaders
• Attributes are provided per-vertex
• Uniforms are provided per-object; have the same value for a group of vertices
• OpenGL has many built in types including vectors and matrices
• To provide this input you must provide an identifier (“location”) of the
Attribute or Uniform
• glGetAttribLocation for attributes
• glGetUniformLocation for uniforms
• The first lab will go into more detail about how to use these functions

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Representing Shapes
• Objects in OpenGL are composed of triangles and quads. We can use
these to build arbitrary polygons, and approximate smooth shapes.
A complex polygon
made of triangle
primitives
A complex polygon
made of quad
primitives
An approximate
circle made of
triangle primitives

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Coordinate Systems (1/3)
• Cartesian coordinates in math, engineering
• typically modeled as floating point
• typically X increasing right, Y increasing up
• Display (physical) coordinates
• integer only
• typically X increasing right, Y increasing down
• 1 unit = 1 pixel
• But we want to be insulated from physical display coordinates
• OpenGL is the intermediary

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• OpenGL Coordinates
• Choose a convention
• For us: X increases right, Y increases up
• Units are based on the size of the window or screen
• Visible area stretches to fill window
• Units are percentage of window size, don’t correspond to physical units or pixels
• Define coordinate system using the projection matrix. Supply it to shader as a
uniform variable (the term projection matrix will become clear)
• Note: 3d glm functions still work in the special case of 2D – just use our defaults
glm::mat4 projection; // Our projection matrix is a 4x4 matrix
projection = glm::ortho(-1, // X coordinate of left edge
1, // X coordinate of right edge
-1, // Y coordinate of bottom edge
1, // Y coordinate of top edge
1, // Z coordinate of the “near” plane
-1); // Z coordinate of the “far” plane

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• Two choices on how to think
• Draw everything in OpenGL coordinate system
• This is inconvenient: instead choose your own abstract coordinate system to suit
your needs for each object, then specify all its primitives to OpenGL using these
coordinates. Specify a transformation to map the object coordinates to OpenGL
coordinates.
• When we say “transformation,” we usually mean a composition of scale, rotate
and translate transforms
Object
Coordinates Display
Application Coordinates

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Transformations (1/3)
• We will use GLM to do linear algebra for us and build the mapping matrix
• In addition to the projection matrix mentioned earlier, also keep track of a
model and a view matrix.
• More about the significance of these matrices in viewing lectures; for now
only modify the model matrix which is used to position objects
• For the following examples assume we are already keeping track of the
model matrix initialized like this:
• glm::mat4 model = glm::mat4(1.0); // Creates an identity matrix

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• Geometric Transformations in 2D (relative to a center for Scale and
Rotate!)
• Positive angles rotate counter-clockwise,
here about the origin (i.e., Z-axis)
Original Translate
model *= glm::translate(.1, .1, 0);
model *= glm::rotate(-45, glm::vec3(0, 0, 1));
Original Rotate
Scale
model *= glm::scale(2, 2, 1);
Original

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• Transformations can be composed (matrix composition) but are NOT
commutative, so proper order is vital

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Clock Demo (1/5)
• Illustrate the use of OpenGL by going through step-by-step how to
create a simple clock application. First a bunch of setup before drawing
• Start by specifying vertex data for a square:
• Create a Vertex Buffer Object (VBO). This is essentially an array of data
stored in the GPU; we’ll copy vertex data to a VBO
GLfloat vertexData[] = {
-.7, -.7, // Vertex 1
.7, -.7, // Vertex 2
.7, .7, // Vertex 3
-.7, .7, // Vertex 4
};
GLuint vboID; // Unsigned Integer
glGenBuffers(1, &vboID); // Generate 1 buffer (array); not initialized

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Clock Demo (2/5)
• Bind the VBO; this tells the GPU which (of potentially an arbitrary
number of buffers you’ve created) to use for subsequent calls
• Now we copy the vertex data to the GPU
glBindBuffer(GL_ARRAY_BUFFER, // Symbolic constant for data
vboID); // This is the vboID we generated on the
// previous slide.
glBufferData(GL_ARRAY_BUFFER,
sizeof(vertexData), // Tell OpenGL how much data we have
vertexData, // Pointer to the data
GL_STATIC_DRAW); // Tell OpenGL that our data will not
// be modified.

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Clock Demo (3/5)
• Now that the data is stored as a VBO, i.e. byte array, on the GPU, we need to tell
OpenGL what the data means. We do this with a Vertex Array Object (VAO).
• First generate and bind a VAO identifier
• Now we can define the VAO’s attributes
GLuint vaoID;
glGenVertexArrays(1, &vaoID); // Create 1 VAO
glBindVertexArray(vaoID); // Bind the VAO
glEnableVertexAttribArray(<vertexIdentifier>);// vertexIdentifier gotten from glGetAttribLocation
glVertexAttribPointer(<vertexIdentifier>,
2, // Elements per vertex (2 for (x, y) in 2D case)
GL_FLOAT, // Type of the data
GL_FALSE, // We don’t want to normalize the vertices
0, // Stride: Use 0 for a tightly packed array
(void*) 0); // Pointer: Byte offset of the first element in the array;
// cast to generic pointer type to match argument type

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Clock Demo (4/5)
• In OpenGL only one buffer bound at any time, now we can release it (this does not erase
the data)
• Now we are done with setup and finally ready to draw the square!
• In the render loop
• The result is a square centered in the window:
glBindBuffer(GL_ARRAY_BUFFER, 0); // Binding buffer 0 is how we unbind
glBindVertexArray(0); // ditto for the VertexArray
glBindVertexArray(vaoID); // Bind our VAO again
glDrawArrays(GL_QUADS, // The drawing mode (quads in this case)
0, // The index to start drawing from
4); // The number of vertices to draw
glBindVertexArray(0); // Unbind the VAO as good practice

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NXN✓
Winding Order
• Order is important: vertices must be specified in counter-clockwise order
relative to the viewer. Otherwise nothing shows up!
• Winding order determines the direction of the normal vector used in the “lighting
calculation”; if the normal is pointing the wrong way, we won’t see anything
• Counter-clockwise winding consistent with the “right-hand rule”
-.7, -.7,
.7, -.7,
.7, .7,
-.7, .7, };
-.7, -.7,
-.7, .7,
.7, .7,
.7, -.7, };

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Clock Demo (5/5)
• We’ll draw a simplified hour hand using a quad rotated around the origin.
One could do the same thing to draw minute and second hands:
float hourAngle = -45; // Rotate 45 degrees clockwise
float width = .01, height = .4;
// Rotate around the Z axis
model *= glm::rotate(hourAngle, glm::vec3(0, 0, 1));
GLfloat hourVertexData[] = {
-width, 0,
width, 0,
width, height,
-width, height };
// Set up VBOs and VAOs as before

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Outline of the Clock Example
• See /course/cs123/src/clock_demo for runnable demo and source
code

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Animation (1/3)
• Rapidly displaying sequence of images to create an illusion of
movement
• Flipbook (http://www.youtube.com/watch?v=AslYxmU8xlc)
• Keyframe animation: spec keyframes, computer interpolates (e.g., ball
bouncing)
Keyframe AnimationFlipbook

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Animation (2/3)
• Idea: Move the seconds hand incrementally every time we render
• Given the number of seconds elapsed, how many degrees should we
rotate the seconds hand?
• need to convert from seconds to degrees
• Idea: Use rotations around the clock as a common conversion factor
• Seconds per revolution: 60
• Degrees per revolution: 360
• Thus,

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Animation (3/3)
Clock lablet:
Run /course/cs123/bin/cs123_clock_demo
Source code: /course/cs123/src/clock_demo
float secondsElapsed = ...; // num seconds since last render
const float SECONDS_PER_REVOLUTION = 60;
const float DEGREES_PER_REVOLUTION = 360;
secondsAngle += -1 // Turn clockwise
* secondsElapsed // Δt
* DEGREES_PER_REVOLUTION // Turn 360 degrees ...
/ SECONDS_PER_REVOLUTION; // ... every 60 seconds

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OpenGL 2D Lab
• We will have a 2D lab that will be held this week: Pong!
• Generate graphics and UI for the classic game using OpenGL

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Book Sections
• Preface, Intro as useful background
• Chapter 2 – while written in terms of MSFT’s WPF, a retained-mode
library, the concepts carry over to OGL. Useful to know about
HTML/XML style syntax, given its prominence, but don’t worry about
the syntactic details

2D graphics

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