Graphics System

CSC 2141Introduction to Computer Graphics

A Graphics System

Separate hardware support: relieves

CPU from graphics related tasks

Raster Graphics

Image produced as a two-dimensional array (the raster) of picture elements (pixels) in the frame buffer Pixel: small area/location in the image

Frame Buffer

Two-dimensional array of pixel values Color and other information (e.g. depth in 3D) per pixel

Not a device, a chunk of RAM memory In early systems, frame buffer was part of system memory Today, virtually all graphics systems have GPUs (graphics

processing units) which may include the frame buffer.

Usually is implemented with special types of memory chips that enable fast redisplay of contents

A hardware device called video controller reads the frame buffer and produces the image on display

Frame Buffer

Depth: number of bits used to represent each pixel How many colors can be represented?

1-bit: 2 colors (black and white) 8-bit: 256 colors (gray scale) 24-bit: (True Color or RGB-color)

8-bits per red, green and blue components R,G and B combined in varying proportions If all full intensity (255, 255, 255): you get white If all are off (0,0,0): you get black

Alternative: color map 8-bits per pixel, index to a 256-element array, each array entry stores an RGB color Called indexed color, or pseudo-color

Frame Buffer

Resolution: number of pixels in the frame buffer Determines the level of detail in the image

Rasterization/Scan conversion

The processor takes specifications of graphical primitives (lines, circles, polygons)

Converts them to pixel assignments in the frame buffer

Output Devices

Standard graphics display: raster display Two main types:

1. CRT (cathode-ray tube) display2. Flat-screen technologies

CRT

Consists of a screen with phosphor coating Each pixel is illuminated for a short time (few milliseconds)

when struck by an electron beam Level of intensity can be varied to achieve gray values Display has to be continuously refreshed to avoid flickering.

Refresh rate Older systems: 60Hz (60 times per second) Modern displays: 85 Hz

CRT (interlaced, noninterlaced)

Two ways of displaying pixels Noninterlaced: row by row (scan line by scan line)

at the refresh rate Interlaced: odd rows and even rows refreshed alternately.

Smaller refresh rate is fine. e.g. 30 times a second seems like 60 times a second.

Color CRT

Three different colored phosphors arranged in small groups Red, Green, Blue

Three electron beams

Flat-screen Technologies

LCD (liquid crystal display) LED (light-emitting diodes) Plasma panels

Image Synthesis

CSC 2141Introduction to Computer Graphics

Image Synthesis

In computer graphics, we form images using a process analogous to how images are formed by optical imaging systems ( Camera, Human visual system)

We will construct a model of the image formation process in optical systems that we can use to understand CG imaging systems

Basic model of viewing A viewer holding up a synthetic camera …to a model of the scene we wish to render

Major elements of our model: Objects and Viewer

Objects: description of the 3D scene, including Positions, geometric structure, color, surface properties

(texture, shininess, transparency) of objects exist independent of the viewer

Viewer: description of the location of the viewer and properties of the synthetic camera (direction, field of view,

etc.)

Geometric models

How to describe our 3D scene in a manner that can be processed by graphics programs?

Mathematically based objects are easy to model Line : two vertices Polygon: an ordered set of vertices Circle: center and a point on the circle Cube, cylinder, sphere…

..but natural objects (hair, water, clouds) are hard

Geometric models

Simplest: Polyhedral models Solid objects are described by

their 2D boundaries Boundaries will be constructed

from flat elements: points, line segments, and planar polygonal faces

Faces: basic rendering element: In OpenGL, just a list of vertices

Advanced models: curved surfaces: Bezier, NURBs, subdivision surfaces, fractals, etc.

69,451 triangles

Light and light sources

Locations of light sources determine shading of the rendered objects: which are dark

which are light? And, the location of the shadows

We assume point light sources (like sun): emit energy from a single location in all directions

Light is a form of electromagnetic energy Over the visible spectrum Different wavelengths are seen as different colors

To simplify: geometric optics model light sources as emitters of energy, and have a fixed

intensity Light travels in straight lines (light ray)

Color of light

We will simply model the color of light as some combination of red, green and blue color components

What we see in an object is not its color, but the color of the light that is reflected from that object toward our eye. If object reflects only red light but light sources emit green

light, then we will see the object as ?

Color of light

We will simply model the color of light as some combination of red, green and blue color components

What we see in an object is not its color, but the color of the light that is reflected from that object toward our eye. If object reflects only red light but light sources emit green

light, then we will see the object as black!

Light propagation in the scene

Light is emitted from light sources

Strikes and illuminates objects in the scene

Interacts with object surfaces depending on surface characteristics Being absorbed all or partially

by some objects Being reflected from or

refracted through surfaces Some light rays eventually

enter our eyes Some leave the scene—no

contribution to what we see

Lighting Models

Global illumination models Simulate this complex interaction of light and objects Computationally expensive!

Local illumination models Adapted by most commercial interactive graphics systems Assume that the light rays emitted from an object come

directly from light sources

Camera model: The pin-hole camera Simple example of an optical imaging system

Small hole at the center of one side: only single ray of light can enter

“center of projection”

Film plane, imaging plane

The pinhole camera: side view

Pointing along positive z-axis The center of projection (COP) is at the origin (0,0,0) Film plane located at distance d from the pinhole

Film plane is at z = -d is projection of

dz

yy p /

dz

xxp /

-d

),,( dyx pp ),,( zyx

Field of view (also called angle of view) Assume height of the box is h A point will be visible on the image if it lies within a cone centered

at the origin with an angle This angle is called field of view (for y). A similar formula holds for

x.

d

h

2tan2 1

Observation

The image is inverted in the projection process. Why?

Observation

The image is inverted in the projection process. Why?

Because the film is behind the pinhole (center of projection)

-

Synthetic camera model

We will move the image plane in front of the camera The image of the point is located where the projector passes

through the projection (image) plane (all projectors are rays emanating from COP)

Projection plane

projector

center of projection

Clipping

We must consider the limited size of the image Recall: field of view in pinhole camera Not all objects can be imaged onto the film

In our synthetic camera: place a clipping window through which the viewer sees the

world given the location of the viewer/camera, the location and

orientation of the projection plane, and the size of the clipping rectangle, we can determine which objects will appear in the image

World coordinate system v.s. Camera coordinate system

Observe that the projection transformation was based on the assumption that objects are represented according to the camera-centered coordinate system.

Camera moves around! Necessary to apply a transformation to map

coordinates of objects from world coordinate system to camera coordinate system

Will see details later

Camera specifications

We need to inform the graphics system of: Camera location: location of the center of projection (COP) Camera direction: what direction is the camera pointed in. Camera orientation: what direction is “up” in the final image Focal length: the distance from the COP to the projection

plane (image plane) Image size: clipping window size and location

Variety of ways to specify these OpenGL asks for field of view and image aspect ratio (ratio

of its width and height) rather than focal length and image size

Application Programmer’s Interface (API) Interface between an application program and the

graphics system can be specified through a set of functions in the graphics library

Programmer only sees the API, and is shielded from details of the both hardware and software implementations of the graphics library

The functions that are available through the API should match our image formation model

Drivers

OpenGL is an API

Based on the synthetic-camera model We need functions to specify (and, we have them)

Objects Viewer/camera Light sources Material properties of objects

Object Specification

Most APIs support a limited set of primitives including Points (0D object) Line segments (1D objects) Polygons (2D objects) Some curves and surfaces

Quadrics Parametric polynomials

All are defined through locations in space or vertices

Example (OpenGL)

glBegin(GL_POLYGON)glVertex3f(0.0, 0.0, 0.0);glVertex3f(0.0, 1.0, 0.0);glVertex3f(0.0, 0.0, 1.0);

glEnd( );

type of object

location of vertex

end of object definition

How is an API implemented?

Physical Approach?

Ray tracing: follow rays of light from center of projection until they either are absorbed by objects or go off to infinity

Can handle global effects Multiple reflections Translucent objects

Slow

Practical Approach

Process objects one at a time in the order they are generated by the application Can consider only local illumination

Pipeline architecture All vertices go through the pipeline

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels

Vertex Processing

Carry out transformations and compute a color for each vertex

Each vertex is processed independently

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels

Transformations

Much of the work in the pipeline is in converting object representations from one coordinate system to another Object coordinates Camera (eye) coordinates Screen coordinates

Every change of coordinates is equivalent to a matrix transformation

Eventually, the geometry is transformed by a perspective projection---also can be represented by matrices

Retain 3D information as long as possible in the pipeline Thus, more general projections than we just saw

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels

Perspective projection

Y

Z

X

View Plane

Center of Projection(0.7, 0.5, -4.0)

Projectors

Clipping

The synthetic camera can only see part of the world Clipping volume

Objects that are not within this volume are clipped out of the scene

Before clipping, sets of vertices are asssembled into primitives (such as line segments or polygons)

Output of this step: set of primitives whose projections can appear in the image

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels

Rasterization

Each primitive is rasterized Generate pixels (that finally will be used to update the frame

buffer) representing this primitive

Output of this step: set of fragments for each primitive Fragment: potential pixel that carries color, location and depth

information with it

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels

Fragment processor

Updates pixels in the frame buffer using the fragments Some fragments may occlude others (use depth

information here)

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels

Fragment processor

Updates pixels in the frame buffer using the fragments

Color of a fragment may be changed by applying textures, etc.

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels

Fragment processor

Updates pixels in the frame buffer using the fragments

Translucent effects may also be generated by blending colors of fragments.

VerticesVertex

Processor

Clipper and primitive

assembler

Rasterizer

Fragment

Processor

Pixels