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CS148: Introduction to Computer Graphics and Imaging

Scanline Rendering

Electric Sheep screensaver by Scott DravesImage created collectively by users on the internet

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Human Eye

Light comes from light sources, is absorbed and reflected off of objects, and goes through the pupil of the eye.

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Without the pupil light scatters everywhere and does not make a coherent image

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With a pinhole model of the pupil light makes a coherent image inside the eye

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Human Retina: Rods and conesRetina contains rods and cones Rods are responsible for light intensity Cones are responsible for color vision

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Three Types of Cones

From http://webvision.med.utah.edu/imageswv/fovmoswv.jpeg

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Rods Capture Intensities

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Color Matching Experiment

Adjust brightness of three primaries

Lasers: R = 700 nm, G = 546 nm, B = 435 nm

until a human mistakenly thinks it matches another color C = x nm

Result: all colors can be matched with three colors

Therefore: humans have trichromatic color vision

C = R “+” G “+” B

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Trichromatic Theory• Since the human eye works in this fashion, we work this way with images, printers, and displays.• Image formats store values in the R, G, and B channels. • The values are between 0 and 255.• The relative values give the color, and the overall values give the intensity. • This is similar to the cones of the human eye.

• The monitor can be used to increase or decrease the image intensities (brightness/darkness).• This is similar to the rods of the human eye.

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Cameras

•A camera works similarly to the eye.

￭ Light passes through the lens, bends to come to a point of focus, and makes an upside-down image on the film.

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Pinhole Camera

Linear perspective with viewpoint at pinhole

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Laws of Pinhole Cameras

Common assumptionsLight leaving an object travels in straight linesThese lines converge to a point (e.g. pinhole) Infinite depth of field which means everything is in focus

Perspective image is formed by the intersection of these lines with an image plane

More distant objects subtend smaller visual angles and appear smaller

Objects in front occlude the objects behind them

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OpenGL Camera

OpenGL uses a pinhole camera.

In OpenGL the image plane is in front of the focal point which means the image is right side up.

The frustum is the volume of our view (shown in blue below).

The image plane is the plane of the frustum nearest to the camera.

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Specifying the Camera in OpenGL

void gluLookAt(eye.x, eye.y, eye.z, at.x, at.y, at.z, up.x, up.y, up.z);- gluLookAt creates a camera from an eye point, a reference point indicating the center of the scene, and an up vector.

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Specifying the Frustum in OpenGL

void gluPerspective(fovy, aspect, near, far);

-gluPerspective specifies a viewing frustum for the camera into the world coordinate system. -fovy specifies the field of view angle.-aspect specifies the aspect ratio of the associated image plane.-near/far specify the distance from the camera to the new/far clipping plane.

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Drawing a Triangle in front of your Camera

glColor3f(1.f,0.f,0.f);glBegin(GL_TRIANGLES);glVertex3f(0.f,0.f,0.f);glVertex3f(1.f,0.f,0.f);glVertex3f(.5f,.86f,0.f);glEnd();

void glBegin(Glenum mode);•glBegin delimits the vertices of a primitive.•mode specifies the primitive that will be created from vertices presented between glBegin and glEnd.

void glVertex(x,y,z);•glVertex specifies a vertex to form the primitive.

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Fundamental Primitive: Triangles

• Why triangles?

• Lowest common denominator

￭ Easily break convex polygons into triangles

￭ Optimize the implementation of one primitive

￭ Triangles have unique properties￭ Guaranteed to be planar

￭ Guaranteed to have a well-defined

interior

￭ Well-defined method (barycentric interpolation) for interpolating values in the interior

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Triangle Meshes

Stanford Bunny69,451 triangles David, Digital Michelangelo Project

28,184,526 vertices, 56,230,343 triangles

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OpenGL Drawing Primitives

Geometric Shapes

Bitmaps Images

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Graphics Rendering Pipeline

Per-vertex ops

Rasterization

Per-fragment ops

Texturing

Vertices

Shadedfragments

Fragments

Transformedvertices

Frame buffer ops

Display

Commands Processor

pixels in the framebuffer

triangles, lines, pointsimages

Primitive assembly

Primitives

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Command queue

Command interpretation

Unpack and perform format conversion

Maintain graphics state

Command Processor

glBegin(GL_TRIANGLE_STRIP);glColor3f(.0f, 1.f, .0f);glVertex3f( .0f, .0f, .0f ); glVertex3f( 0.f, 1.f, .0f ); glColor3f(1.f, .0f, .0f);glVertex3f( 1.f, .0f, .0f ); glVertex3f( 1.f, 1.f, .0f ); glEnd();

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Vertex transformation

Normal transformation

Texture coordinate generation

Texture coordinate transformation

Lighting (light sources and surface reflection)

Projection

Per-vertex Operations

World-space triangles

Screen-space shaded triangles

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Primitive Assembly

Combine transformed/shaded vertices into primitives

￭ 1 vert -> point

￭ 2 verts -> line

￭ 3 verts -> triangle

Clipping

Transform to window coordinates (viewport)

Determine orientation (CW/CCW)

Back-face cull

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Setup (per-triangle)

Sampling (triangle = {fragments})

Interpolation (interpolate colors and coordinates)

Rasterization

Triangles Fragments

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Textures are arrays indexed by floats (Sampler)

Texture address calculation

Texture bilinear interpolation and filtering

Texturing

Fragments Texture Fragments

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Per-fragment Operations

Combine texture sampler outputs

Per-fragment shading

Fragments Textured Fragments

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Operation

￭ Test window ownership

￭ Test scissor and stencil mask

￭ Test alpha

￭ Test depth

Blending or compositing

Frame buffer Operations

Textured Fragments Framebuffer Pixels

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Testing Depth using Z-Buffer

Initialize z-buffer to zmax

Interpolate z across the triangle

Draw fragment if closer

if(frag.Z<Z[frag.X][frag.Y]){

Z[frag.X][frag.Y]=frag.Z;

C[frag.X][frag.Y]=frag.C;

}

http://en.wikipedia.org/wiki/File:Z_buffer.svg

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Frame Buffering

Frame Buffer

￭ Store image in a buffer to separate refresh rate from drawing rate

Single-buffer

￭ Draw into display buffer directly

￭ May see picture being drawn

Double-buffer

￭ Display “front” buffer

￭ Draw into “back” buffer (can’t see drawing)

￭ Swap front and back (wait until vertical sync)

Triple buffer

￭ Avoid waiting for vertical sync

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Framebuffer

Example Framebuffer: 1440 x 900

All coordinates are integers; they refer to pixel locations in the framebuffer

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Window

Example Framebuffer: 1440 x 900

The window is the portion of the display usable by the application(under control of the “window system”)

All coordinates are integers; they refer to pixel locations in the framebuffer

Window(512 x 512)

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Viewport

Example Framebuffer: 1440 x 900

Viewport(256x256)

All coordinates are integers; they refer to pixel locations in the framebuffer

The viewport is the portion of the window that can be drawn in,no pixels will appearoutside the viewport

Window(512 x 512)

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Specifying the Viewport in OpenGL

void glViewport(x, y, w, h);

-glViewport specifies the location and the size of the viewport in the screen coordinate system. Here x, y, w, and h are all integers.-x and y specify the lower left corner of the viewport rectangle.-w and h specify the width and height of the viewport. w/h should agree with the aspect ratio you set in gluPerspective.

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Windows = Virtual Framebuffers

Like virtual memory enables us to share the physical memory,

virtual framebuffers allows us to share the physical framebuffer

Abstract properties

￭ Location and size on the screen

￭ Stacking order

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Window Coordinate Systems

Window(512 x 512)

Each window has a user coordinate systemA 2D coordinate system is specified by assigning coordinates to the edges of the windowleft need not be less than right ...

right = 1.0left = -1.0

bottom = -1.0

top = 1.0

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Exposure

Parts of the window that are not visible can become visible

￭ When opening

￭ When unhiding

￭ When brought to front

How do you update the visible parts of the window?

￭ Redraw entire window (or a part of it)

￭ Save the drawn window in a “backing store”, and copy onto screen when needed

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Display

Gamma correction

Analog to digital conversion

Display

LightFramebuffer Pixels

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glBegin(GL_TRIANGLES) glVertex3fv(v1); glVertex3fv(v2); glVertex3fv(v3);glEnd()

-90

-90

OpenGL GPU

CPU

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Graphics processing unit

A graphics processing unit (GPU), also occasionally called visual processing unit (VPU), is a specialized electronic circuit designed to rapidly manipulate and alter memory to accelerate the building of images in a frame buffer intended for output to a display.

NVIDIA’s GeForce GTX 690

VisionTek Radeon 7970

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What’s in a GPU?

ShaderCore

Tex

Rasterizer

Framebuffer Ops

Work Distributor

Primitive AssemblyShaderCore

ShaderCore

ShaderCore

ShaderCore

ShaderCore

ShaderCore

ShaderCore

Tex

Tex

Tex

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Modern PC

3.0 Ghz Intel Core2 Duo

NVIDIA GeForce8800 GTX (575 MHz)

(16 cores)

512MBvideo

Memory(GDDR3)

4MB L2 Cache

2GB mainmemory(DDR2)

Core 1 Core 2

NVIDIA 8800GTX

PCIe Bus (v1 = 4 GB/sec)

84 GB/sec

System board (Intel D975)

12.8 GB/sec

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Game Machines – Xbox 360

3.2 Ghz PowerPC CPU

Core 1 Core 2 Core 3

500 Mhz ATI GPU 512 MBmemory

L2 Cache

IOChip

48 3DCores Video

out

Framebuffer

Display (TV)

controllers/ethernet/audio/DVD/etc.

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Game Machines – PS3

3.2 Ghz Cell

PPCCore

SPU0

550 Mhz NVIDIA RSX GPU 256 MBvideo

Memory(GDDR3)

L2 Cache

IO Chip

Multiple 3Dcores Video

out

Display (TV)

controllers/ethernet/audio/DVD/etc.

SPU1 SPU2 SPU3

SPU4 SPU5 SPU6 SPU7 256 MBMemory(XDR)

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Hybrid CPU-GPUs

Intel Sandybridge

Apple A5

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NVIDIA GPU Performance

Year Product Triangle/s Fragment/s

1998 Riva ZX 3m 100m

1999 Riva TNT2 9m 350m

2000 GeForce2 GTS 25m 664m

2001 GeForce3 30m 800m

2002 GeForce Ti 4600 60m 1200m

2003 GeForce FX 167m 2000m

2004 GeForce 6800 Ultra 170m 6800m

2005 GeForce 7800 GTX 940m 10300m

2006 GeForce 7900 GTX 1400m 15600m

2007 GeForce 8800 GTX 1800m 36800m

2008 GeForce GTX 280 48160m

2010 GeForce GTX 480 42000m

2011 GeForce GTX 580 49400m