Lecture 1: Introduction to Computer Graphics

Transcription

1 Lecture 1: Introduction to Computer Graphics Bernhard Jung TU-BAF, Summer 26!"#$%&'( )*+!,,%,-./!%1,2 3,4%1 /+--,1,,(6( 3$$78-3%898 $! $/(7-3!$:$;%!/</.$%%3$/<8/= 7>%/7>%!/!/?%!/= '?$*9 %;%9/$/8 &' $! $ 8$ %/ ' &(?( $ $A8B! $C?$%<( 98 '((8%#8&)< '( 1

2 . Main text books Alan Watt. 3D Computer Graphics. Addison-Wesley. 2. Akenine-Möller & Haines. Real Time Rendering. 2nd Ed. A K Peters. 22. Further reading Slater, Steed, Chysanthou. Computer Graphics and Virtual Environments. Addision Wesley, 21. Foley, van Dam, Feiner & Hughes. Computer Graphics. Addision Wesley Watt, A. & Policarpo, F. The Computer Image. Addison Wesley )';D$ What is interactive Computer Graphics (CG)? History of CG & new forms of computing Sample-based versus geometry-based CG Rendering Pipeline Applications areas of CG 2

3 # E "Boeing Man" The term computer graphics credited to William Fetter ( ), 196 name for new design methods he was pursuing at Boeing Fetter created widely reproduced images on a pen plotter exploring cockpit design, using a 3D model of a human body Perhaps the best way to define computer graphics is to find out what it is not. It is not a machine. It is not a computer, nor a group of computer programs. It is not the know-how of a graphic designer, a programmer, a writer, a motion picture specialist, or a reproduction specialist. Computer graphics is all these a consciously managed and documented technology directed toward communicating information accurately and descriptively. Computer Graphics, by William A. Fetter, 1966 # E Computer graphics (CG) is the field of visual computing, where one utilizes computers both to generate visual images synthetically and to integrate or alter visual and spatial information sampled from the real world. Wikipedia, accessed 3/26 geometry-based graphics mainly discussed in course, in particular 3D computer graphics sample-based graphics 3

4 # E Modeling = representing 3D objects Rendering = constructing 2D images from 3D models Animation = simulating changes over time ;' character displays (196-now) text plus alphamosaic pseudo-graphics vector displays ( s) line drawings and stroke text 2D bitmap raster displays for PCs and workstations (1972 at Xerox PARC - now) windows, icons, legible text and flat earth graphics Note: late 6 s saw first use of raster graphics, especially for flight simulators 3D graphics workstations (1984 at SGI now) real-time, pseudo-realistic images of 3D scenes $$;( ((F';;$($ 4

5 "'9,221%' Virtual Reality: fully immersive VR (via Head-mounted Displays, Cave) CAVE HMD "'9,221%' semi-immersive VR Barco, Immersadesk GMD s Responsive workbench Fishtank VR on a monitor Elumens VisionStation

6 "'9,221%11G augmented VR (via video see-through optics) Video or optics superimposes computer-generated data on real world H8 $; $H8 6

7 7$; *; New game platforms and set-top boxes use high-end processors (128-bit architectures, great graphics capabilities) Nintendo GameCube (powered by ATI) Microsoft XBox (powered by nvidia) Sony Playstation 2, PSP (PS3 to be powered by nvidia) Top graphics cards (spring 26) ATI Radeon X19 XTX nvidia GeForce 78 GTX (announced: 79 GTX) Significant advances in commodity graphics chips every 6 months, outrunning CPU chip advances Intel Pentium Pentium Extreme Edition 9 (Cedar Mill) has 188 million transistors Athlon 64 X2 (Toledo) million transistors GeForce 78 GTX chip has 32 millions (79 GTX has "only" 278 million) Radeon X19 XTX has 384 millions GPUs are now arguably more powerful than CPUs and programmable (vertex and pixel shaders) $3 7' Sample-based graphics: discrete samples are used to describe visual information pixels can be created by digitizing images, using a sample-based painting program, etc. often some aspect of the physical world is sampled for visualization, e.g., temperature across the Europe example programs: Adobe Photoshop, Macromedia Fireworks, Microsoft Paint, The GIMP (open source, on UNIX / Linux and Windows) Geometry-based graphics: a geometrical model is created, along with various attributes, and is then sampled for visualization (this process is called rendering) often some aspect of the physical world is visually simulated, or synthesized example 2D programs: Adobe Illustrator, Macromedia Freehand, Corel CorelDRAW!, Microsoft PhotoDraw example 3D programs: Alias Wavefront s Maya, Autodesk s AutoCAD and 3D Studio Max, Curious Labs'Poser, Blender 7

8 <$%? Images are made up of a grid of discrete pixels for 2D picture elements CRT beam illumination pattern Mathematical pixel grid LCD display Pixels are point locations with associated sample values, usually of light intensities/colors, transparency, and other control information. <$%? <$@ The 3D scene A color value is measured at every grid point and used to color a corresponding grid square = white = gray 1 = black Note: this poor sampling and image reconstruction method creates a blocky image 8

9 <$%? Once image is defined in terms of colors at (x, y) locations on grid, can change image easily by altering location or color values E.g., if we reverse our mapping above and make 1 = white and = black, the image would look like this: Pixel information from one image can be copied and pasted into another, replacing or combining with previously stored pixels <$%? 3 WYSIAYG (What You See Is All You Get): There is no additional information no depth information can t examine scene from a different point of view at most can play with the individual pixels or groups of pixels to change colors, enhance contrast, find edges, etc. But recently, strong interest in image-based rendering to fake 3D scenes and arbitrary camera positions. New images are constructed from old ones by interpolation, composition, warping and other operations an early example is QuickTime VR: 9

10 There are many things one can do with sampled images: uses of computer imaging range from entertainment to medicine, art, design and military applications. The news: digitally enhanced images are more and more common. Usually just sharpening, color balancing, but sometimes a lot more. To Photoshop something in ; TV Guide s Oprah cover Time Magazine s O.J. Simpson cover BR-Online's report on Angela Merkel's visit to Bayreuth festival (July 2) ;%? Geometry-based graphics applications store mathematical descriptions, or models, of geometric elements (lines, polygons, polyhedrons ) and their associated attributes (e.g., color, material properties). Images are created as pixel arrays (via sampling of the geometry) for viewing, but are not stored as part of the model. Images of many different views can be generated from the same model. Increasingly rendering combines geometric and sample-based graphics, both as a performance hack and to increase quality of the final product texture maps, image-based lighting Through 3D computer graphics, for the first time in human history we have abstract, easily changeable 3D forms. This has revolutionized the working process of many fields science, engineering, industrial design, architecture, commerce, entertainment, etc. 1

11 :$ Transform 3D world into (normalized) camera coordinates Clipping & visible surface determination Compute set of surfaces visible from the viewpoint Rasterization (scan conversion) illumination and shading (local, direct illumination-models): Render depth, lighting effects, material properties to improve 3D perception. Data in local Object Coordinates Data in 3D World Coordinates Data in 3D Camera Coordinates Entire World in Normalized Device Coordinates (NDC) Viewable World in Normalized Device Coordinates (NDC) Transform Object to World Coordinates Transform World into Camera Coordinates Apply Normalizing Transformation Clip Against View Volume Visible Surface Determination Shading and Rasterization :$ $; 3D is just like taking a photograph (lots of photographs!) viewing volume camera tripod model 11

12 :$% <; Camera/Viewpoint Location Camera/Viewpoint Direction Camera/Viewpoint Orientation Camera/Viewpoint Lens (View Volume) Width/Height of Lens Front/Back Clipping Planes Parallel or Perspective Projections Parallel is special case of Perspective 3 deg frustum 4 deg frustum :$% <; :J Perspective Projection Parallel Projection view volume view volume 12

13 :$% <; $'$ Distort world until viewing volume in world fits into a parallel canonical view volume simplifies clipping / hidden surface removal / shading accomplished by the multiplication with a 4 x 4 transformation matrix Z (xmax, ymax, -far) Z Y Z Y Y (xmin,ymin,-near) X X X (1,1,) :$% <; $'$ 3D -> 2D projection (into projection plane ) is now easy: Just ignore the z value! In reality, we retain the z-value for hidden-surface removal and shading effects. 13

14 :$ $ Discard polygons outside view volumes Clip polygons against view volume Front Clipping Plane View Volume Back Clipping Plane DOP :$ $<3 visible object-precision methods invisible per polygon; world / camera coordinates; floating point values e.g. backface culling discard polygons facing away from viewer e.g. occlusion culling discard polygons occluded by other polygons image-precision methods per pixel; screen coordinates; integer values e.g. z-buffer 14

15 1 :$% $<3 +%? requires two buffers with pixel information frame buffer, with pixel color z-buffer, with pixel depth information polygons are rendered in arbitrary order all polygons are rendered use Z-buffer to decide which polygon gets pixel when polygons overlap no pre-sorting of polygons necessary very fast, implemented in most graphics cards but cannot do anti-aliasing requires knowing all polygons involved in a given pixel related A-buffer algorithm used for anti-aliasing = + = :$ $$; simple sequence of line renderings line rendering: Midpoint (Bresenham) Algorithm

16 :$. Assume line starts and ends at raster points (i.e. integer values) y e slope m = x / y with -1 m 1 other slopes: similar Basic algorithm y = y s for x = x s, x s+1,, x e draw pixel at (x, round(y) ) y = y + m Drawbacks of basic algorithm needs floating point arithmetic (slow) rounding operation needs additional time y y s x s x x y x e :$. The classic midpoint (Bresenham) algorithm draws a line using integer arithmetic only Key idea: For slope m, m 1, need only to decide if next pixel is E (east) or NE (northeast) or: is line above or below midpoint between E and NE? Find more information: google "midpoint bresenham" any computer graphics textbook Q NE M i=(x Mi,y Mi) void MidpointLine(int x, int y, int x1, int y1, int value) { int dx = x1 - x; int dy = y1 - y; int d = 2 * dy - dx; int incre = 2 * dy; int incrne = 2 * (dy - dx); int x = x; int y = y; writepixel(x, y, value); while (x < x1) { if (d <= ) { //East Case d = d + incre; } else { // Northeast Case d = d + incrne; y++; } x++; writepixel(x, y, value); } /* while */ } /* MidpointLine */ E 16

17 :$ %. $ Rasterization problems Representing a line with discrete pixel values is sampling a continuous function Jaggies are a manifestation of sampling error and loss of information Antialiasing idea: sample a rectangle (1 pixel wide) rather than a mathematical line pixel intensity dependent on overlap with unit rectangle: how much overlap where overlap occurs interactive demo midpoint algorithm midpoint algorithm + antialiasing :$ $ more antialiasing examples with jaggies antialiased 17

18 :$ 9$:$; Inside test: A point P is inside a polygon if and only if a scanline intersects the polygon edges an odd number of times moving from P in either direction. 1 P Does the vertex count as two points? Or should it count as one point? :$B 9$:$;!>%!7 When crossing a vertex, if the vertex is a local maximum or minimum then count it twice, else count it once. or or Count twice Count once 18

19 :$B 9$:$; 9$:$; Fill the polygon 1 scanline at a time Determine which pixels on each scanline are inside the polygon and set those pixels to the appropriate value. Key idea: Don t check each pixel for inside-ness. Instead, look only for those pixels at which changes occur. :$B 9$:$; <%.$ For each scan-line: 1. Find the intersections of the scan line with all edges of the polygon. 2. Sort the intersections by increasing x- coordinate. 3. Fill in all pixels between pairs of intersections. For scan-line number 7 the sorted list of x-coordinates is (1,3,7,9) Therefore fill pixels with x- coordinates 1-3 and

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