Rendering Pipeline and Graphics Hardware Aaron Bloomfield CS 445: Introduction to Graphics Fall 2006

2 Overview  Framebuffers Rendering Pipeline Transformations Lighting Clipping Modeling Camera Visible Surface Determination History How is the rasterized scene kept in memory? How is the rasterized scene kept in memory?

3 Framebuffers So far we’ve talked about the physical display device How does the interface between the device and the computer’s notion of an image look? Framebuffer: A memory array in which the computer stores an image On most computers, separate memory bank from main memory (why?) Many different variations, motivated by cost of memory

4 Framebuffers: True-Color A true-color (aka 24-bit or 32-bit) framebuffer stores one byte each for red, green, and blue Each pixel can thus be one of 2 24 colors Pay attention to Endian-ness How can 24-bit and 32-bit mean the same thing here?

5 Framebuffers: Indexed-Color An indexed-color (8-bit or PseudoColor) framebuffer stores one byte per pixel (also: GIF image format) This byte indexes into a color map: How many colors can a pixel be? Still common on low-end displays (cell phones, PDAs, GameBoys) Cute trick: color-map animation

6 Framebuffers: Hi-Color Hi-Color was a popular PC SVGA standard Packs pixels into 16 bits: 5 Red, 6 Green, 5 Blue (why would green get more?) Sometimes just 5,5,5 Each pixel can be one of 2 16 colors Hi-color images can exhibit worse quantization artifacts than a well-mapped 8-bit image

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8 Overview Framebuffers  Rendering Pipeline Transformations Lighting Clipping Modeling Camera Visible Surface Determination History How does the graphics hardware process the graphical display? How does the graphics hardware process the graphical display?

9 The Rendering Pipeline: A Tour Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters Rendering Pipeline FramebufferDisplay

10 The Parts You Know Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters Rendering Pipeline FramebufferDisplay

11 The Rendering Pipeline Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters Rendering Pipeline FramebufferDisplay

12 We’ll talk about this soon… 2-D Rendering: Rasterization Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters Rendering Pipeline FramebufferDisplay

13 The Rendering Pipeline: 3-D Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters Rendering Pipeline FramebufferDisplay

14 The Rendering Pipeline: 3-D Modeling Transforms Scene graph Object geometry Lighting Calculations Viewing Transform Clipping Projection Transform Result: All vertices of scene in shared 3-D “world” coordinate system All vertices of scene in shared 3-D “world” coordinate system Vertices shaded according to lighting model Vertices shaded according to lighting model Scene vertices in 3-D “view” or “camera” coordinate system Scene vertices in 3-D “view” or “camera” coordinate system Exactly those vertices & portions of polygons in view frustum Exactly those vertices & portions of polygons in view frustum 2-D screen coordinates of clipped vertices 2-D screen coordinates of clipped vertices

15 The Rendering Pipeline: 3-D Scene graph Object geometry Lighting Calculations Clipping Result: All vertices of scene in shared 3-D “world” coordinate system All vertices of scene in shared 3-D “world” coordinate system Vertices shaded according to lighting model Vertices shaded according to lighting model Scene vertices in 3-D “view” or “camera” coordinate system Scene vertices in 3-D “view” or “camera” coordinate system Exactly those vertices & portions of polygons in view frustum Exactly those vertices & portions of polygons in view frustum 2-D screen coordinates of clipped vertices 2-D screen coordinates of clipped vertices Modeling Transforms Viewing Transform Projection Transform

16 Overview Framebuffers Rendering Pipeline  Transformations Lighting Clipping Modeling Camera Visible Surface Determination History How do you transform the objects so they can be displayed? How do you transform the objects so they can be displayed?

17 Rendering: Transformations So far, discussion has been in screen space But model is stored in model space (a.k.a. object space or world space) Three sets of geometric transformations: Modeling transforms Viewing transforms Projection transforms

18 Rendering: Transformations Modeling transforms Size, place, scale, and rotate objects parts of the model w.r.t. each other Object coordinates  world coordinates The scene now has it’s origin at (0,0,0) Z X Y X Z Y

19 Rendering: Transformations Viewing transform Rotate & translate the world to lie directly in front of the camera Typically place camera at origin Typically looking down -Z axis World coordinates  view coordinates The scene now has it’s origin at the camera

20 Rendering: Transformations Projection transform Apply perspective foreshortening Distant = small: the pinhole camera model View coordinates  screen coordinates The scene is now in 2 dimensions

21 Rendering: Transformations All these transformations involve shifting coordinate systems (i.e., basis sets) Matrices do that Represent coordinates as vectors, transforms as matrices Multiply matrices = concatenate transforms!                     Y X Y X   cossin cos

22 Rendering: Transformations Homogeneous coordinates: represent coordinates in 3 dimensions with a 4-vector Denoted [x, y, z, w] T Note that w = 1 in model coordinates To get 3-D coordinates, divide by w: [x’, y’, z’] T = [x/w, y/w, z/w] T Transformations are 4x4 matrices Why? To handle translation and projection We’ll see this a bit more later in the semester

23 Overview Framebuffers Rendering Pipeline Transformations  Lighting Clipping Modeling Camera Visible Surface Determination History How do we compute the radiance for each sample ray? How do we compute the radiance for each sample ray?

24 The Rendering Pipeline: 3-D Modeling Transforms Scene graph Object geometry Lighting Calculations Viewing Transform Clipping Projection Transform Result: All vertices of scene in shared 3-D “world” coordinate system All vertices of scene in shared 3-D “world” coordinate system Vertices shaded according to lighting model Vertices shaded according to lighting model Scene vertices in 3-D “view” or “camera” coordinate system Scene vertices in 3-D “view” or “camera” coordinate system Exactly those vertices & portions of polygons in view frustum Exactly those vertices & portions of polygons in view frustum 2-D screen coordinates of clipped vertices 2-D screen coordinates of clipped vertices

25 Illuminating a scene: coloring pixels according to some approximation of lighting Global illumination: solves for lighting of the whole scene at once Local illumination: local approximation, typically lighting each polygon separately Interactive graphics (e.g., hardware) does only local illumination at run time Rendering: Lighting

26 Lighting Simulation Lighting parameters Light source emission Surface reflectance Atmospheric attenuation Camera response N N Camera Surface Light Source

27 Lighting Simulation Local illumination Ray casting Polygon shading Global illumination Ray tracing Monte Carlo methods Radiosity methods More on these methods later! More on these methods later! N N Camera Surface Light Source N

28 Overview Framebuffers Rendering Pipeline Transformations Lighting  Clipping Modeling Camera Visible Surface Determination History How do you only display those parts of the scene that are visible? How do you only display those parts of the scene that are visible?

29 The Rendering Pipeline: 3-D Modeling Transforms Scene graph Object geometry Lighting Calculations Viewing Transform Clipping Projection Transform Result: All vertices of scene in shared 3-D “world” coordinate system All vertices of scene in shared 3-D “world” coordinate system Vertices shaded according to lighting model Vertices shaded according to lighting model Scene vertices in 3-D “view” or “camera” coordinate system Scene vertices in 3-D “view” or “camera” coordinate system Exactly those vertices & portions of polygons in view frustum Exactly those vertices & portions of polygons in view frustum 2-D screen coordinates of clipped vertices 2-D screen coordinates of clipped vertices

30 Rendering: Clipping Clipping a 3-D primitive returns its intersection with the view frustum:

31 Rendering: Clipping Clipping is tricky! We will a lot more on clipping In: 3 vertices Out: 6 vertices Clip In: 1 polygon Out: 2 polygons

32 Overview Framebuffers Rendering Pipeline Transformations Lighting Clipping  Modeling Camera Visible Surface Determination History How is the 3D scene described in a computer? How is the 3D scene described in a computer?

33 The Rendering Pipeline: 3-D Transform Illuminate Transform Clip Project Rasterize Model & Camera Parameters Rendering Pipeline FramebufferDisplay

34 Modeling: The Basics Common interactive 3-D primitives: points, lines, polygons (i.e., triangles) Organized into “objects” Not necessarily in the OOP sense Collection of primitives, other objects Associated matrix for transformations Instancing: using same geometry for multiple objects 4 wheels on a car, 2 arms on a robot

35 Modeling: The Scene Graph The scene graph captures transformations and object-object relationships in a DAG Nodes are objects; Arcs indicate instancing Each has a matrix Robot BodyHead ArmTrunkLegEyeMouth

36 Modeling: The Scene Graph Traverse the scene graph in depth-first order, concatenating transformations Maintain a matrix stack of transformations ArmTrunk Leg EyeMouth HeadBody Robot Foot Matrix Stack Visited Unvisited Active

37 Overview Framebuffers Rendering Pipeline Transformations Lighting Clipping Modeling  Camera Visible Surface Determination History How is the viewing device described in a computer? How is the viewing device described in a computer?

38 Modeling: The Camera Finally: need a model of the virtual camera Can be very sophisticated Field of view, depth of field, distortion, chromatic aberration… Interactive graphics (OpenGL): Camera pose: position & orientation Captured in viewing transform (i.e., modelview matrix) Pinhole camera model Field of view Aspect ratio Near & far clipping planes

39 Modeling: The Camera Camera parameters (FOV, etc) are encapsulated in a projection matrix Homogeneous coordinates  4x4 matrix! See OpenGL Appendix F for the matrix The projection matrix pre-multiplies the viewing matrix, which pre-multiplies the modeling matrices Actually, OpenGL lumps viewing and modeling transforms into modelview matrix

40 Camera Models The most common model is pin-hole camera All captured light rays arrive along paths toward focal point without lens distortion (everything is in focus) Sensor response proportional to radiance Other models consider... Depth of field Motion blur Lens distortion View plane Eye position (focal point)

41 Camera Parameters Position Eye position (px, py, pz) Orientation View direction (dx, dy, dz) Up direction (ux, uy, uz) Aperture Field of view (xfov, yfov) Film plane “Look at” point View plane normal right back Up direction Eye Position View direction View Plane “Look at” Point

42 Overview Framebuffers Rendering Pipeline Transformations Lighting Clipping Modeling Camera  Visible Surface Determination History How can the front-most surface be found with an algorithm? How can the front-most surface be found with an algorithm?

43 Visible Surface Determination The color of each pixel on the view plane depends on the radiance emanating from visible surfaces View plane Eye position Simplest method is ray casting Simplest method is ray casting Rays through view plane

44 Ray Casting For each sample … Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color of sample based on surface radiance

45 Ray Casting For each sample … Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color of sample based on surface radiance

46 Visible Surface Determination For each sample … Construct ray from eye position through view plane Find first surface intersected by ray through pixel Compute color of sample based on surface radiance More efficient algorithms utilize spatial coherence!

47 Rendering Algorithms Rendering is a problem in sampling and reconstruction!

48 Overview Framebuffers Rendering Pipeline Transformations Lighting Clipping Modeling Camera Visible Surface Determination  History What’s the history of computer graphics hardware? What’s the history of computer graphics hardware?

49 Graphical Hardware Companies In the beginning there was SGI … and they remained the king for 15+ years Are now in bankruptcy protection Why buy a really expensive server when you can get a PC that is almost as fast, but 1/10 th the cost? NVidia and ATI provide high-end graphics cards for PCs ATI tens to focus more on increasing the number of triangles rendered per frame NVidia tends to focus more on adding new graphical capabilities So researchers use it more

50 A much older graphics pipeline SGI Onyx2 From 1997 or so A fully configured system could easily run 100+k A $200 graphics card today can perform 2-3 times as much In all fairness, the Onyx2 had a lot of advantages…

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52 Summary Major issues in 3D rendering 3D scene representation 3D viewer representation Visible surface determination Lighting simulation Concluding note Accurate physical simulation is complex and intractable Rendering algorithms apply many approximations to simplify representations and computations