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CS 352: Computer Graphics Chapter 7: The Rendering Pipeline Chapter 8 - 2 Interactive Computer Graphics Overview Geometric processing: normalization, clipping, hidden surface removal, lighting, projection (front end) Rasterization or scan conversion, including texture mapping (back end) Fragment processing and display Chapter 8 - 3 Interactive Computer Graphics Geometric Processing Front-end processing steps (3D floating point; may be done on the CPU) Evaluators (converting curved surfaces to polygons) Normalization (modeling transform, convert to world coordinates) Projection (convert to screen coordinates) Hidden-surface removal (object space) Computing texture coordinates Computing vertex normals Lighting (assign vertex colors) Clipping Perspective division Backface culling Chapter 8 - 4 Interactive Computer Graphics Rasterization Back-end processing works on 2D objects in screen coordinates Processing includes Scan conversion of primitives including shading Texture mapping Fog Scissors test Alpha test Stencil test Depth-buffer test Other fragment operations: blending, dithering, logical operations Chapter 8 - 5 Interactive Computer Graphics Display Convert frame buffer to video signal Other considerations: Color correction Antialiasing Chapter 8 - 6 Interactive Computer Graphics Geometric Transformations Five coordinate systems of interest: Object coordinates Eye (world) coordinates [after modeling transform, viewer at the origin] Clip coordinates [after projection] Normalized device coordinates [after ÷w] Window (screen) coordinates [scale to screensize] Chapter 8 - 7 Interactive Computer Graphics Line-Segment Clipping Clipping may happen in multiple places in the pipeline (e.g. early trivial accept/reject) After projection, have lines in plane, with rectangle to clip against Chapter 8 - 8 Interactive Computer Graphics Clipping a Line Against xmin Given a line segment from (x1,y1) to (x2,y2), Compute m=(y2–y1)/(x2–x1) Line equation: y = mx + h h = y1 – m x1 (y intercept) Plug in xmin to get y Check if y is between y1 and y2. This take a lot of floating-point math. How to minimize? Chapter 8 - 9 Interactive Computer Graphics Cohen-Sutherland Clipping For both endpoints compute a 4-bit outcode (o1, o2) depending on whether coordinate is outside cliprect side Some situations can be handled easily Chapter 8 - 10 Interactive Computer Graphics Cohen-Sutherland Conditions Cases. 1. If o1=o2=0, accept 2. If one is zero, one nonzero, compute an intercept. If necessary compute another intercept. Accept. 3. If o1 & o2 0. If both outcodes are nonzero and the bitwise AND is nonzero, two endpoints lie on same outside side. Reject. 3. If o1 & o2 0. If both outcodes are nonzero and the bitwise AND is zero, may or may not have to draw the line. Intersect with one of the window sides and check the result. Chapter 8 - 11 Interactive Computer Graphics Cohen-Sutherland Results In many cases, a few integer comparisons and Boolean operations suffice. This algorithm works best when there are many line segments, and most are clipped But note that the y=mx+h form of equation for a line doesn’t work for vertical lines (need a special case in your code) Chapter 8 - 12 Interactive Computer Graphics Polygon Clipping Clipping a polygon can result in lots of pieces Replacing one polygon with many may be a problem in the rendering pipeline Could treat result as one polygon: but this kind of polygon can cause other difficulties Some systems allow only convex polygons, which don’t have such problems (OpenGL has tessellate function in glu library) Chapter 8 - 13 Interactive Computer Graphics Sutherland-Hodgeman Polygon Clipping Could clip each edge of polygon individually Pipelined approach: clip polygon against each side of rectangle in turn Treat clipper as “black box” pipeline stage Chapter 8 - 14 Clipping Pipeline Clip each bound in turn Interactive Computer Graphics Chapter 8 - 15 Interactive Computer Graphics Clipping in Hardware Build the pipeline stages in hardware so you can perform four clipping stages at once [A partial answer to the question of what to do with all that chip area, 1 billion + transistors…] Chapter 8 - 16 Interactive Computer Graphics Clipping complicated objects Suppose you have many complicated objects, such as models of parts of a person with thousands of polygons each When and how to clip for maximum efficiency? How to clip text? Curves? Chapter 8 - 17 Interactive Computer Graphics Clipping Other Primitives It may help to clip more complex shape early in the pipeline This may be simpler and less accurate One approach: bounding boxes (sometimes called trivial accept-reject) This is so useful that modeling systems often store bounding box Chapter 8 - 18 Interactive Computer Graphics Clipping Curves, Text Some shapes are so complex that they are difficult to clip analytically Can approximate with line segments Can allow the clipping to occur in the frame buffer (pixels outside the screen rectangle aren’t drawn) Called “scissoring” How does performance compare? Chapter 8 - 19 Interactive Computer Graphics Hidden surface removal Object space vs. Image space The main image-space algorithm: depth buffer Drawbacks Aliasing Rendering invisible objects Doesn’t handle transparency correctly How would object-space hidden surface removal work? Chapter 8 - 20 Interactive Computer Graphics Depth sorting The painter’s algorithm: draw from back to front Depth-sort hidden surface removal: sort display list by z-coordinate from back to front render Drawbacks it takes some time (especially with bubble sort!) it doesn’t work Chapter 8 - 21 Interactive Computer Graphics Depth-sort difficulties Polygons with overlapping projections Cyclic overlap Interpenetrating polygons What to do? Chapter 8 - 22 Interactive Computer Graphics Scan Conversion At this point in the pipeline, we have only polygons and line segments. Render! To render, convert to pixels (“fragments”) with integer screen coordinates (ix, iy), depth, and color Send fragments into fragment-processing pipeline Chapter 8 - 23 Interactive Computer Graphics Rendering Line Segments How to render a line segment from (x1, y1) to (x2, y2)? Use the equation y = mx + h What about horizontal vs. vertical lines? Chapter 8 - 24 Interactive Computer Graphics DDA Algorithm DDA: Digital Differential Analyzer for (x=x1; x<=x2; x++) y += m; draw_pixel(x, y, color) Handle slopes 0 <= m <= 1; handle others symmetrically Does this need floating point math? Chapter 8 - 25 Interactive Computer Graphics Bresenham’s Algorithm The DDA algorithm requires a floating point add and round for each pixel: eliminate? Note that at each step we will go E or NE. How to decide which? − Chapter 8 - 26 Interactive Computer Graphics Bresenham Decision Variable Note that at each step we will go E or NE. How to decide which? Hint: consider d=a-b, where a and b are distances to NE and E pixels − Chapter 8 - 27 Interactive Computer Graphics Bresenham Decision Variable Bresenham algorithm uses decision variable d=a-b, where a and b are distances to NE and E pixels If d<=0, go NE; if d>0, go E Let dx = x2-x1, dy=y2-y1 Use decision variable − d = dx (a-b) [only sign matters] Chapter 8 - 28 Interactive Computer Graphics Bresenham Decision Variable d =(a-b) dx Let dk be the value of d at x = k + ½ Move E: dk = dx(a-b) = dx((j+3/2–yk) – (yk–(j+1/2))) dk+1 = dx(a-b) = dx((j+3/2–yk–m) – (yk+m–(j+1/2))) dx+1 – dk = dx (-2m) = - 2 dY − Algorithm: dk+1 = dk – 2 dy (if dk > 0) (last move was E) dk+1 = dk – 2 (dy-dx) (if dk <= 0) (last move was NE) Chapter 8 - 29 Interactive Computer Graphics Bresenham’s Algorithm Set up loop computing d at x1, y1 for (x=x1; x<=x2; ) x++; d += 2dy; if (d >= 0) { y++; d –= 2dx; } drawpoint(x,y); Pure integer math, and not much of it So easy that it’s usually implemented in one graphics instruction for several points in parallel Chapter 8 - 30 Interactive Computer Graphics Rasterizing Polygons Polygons may be or may not be simple, convex, flat. How to render? Amounts to inside-outside testing: how to tell if a point is in a polygon? Chapter 8 - 31 Interactive Computer Graphics Winding Test Most common way to tell if a point is in a polygon: the winding test. Define “winding number” w for a point: signed number of revolutions around the point when traversing boundary of polygon once When is a point “inside” the polygon? Chapter 8 - 32 Interactive Computer Graphics OpenGL and Complex Polygons OpenGL guarantees correct rendering only for simple, convex, planar polygons OpenGL tessellates concave polygons Tessellation depends on winding rule you tell OpenGL to use: Odd, Nonzero, Pos, Neg, ABS_GEQ_TWO Chapter 8 - 33 Winding Rules Interactive Computer Graphics Chapter 8 - 34 Interactive Computer Graphics Scan-Converting a Polygon General approach: ideas? One idea: flood fill Draw polygon edges Pick a point (x,y) inside and flood fill with DFS flood_fill(x,y) { if (read_pixel(x,y)==white) { write_pixel(x,y,black); flood_fill(x-1,y); flood_fill(x+1,y); flood_fill(x,y-1); flood_fill(x,y+1); } } Chapter 8 - 35 Interactive Computer Graphics Scan-Line Approach More efficient: use a scan-line rasterization algorithm For each y value, compute x intersections. Fill according to winding rule How to compute intersection points? How to handle shading? Some hardware can handle multiple scanlines in parallel Chapter 8 - 36 Interactive Computer Graphics Singularities If a vertex lies on a scanline, does that count as 0, 1, or 2 crossings? How to handle singularities? One approach: don’t allow. Perturb vertex coordinates OpenGL’s approach: place pixel centers half way between integers (e.g. 3.5, 7.5), so scanlines never hit vertices Chapter 8 - 37 Interactive Computer Graphics Aliasing How to render the line with reduced aliasing? What to do when polygons share a pixel? Chapter 8 - 38 Interactive Computer Graphics Anti-Aliasing Simplest approach: area-based weighting Fastest approach: averaging nearby pixels Most common approach: supersampling (compute four values per pixel and avg, e.g.) Best approach: weighting based on distance of pixel from center of line; Gaussian fall-off Chapter 8 - 39 Interactive Computer Graphics Temporal Aliasing Need motion blur for motion that doesn’t flicker Common approach: temporal supersampling render images at several times within frame time interval average results Chapter 8 - 40 Interactive Computer Graphics Display Considerations Color systems Color quantization Gamma correction Dithering and Halftoning Chapter 8 - 41 Interactive Computer Graphics Additive and Subtractive Color Chapter 8 - 42 Interactive Computer Graphics Common Color Models Chapter 8 - 43 Color Systems RGB YIQ CMYK HSV, HLS Chromaticity Color gamut Interactive Computer Graphics Chapter 8 - 44 HLS Hue: “direction” of color: red, green, purple, etc. Saturation: intensity. E.g. red vs. pink Lightness: how bright To the right: original, H, S, L Interactive Computer Graphics Chapter 8 - 45 Interactive Computer Graphics YIQ Used by NTSC TV Y = luma, same as black and white I = in-phase Q = quadrature The eye is more sensitive to blue-orange than purple-green, so more bandwidth is allotted Y = 4 MHz, I = 1.3 MHz, Q = 0.4 MHz, overall bandwidth 4.2 MHz Linear transformation from RBG: Y = 0.299 R + 0.587 G + 0.114 B I = 0.596 R – 0.274 G – 0.321 B Q = 0.211 R – 0.523 G + 0.311 B Chapter 8 - 46 Interactive Computer Graphics Chromaticity Color researchers often prefer chromaticity coordinates: t1 = T1 / (T1 + T2 + T3) t2 = T2 / (T1 + T2 + T3) t3 = T3 / (T1 + T2 + T3) Thus, t1+t2+t3 = 1.0. Use t1 and t2; t3 can be computed as 1-t1-t2 Chromaticity diagram uses XYZ color system based on human perception experiments Y, luminance X, redness (roughly) Z, blueness (roughly) Chapter 8 - 47 Interactive Computer Graphics Color temperature Compute color temperature by comparing chromaticity with that of an ideal blackbody radiator Color temperature is that were the headed blackbody radiator matches color of light source Higher temperatures are “cooler” colors – more green/blue; warmer colors (yellow-red) have lower temperatures CIE 1931 chromaticity diagram (wikipedia) Chapter 8 - 48 Interactive Computer Graphics Halftoning How do you render a colored image when colors can only be on or off (e.g. inks, for print)? Halftoning: dots of varying sizes [But what if only fixed-sized pixels are available?] Chapter 8 - 49 Interactive Computer Graphics Dithering Dithering (patterns of b/w or colored dots) used for computer screens OpenGL can dither But, patterns can be visible and bothersome. A better approach? Chapter 8 - 50 Interactive Computer Graphics Floyd-Steinberg Error Diffusion Dither Spread out “error term” 7/16 3/16 5/16 1/16 right below left below below right Note that you can also do this for color images (dither a color image onto a fixed 256-color palette) Chapter 8 - 51 Interactive Computer Graphics Color Quantization Color quantization: modifying a full-color image to render with a 256-color palette For a fixed palette (e.g. web-safe colors), can use closest available color, possibly with error-diffusion dither Algorithm for selecting an adaptive palette? E.g. Heckbert Median-Cut algorithm Make a 3-D color histogram Recursively cut the color cube in half at a median Use average color from each resulting box Chapter 8 - 52 Interactive Computer Graphics Hardware Implementations Pipeline architecture for speed (but what about latency?) Originally, whole pipeline on CPU Later, back-end on graphics card Then, whole pipeline in hardware on graphics card Then, parts of pipeline done on GPUs Now, hardware pipeline is gone—done in software on a large number of GPUs Chapter 8 - 53 Interactive Computer Graphics Future Architectures? 20 years ago, performance of 1 M polygons per second cost millions Performance limited by memory bandwidth Main component of price was lots of memory chips Now an iPhone 5 does 115 million triangles (1.8 billion texels) per second Fastest performance today achieved with many cores on each graphics chip (and several chips in parallel) How to use parallel graphics cores/chips? All vertices go through vertex shaders – can do in parallel All fragments go through fragment shaders – can do in parallel Resulting fragments combined into a single image – easy with sufficient memory bandwidth Chapter 8 - 54 Interactive Computer Graphics NVidia GeForce GTX 590 Facts “Most powerful graphics card ever built” (of 2011) Dual 512-core GTX 500 GPUs (1024 CUDA unified shaders) 2 x 16 Streaming Multiprocessor (SM) processor groups, each with 32 Streaming Processors (SPs) PhysX physics engine on the card (used for flowing clothing, smoke, debris, turbulence, etc) Memory bandwidth: 327.7 GB/sec Texture fill rate: 77.7 billion/sec 4X antialiasing 3 billion transistors x 2 Real-time ray tracing Power: 365 w