Graphics Pipeline Rendering Operations: Clipping, Rasterization, & Hidden Surface Removal Adapted from 3D Computer Graphics by Alan Watt Third Edition, Pearson Education Limited, 2000 1 Graphics Pipeline 3D scene mapped as a two-dimensional surface. Find the color of the pixel. Two process Geometric CPU intensive Algorithmic – Rendering Video Card - GPU 3D Space 2D Space 2 Graphics Pipeline Object Space World Space World Coordinate - geometric Compose Scene - geometric Define View - geometric Define Lighting - geometric Radiosity & Photon Mapping – rendering Modeling Transformation View Transformation Projection Transformation World Space View Space View Space Local Coordinates - geometric Object Definition - geometric Local Space View volume - geometric Cull - geometric Clip to View Volume – geometric/rendering 3D Screen Space 3D Screen Space Rasterization – rendering Hidden surface removal - rendering Shading – rendering Display or Image Space 3 Rendering Operations 1. Clipping to the View Volume 2. Rasterization 3. Finding the set of pixels in which a polygon projects. Hidden Surface Removal 4. Determining what portion of a polygon that crosses the View Volume should be rendered. Determines which polygons will not be seen. Shading Interpolating the value of the pixels within a polygon. 4 Clipping to the View Volume Cull then Clip. Geometric Operation Cull to View Volume View Space – View Coordinates Determine if polygons are outside or inside the View Volume Determine if polygons straddle the View Volume Discard as many polygons as possible 5 Projection Transformation Geometric Operation Transforming scene geometry from View Space into 3D Screen Space. View Space - Perspective Cube Projection Transformation 3D Screen Space - Orthographic Clip rectangle Transformed Cube 6 Clipping to the View Volume Clip boundary Each polygon is evaluated against the clipping boundary of the View Volume and clipped accordingly. View Inside S1 Space - Perspective F1 S2 F1 I1 Cube Polygon F2 Outside Polygon View Transformation Clip rectangle Case 1 Case 2 F4 F1 I2 I2 I1 I1 F3 S4 S3 Bottom Clip Figure 1 Left Clip Right Clip Top Clip Case 3 Sutherland-Hodgman clipper F4 3D Screen Space - Orthographic F1 F1 Transformed I1 Cube Case 4 Figure 2 Case 5 7 3D Screen Space Geometric Operations Point projection onto Screen Space Geometric Transformation Figure 1 - Geometric Transformation a) View Space b) 3d Screen Space Object Space World Space View Space 3D Screen Space Display or Image Space Figure 2 – Projection of object’s vertices into 3d Screen Space 8 Rasterization Rasterizing edges Generate a linear set of pixels with no gaps Raster Grid Figure 1b 1a – Projection of edges vertices into 3D Screen Space. Raster Grid 9 Rasterization 3D Screen Space Rasterization Find pixel coordinates of interior points Scan line Procedure “Filling the polygon” Assign a value based on shading scheme Object Space World Space View Space 3D Screen Space Display or Image Space Raster Grid y Scan line plane Scan line scan lines z 3D Screen Space Figure 1 - Raster Grid / Scan Line x Figure 2 – Scan Line Plane 10 Rasterization 3D Screen Space Rasterization Find pixel coordinates of interior points Scan line Procedure “Filling the polygon” Assign a value based on shading scheme Object Space World Space View Space 3D Screen Space Display or Image Space Raster Grid y Scan line plane Scan line scan lines z 3D Screen Space Figure 1 - Raster Grid / Scan Line x Figure 2 – Scan Line Plane 11 Hidden Surface Removal (HSR) Hidden Surface Removal (HSR) Hidden Surface Determination Visible Surface Determination Hidden Line Removal (HLR). Determining which surface are visible . 12 Hidden Surface Removal Geometric Operations Tessellation Culling Converting all geometry to triangles. View Volume - surfaces outside of the view volume are culled. Backface - Orientation of Surface Normal to the Camera. Geometric Transformation Patch Poly Three sided Polygon Converting Geometry from View Space to Orthographic 3D Screen Space. 13 Hidden Surface Removal Geometric Operations Tessellation Culling Converting all geometry to triangles. View Volume - surfaces outside of the view volume are culled. Backface - Orientation of Surface Normal to the Camera. Geometric Transformation Converting Geometry from View Space to Orthographic 3D Screen Space. Back Face Culling Culling to the View Volume 14 Hidden Surface Removal Geometric Operations Tessellation Culling Converting all geometry to triangles. View Volume - surfaces outside of the view volume are culled. Backface - Orientation of Surface Normal to the Camera. Geometric Transformation Converting Geometry from View Space to Orthographic 3D Screen Space. Transformed Cube Cube View Space - Perspective 3D Screen Space - Orthographic 15 Hidden Surface Removal Z-Buffer the depth of a generated pixel z coordinate is stored in a buffer (z-buffer). Two-dimensional X-Y array Excerpted from Wikipedia, http://en.wikipedia.org/wiki/Z-buffering 16 Hidden Surface Removal (HSR) Polygon-by-Polygon or Painter’s Algorithm Scanline Renderer 17 Hidden Surface Removal (HSR) Polygon-by-Polygon or Painter’s Algorithm Simple to implement No upper limit on scene complexity Overlapping of polygons are difficult to render. Inefficient Hidden Line Removal - Z-buffer – memory intensive Wikipedia, http://en.wikipedia.org/wiki/Image:Painter%27s_algorithm.png 18 Hidden Surface Removal (HSR) y Scan Line /w Z-buffer Most commonly used Polygons rendered row by row. Polygons sorted based on Z-depth. HLR - Z-buffer, scan-line zbuffer, spanning scan line algorithm. Scan line order – efficient for anti-aliasing. Not as memory intensive Limits complexity of scene Scan line z 3D Screen Space Scan Line Rendering x Excerpted from Wikipedia: http://en.wikipedia.org/wiki/Scanline_rendering 19 Hidden Surface Removal Advantage – Simplicity Dedicated Z-Buffer memory Unseen polygons are rendered Z-depth precision Scan line Scanline algorithm Advantages Machine efficient Needs limited memory z Disadvantages Fetch individual polygons in any order No upward limit of polygons (scene complexity) Disadvantage – Memory y Z-buffer algorithm Limited scene complexity 3D Screen Space De facto standard - Scanline Z-buffer Scan-lined – algorithm intensive – Screen Space Z-Buffered – memory intensive – Object Space Scan Line Rendering x 20 Graphics Pipeline Object Space World Space World Coordinate - geometric Compose Scene - geometric Define View - geometric Define Lighting - geometric Radiosity & Photon Mapping – rendering Modeling Transformation View Transformation Projection Transformation World Space View Space View Space Local Coordinates - geometric Object Definition - geometric Local Space View volume - geometric Cull - geometric Clip to 3D – geometric/rendering 3D Screen Space 3D Screen Space Rasterization – rendering Hidden surface removal - rendering Shading – rendering Display or Image Space 21 END 22
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