14_ln_clp_raster

14_ln_clp_raster - The Graphics Pipeline Line Clipping Line...

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MIT EECS 6.837, Durand and Cutler The Graphics Pipeline: Line Clipping & Line Rasterization
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MIT EECS 6.837, Durand and Cutler Last Time? • Ray Tracing vs. Scan Conversion • Overview of the Graphics Pipeline • Projective Transformations Modeling Transformations Illumination (Shading) Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion (Rasterization) Visibility / Display
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MIT EECS 6.837, Durand and Cutler Questions?
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MIT EECS 6.837, Durand and Cutler • Portions of the object outside the view frustum are removed • Rasterize objects into pixels Modeling Transformations Illumination (Shading) Viewing Transformation (Perspective / Orthographic) Clipping Projection (to Screen Space) Scan Conversion (Rasterization) Visibility / Display
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MIT EECS 6.837, Durand and Cutler Today Why Clip? • Line Clipping • Overview of Rasterization • Line Rasterization • Circle Rasterization • Antialiased Lines
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MIT EECS 6.837, Durand and Cutler Clipping • Eliminate portions of objects outside the viewing frustum • View Frustum – boundaries of the image plane projected in 3D – a near & far clipping plane • User may define additional clipping planes bottom top right left near far
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MIT EECS 6.837, Durand and Cutler Why clip? • Avoid degeneracies – Don’t draw stuff behind the eye – Avoid division by 0 and overflow • Efficiency – Don’t waste time on objects outside the image boundary • Other graphics applications (often non-convex) – Hidden-surface removal, Shadows, Picking, Binning, CSG (Boolean) operations (2D & 3D)
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MIT EECS 6.837, Durand and Cutler Clipping strategies • Don’t clip (and hope for the best) • Clip on-the-fly during rasterization • Analytical clipping: alter input geometry
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MIT EECS 6.837, Durand and Cutler Questions?
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MIT EECS 6.837, Durand and Cutler Today • Why Clip? Plane – Line intersection Segment Clipping Acceleration using outcodes • Overview of Rasterization • Line Rasterization • Circle Rasterization • Antialiased Lines
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MIT EECS 6.837, Durand and Cutler Implicit 3D Plane Equation • Plane defined by: point p & normal n OR normal n & offset d OR 3 points • Implicit plane equation A x +B y +C z +D = 0 P 0 P
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MIT EECS 6.837, Durand and Cutler Homogeneous Coordinates • Homogenous point: (x,y,z,w) infinite number of equivalent homogenous coordinates: (sx, sy, sz, sw) • Homogenous Plane Equation: A x +B y +C z +D = 0 H = (A,B,C,D) Infinite number of equivalent plane expressions: sA x +sB y +sC z +sD = 0 H = (sA,sB,sC,sD) P 0 P H = (A,B,C,D)
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MIT EECS 6.837, Durand and Cutler Point-to-Plane Distance P’ P 0 P H = (A,B,C,D) d • If (A,B,C) is normalized: d = H•p = H T p (the dot product in homogeneous coordinates) •d i s a
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MIT EECS 6.837, Durand and Cutler P’
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14_ln_clp_raster - The Graphics Pipeline Line Clipping Line...

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