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MIT 6 837 - Graphics Pipeline- Projective Transformations

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1MIT EECS 6.837, Durand and CutlerGraphics Pipeline: Projective TransformationsMIT EECS 6.837, Durand and CutlerLast Time• Shadows– cast ray to light– stop after first intersection• Reflection & Refraction– compute direction of recursive ray• Recursive Ray Tracing– maximum number of bounces OR– contribution < error threshhold• Epsilon…MIT EECS 6.837, Durand and CutlerDoes Ray Tracing Simulate Physics?• Ray Tracing is full of dirty tricks • For example, shadows of transparent objects:– opaque?– multiply by transparency color? (ignores refraction & does not produce caustics)MIT EECS 6.837, Durand and CutlerCorrect Transparent ShadowAnimation by Henrik Wann JensenUsing advanced refraction technique (refraction for illumination is usually not handled that well)MIT EECS 6.837, Durand and CutlerRefraction and the Lifeguard Problem• Running is faster than swimming BeachPerson in troubleLifeguardWaterRunSwimMIT EECS 6.837, Durand and CutlerDoes Ray Tracing Simulate Physics?• Photons go from the light to the eye, not the other way• What we do is backward ray tracing2MIT EECS 6.837, Durand and CutlerForward Ray Tracing• Start from the light source– But low probability to reach the eye• What can we do about it?– Always send a ray to the eye…. still not efficientMIT EECS 6.837, Durand and CutlerThe Rendering Equation• Clean mathematical framework for light-transport simulation• At each point, outgoing light in one directionis the integral of incoming light in all directionsmultiplied by reflectance property • We’ll see this later…MIT EECS 6.837, Durand and CutlerQuestions?MIT EECS 6.837, Durand and CutlerToday• Ray Casting / Tracing vs. Scan Conversion– advantages & disadvantages– when is each appropriate?• The Graphics Pipeline• Projective Transformations• Introduction to ClippingMIT EECS 6.837, Durand and CutlerRay Casting / Tracing• Advantages?– Smooth variation of normal, silhouettes– Generality: can render anything that can be intersected with a ray– Atomic operation, allows recursion• Disadvantages?– Time complexity (N objects, R pixels)– Usually too slow for interactive applications– Hard to implement in hardware (lacks computation coherence, must fit entire scene in memory)MIT EECS 6.837, Durand and CutlerHow Do We Render Interactively?• Use graphics hardware (the graphics pipeline), via OpenGL, MesaGL, or DirectX• Most global effects available in ray tracing will be sacrificed, but some can be approximatedassignment 3assignment 4…3MIT EECS 6.837, Durand and CutlerScan Conversion• Given a primitive's vertices & the illumination at each vertex:• Figure out which pixels to "turn on" to render the primitive• Interpolate the illumination values to "fill in" the primitive• At each pixel, keep track of the closest primitive (z-buffer)glBegin(GL_TRIANGLES)glNormal3f(...)glVertex3f(...)glVertex3f(...)glVertex3f(...)glEnd();MIT EECS 6.837, Durand and CutlerLimitations of Scan Conversion• Restricted to scan- convertible primitives– Object polygonization• Faceting, shading artifacts• Effective resolution is hardware dependent • No handling of shadows, reflection, transparency• Problem of overdraw (high depth complexity)• What if there are many more triangles than pixels?scan conversiongouraud shadingray tracingscan conversionflat shadingMIT EECS 6.837, Durand and CutlerRay Casting vs. Rendering PipelineRay CastingFor each pixelFor each objectSend pixels to the sceneDiscretize firstRendering PipelineFor each triangleFor each pixelProject scene to the pixelsDiscretize lastMIT EECS 6.837, Durand and CutlerRay CastingFor each pixelFor each object• Whole scene must be in memory• Depth complexity: no computation for hidden parts• Atomic computation• More general, more flexible– Primitives, lighting effects, adaptive antialiasingRendering PipelineFor each triangleFor each pixel• Primitives processed one at a time• Coherence: geometric transforms for vertices only• Early stages involve analytic processing • Computation increases with depth of the pipeline– Good bandwidth/computation ratio• Sampling occurs late in the pipeline• Minimal state requiredRay Casting vs. Rendering PipelineMIT EECS 6.837, Durand and CutlerMoviesboth pipeline and ray tracingMIT EECS 6.837, Durand and CutlerGamespipeline4MIT EECS 6.837, Durand and CutlerSimulationpipeline (painter for a long time)MIT EECS 6.837, Durand and CutlerCAD-CAM & Designpipeline during design, anything for final imageMIT EECS 6.837, Durand and CutlerArchitectureray-tracing, pipeline with preprocessing for complex lightingMIT EECS 6.837, Durand and CutlerVirtual RealitypipelineMIT EECS 6.837, Durand and CutlerVisualizationmostly pipeline, ray-tracing for high-quality eye candy, interactive ray-tracing is startingMIT EECS 6.837, Durand and CutlerMedical Imagingsame as visualization5MIT EECS 6.837, Durand and CutlerQuestions?MIT EECS 6.837, Durand and CutlerToday• Ray Casting / Tracing vs. Scan Conversion• The Graphics Pipeline• Projective Transformations• Introduction to ClippingMIT EECS 6.837, Durand and CutlerThe Graphics PipelineModeling TransformationsIllumination(Shading)Viewing Transformation(Perspective / Orthographic)ClippingProjection (to Screen Space)Scan Conversion(Rasterization)Visibility / DisplayMIT EECS 6.837, Durand and CutlerThe Graphics Pipeline• Primitives are processed in a series of stages• Each stage forwards its result on to the next stage• The pipeline can be drawn and implemented in different ways• Some stages may be in hardware, others in software• Optimizations & additional programmability are available at some stagesModeling TransformationsIllumination(Shading)Viewing Transformation(Perspective / Orthographic)ClippingProjection (to Screen Space)Scan Conversion(Rasterization)Visibility / DisplayMIT EECS 6.837, Durand and CutlerModeling Transformations• 3D models defined in their own coordinate system (object space)• Modeling transforms orient the models within a common coordinate frame (world space)Modeling TransformationsIllumination(Shading)Viewing Transformation(Perspective / Orthographic)ClippingProjection (to Screen Space)Scan Conversion(Rasterization)Visibility / DisplayObject space World spaceMIT EECS 6.837, Durand and CutlerIllumination (Shading) (Lighting)• Vertices lit (shaded) according to material properties, surface properties (normal) and light sources•


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MIT 6 837 - Graphics Pipeline- Projective Transformations

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