CS5620 Intro to Computer Graphics
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1 Ra Tracing Ra-Tracing A B C D Photorealism Objective: To generate images that are as close as possible to those perceived b the human ee. Method: Accurate simulation of optical phenomena. Copright Page 1
2 Ra Tracing Illumination Models Local: Depends onl on the model, the light sources and the viewer. Eas to simulate. Eamples: Diffuse and specular illumination models. Flat, Gourard and Phong shading of polhedra. Global: Depends on the entire scene, the light sources and the viewer. Comple to simulate. Eamples: Shadow algorithms, ra-tracing, radiosit methods Copright Page
3 Ra Tracing The Phsics Basic Illumination Model Light ras are emitted from light sources and bounce (reflect) in the scene until the reach the ee Copright Page 3
4 Ra Tracing Rendering Equation I (, ) g(, )[ e(, ) s(,, ) I(, ) d] Surf Bring the objects to the screen Bring the screen to the objects 19 0 Ra-Casting Algorithm A Basic Ra-Casting Algorithm Ee RaCast (r, scene) Primar Ra <obj, p> := FirstIntersection(r, scene); if (no obj) return BackgroundColor; else return Shade(p, obj); end; 1 Ra-Object Intersection Ra-Tracing Algorithm In the kernel of ever ra-tracer Ra-object intersections are computed millions of times for a single image, hence must be ver efficient Eample: Ra-Sphere intersection ra: ( t) p v t, ( t) p v t, ( t) p v t (unit) sphere: 1 Solve a quadratic equation in t : p v (,,) Ee Primar Ra Reflected Ra Reflected Ra 0 ( p v t) ( p v t) ( p v t) 1 t ( v v v ) t( p v p v p v ) ( p p p ) 1 Refracted Ra 3 4 Copright Page 4
5 Ra Tracing Reflection and Refraction A Basic Ra-Tracing Algorithm Snell s law sin 1 c1 sin c n n 1 RaTrace(r, scene) <obj, p> := FirstIntersection(r, scene); if (no obj) return BackgroundColor; else begin if ( Reflect(obj) ) then ReflectColor := RaTrace(ReflectRa(r, p, obj)); else ReflectColor := Black; if ( Transparent(obj) ) then RefractColor := RaTrace(RefractRa(r, p, obj)); else RefractColor := Black; return Shade(ReflectColor, RefractColor, p, obj); end; 5 6 Termination in Ra-Tracing Possible termination criteria: No intersection Contribution of secondar ra attenuated below a threshold Maimal depth 7 8 Ra-Tracing as a Sampling Process Supersampling Trace multiple primar ras per piel and average their results. Ee 1 ra/piel 16 ras/piel 64 ras/piel 30 Copright Page 5
6 Ra Tracing Optimied Ra-Tracing Bounding Volumes Basic algorithm is simple but VERY epensive. Optimied ra-tracing is critical Reduce number of ras traced Reduce number of ra-object intersection calculations Methods Bounding Boes Object Hierarchies Spatial Subdivision (Octrees/BSP) Tree Pruning (Randomied) Bound each scene object b a simple volume (e.g. sphere). This enables fast reject of non-intersections. More work is performed when there is an intersection (or near intersection). Since, on the average, a tpical ra will not intersect the vast majorit of the scene objects, this results in a significant speedup. The time compleit is still linear in the number of scene objects. 31 Choosing Bounding Volumes Bounding volume should be: As tight-fitting as possible As simple as possible Uniform Spatial Partition 3D space is divided into voels of identical sie. Each voel contains a list of objects it intersects. A tradeoff eists between voel sie and list length. Disadvantage: The subdivision is totall independent of the scene structure. Advantages: Simple! The voels pierced b a ra ma be accessed ver efficientl b incremental calculation. A 3D version of Bresenham's algorithm is used. A B {C} {A,B} C {} 34 Simulating Shadows Simulating Shadows Ee Reflected Ra Light Source Trace ra from each ra-object intersection point to light source(s) If no line-of-sight point is shadowed Shadow computation routine: shadow = RaTrace(LightRa(p,obj,light)); to be included in the final shading: return Shade(shadow, ReflectColor, RefractColor, p, obj); Refracted Ra Copright Page 6
7 Ra Tracing Copright Page 7
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