Lecture 12 Thursday 17 October 2002 Assignment 5 Ray Casting extension Eye ray generation ray primitive intersection New due date is Monday 21 October at 5pm Assignment 6 Ray Tracing extension Shadows re ection refraction super sampling New due date is Monday 28 October at 5pm Adjusted o ce hours Thursday today Addy 4 7pm W20 Linux Cluster Prof Durand 4 6pm Bldg 4 SGI Cluster Friday Prof Teller 3 5pm W20 Linux Cluster Monday Addy 10am Noon NE43 256 Prof Durand 2 4pm NE43 254 MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 1 Today Planning for the second half of the term Getting started on your nal team projects Lecture Ray Tracing Contrast scan conversion ray casting ray tracing Appropriate physical units for ray tracing Ray tracing pseudocode Assignments 5 6 Ray tracing extensions MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 2 Final Projects Start thinking about what you d like to do Animation Game Visualization Algorithm Interaction method Etc Representative nal project reports linked from F99 course page Team building page with list of past project titles at http graphics lcs mit edu classes 6 837 F02 projects teams htm Enter a brief description of your project idea or interests along with your contact info relevant background skills etc there Next Thursday in class Brain storming and team building session Come with project ideas in mind we ll discuss as a group Students watching o line come to Prof s o ce hours Teams formed project proposals due by November 1 That s two weeks from tomorrow Thereafter weekly meetings with TA through end of term MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 3 Scan Conversion Visibility Resolution Feed forward rendering method one polygon at a time Polygons issued in immediate mode to graphics pipeline Full frame single raster or single pixel depth bu er Visibility depth information computed many times at each pixel Limitations of scan conversion method for visibility Restricted to scan convertable primitives simple surface types Requires polygonalization tessellation choice for all primitives Causes faceting geometric artifacts at silhouettes interior MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 4 Scan Conversion Shading Computation Shading computed with a constant amount of state Typically small number of hardware supported light sources Local shading computation f position material light viewer Evaluated at polygon vertices Gouraud interpolated Limitations of local shading computation interpolation Cartoonish look incorrect highlights no shadows occlusion of light sources secondary illumination re ection transmission transparency focusing e ects refraction No obvious way to add these e ects to local shading model MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 5 Ray Casting for Analytic Geometry Sampling Address Visibility Shading separately Resolve visibility per pixel using ray primitive intersection Evaluate local lighting model once at each visible pixel eye n light source no eye p n p Use routine Shade for lighting evaluation Phong model Shade obj surface at point ShadeP normal ShadeN as seen along direction Along Radiance Shade Object obj Ray Along Point ShadeP Vector ShadeN sum Phong term for each light MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 6 Ray Casting with Analytic Visibility Hit Cast Point R Ray D find minimum t 0 such that R t D hits object if object hit return object identifier t N else return background object identifier t Cast eye ivray raycast iv e raycast env s L FrameBuffer Render frustum viewport Framebuffer FB w h For each raster y For each pixel x E direction from eye through pixel x y hit Cast eye E FB x y Shade hit obj E eye hit t E hit N return FB Render by Ray Casting MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 7 Ray Casting for Visibility Advantages Smooth variation of silhouettes depth normal shading Generality can render anything with which a ray can be intersected Compactness of representation Disadvantages Time complexity N objects R pixels Wasted work at background pixels MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 8 Ray Casting and Shadow Tests Idea Appel 1968 Cast ray from eye through each pixel Determine closest object along ray and visible point there Shade by summing contributions from unoccluded lights Non recursive But improved quality realism Primary shadows handled w existing capability light light eye ivray raycast iv e raycast env s S MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 9 Recursive Ray Tracing Extend to re ection refraction Shading must take entire scene into account Ray tracing is a global illumination algorithm Idea Light originates at light sources so trace photon paths from the light source Known as Forward Ray Tracing At each interaction surface properties dictate absorption reemission transmission probability light eye O Typically expressed as BRDF f i i e e 0 1 Disadvantages of Forward Ray Tracing MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 10 Forward Ray Tracing Disadvantages very few of the photons end up at the eye very hard to know in which directions photons should be sent enormous number of cycles expended per photon can be ameliorated by packet tracing result is usually objectionable noise MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 11 Backward Ray Tracing Insight we see only those rays that arrive at the eye So trace eye rays E backward into scene Find contributions to shading only at surface points Evaluate contributions along the viewing direction light S N R T E eye O ivray raycast iv e raycast env s R d 1 Likely directions in which to sample Shadow rays S to light sources Re ection rays R along specular direction Refraction rays T along refraction direction Note Shading operation is recursive MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 12 Recursive Ray Tracing Examples ivray raycast iv e raycast env s R d 0 ivray raycast iv e raycast env s R d 1 ivray sphereplane iv e raycast env s R d 2 Experiment with reference ivray to understand these MIT 6 837 Computer Graphics Thursday 17 October 2002 L12 Page 13 Physical Units for Ray Tracing From radiometry measurement of EM energy distinct from photometry visual sensation of EM energy Radiance L power src area rcvr steradian Power per unit projected area perpendicular to the ray per unit solid angle in the direction of the
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