Raytracing. Flat shading Phong Shading. COSC 4328/5327 Scott A. King

Transcription

1 Raytracing COSC 4328/5327 Scott A. King Render With Triangles Flat shading Phong Shading Now what? What lighting effects would we have trouble Shadows (can fake) Reflection (can fake) Refraction (can fake, but not easily) Reflected refraction? Harder to fake if moving camera So how will we do this? "Villarceau Circles" by Tor Olav Kristensen (2004) Marc Jacquier (2004) "Glasses" by Gilles Tran (2006) 5 6 "Christmas Baubles" by Jaime Vives Piqueres (2005) "Office" by Jaime Vives Piqueres (2004) 1

2 7 8 "Villarceau Circles" by Tor Olav Kristensen (2004) "Autobahn WIP" by Jaime Vives Piqueres (2005) 9 10 "Car Study" by René Bui (2006) Jaime Vives Piqueres (2003) "Small World" by Stephen M. Farrell (2002) 2

3 13 14 "Urban Tree" by Jaime Vives Piqueres (1999) "Rocket" by Jochen Diehl (2004) Gilles Tran (2000) "The Dark Side of the Trees" by Gilles Tran (2002) "Techno Garb" by Samuel Benge (2003) "Dancing Cube" by Friedrich A. Lohmueller (2003) "Balanza" by Jaime Vives Piqueres (2002) 3

4 19 20 "BL Object 5" by Douglas Eichenberg (2003) "Travieso" by Jaime Vives Piqueres (1997) "Harvest Time" by Gilles Tran (1999) This image won the IRTC competition of November - December 1999, "Gardens" topic "Still with Bolts" by Jaime Vives Piqueres (2002) 23 Radiance Movies by Martin Moeck, Siemens Lighting 4

5 Consider This Room. 25 Pinhole Camera 26 When I m looking towards the wall, what can I see behind me? Do I get any clues about what is behind me? How do we see? Our eyes are sensors. What do they sense? We are detecting light at different wavelengths (roughly) Where does this light come from? From the desk, the wall, the table? From some light source. Why a camera? Lets use a pinhole camera model. Why? Should we flip image? Light Comes Forward From its Source(s) Forward Tracing Can this be done? Yes How would we do it? Well, we would have to trace all rays from all lights. If they end up hitting our eye (camera) then we add in it s contribution. Is this efficient? No Is it accurate? Yes What could we do instead? Tracing from light source Traditional ray-tracing Backward Tracing Basic Ray Casting 5

6 Basic Ray Casting Basic Ray Casting Basic Ray Casting u is the starting point 6

7 u is the starting point v is the direction u is the starting point v is the direction t is how far we ve travelled along ray. Ray/Sphere Intersection Ray/Sphere Intersection u 2 + 2uvt + v 2 t 2 = 1 Let s use a sphere of radius 1 centered at the origin In vector form The ray p intersects the sphere when satisfies the equation for the sphere. Plug in the ray into sphere equation Let s expand We have a lot of vector times vector operations? What is that? What is the result? x 2 + y 2 + z 2 = 1 p 2 = 1 u + vt 2 = 1 u 2 + 2uvt + v 2 t 2 = 1 p 2 = 1 Solve using quadratic formula Let s solve this in three steps. 1. if b 2 4ac, we don t get a solution. if b 2 = 4ac, p is a tangent ray, which we can consider a miss. 2. if b > 0 then t 1 = b b2 4ac else 2a t 1 = b+ b2 4ac 2a 3. t 2 = c at 1 u uvt + v 2 t 2 = 0 c b a rad=b*b-4*a*c if (rad <= 0) return no int if (b > 0) t1 = (-b-sqrt(rad))/(2*a) else t1 = (-b+sqrt(rad))/(2*a) T2 = c/(a*t1); Ray/Sphere Intersection D = B*B - 4*AC; if (D < 0.0) return NULL; rootd = sqrt(d); t0 = 0.5*(-B - rootd)/a; t1 = 0.5*(-B + rootd)/a; if (t0 >= 0) hit->t = t0, return hit; if (t1 >= 0) hit->t = t1, return hit; return NULL; rad=b*b-4*a*c if (rad <= 0) return no int if (b > 0) t1 = (-b-sqrt(rad))/(2*a) else t1 = (-b+sqrt(rad))/(2*a) T2 = c/(a*t1); * / + - A B