Ray Tracing Assignment Goal is to reproduce the following So You - PDF document

Ray Tracing Assignment  Goal is to reproduce the following So You Want to Write a Ray Tracer Checkpoint 6 – Refraction Whitted, 1980 Ray Tracing Assignment Ray Tracing Assignment Seven checkpoints Seven checkpoints    Setting the Scene  Setting the Scene    Camera Modeling  Camera Modeling  Basic Shading  Basic Shading  Procedural Shading  Procedural Shading    Recursive Ray Tracing – Reflection  Recursive Ray Tracing – Reflection  Recursive Ray Tracing – Transmission  Recursive Ray Tracing – Transmission  Tone Reproduction  Tone Reproduction   Refraction Recursive Ray Tracing color illuminate (ray, depth)  Perform recursive ray tracing by find closest intersect considering reflection and refraction if (!intersection) return background color else  Parameters to add: spawn shadow ray  For each object retcolor = local illumination if (depth < MAX_DEPTH)  k r , k t – reflection and transmission constants if (k r > 0)  k t ≠ 0 for this checkpoint spawn reflection ray retcolor += k r * illuminate (reflect ray, depth+1)  Index of refraction (example 0.95) if (k t > 0) spawn transmission ray retcolor += k t * illuminate (trans ray, depth +1) return retcolor 1

Total Internal Reflection Recursive Ray Tracing Calculating Transmission Ray For each pixel Starting with Snell’s law d n � i spawn ray from camera pos to pixel η sin θ = η sin θ � i i i t t pixel_color = illuminate (ray, 1) η t θ Assume d and n are normalized. t t We can find the equation for t, the transmission ray: d is the incoming ray, t is the 2 η ( d − n(d • n) ) η ( 1 − ( d • n ) 2 ) transmission ray. i i t = + n 1 - 2 η η t t If negative – total internal reflection Total Internal Reflection  an optical phenomenon that occurs when light is refracted (bent) at a medium boundary enough to send it backwards, effectively reflecting all of the light.  In these cases, the transmission ray will be spawned in the reflection direction. Wikipedia Total Internal Reflection Calculating transmission ray  Snell’s law applet  http://www.physics.northwestern.edu/ugrad/vpl/opt ics/snell.html  Index of refraction of air = 1.0  Optimization  If indices of refractions are the same Total internal reflection occurs around boundary of  no bending  Transmission direction is the same as incoming direction transparent sphere 2

Things to think about Things to think about  Must keep track if you are inside or  2 ways to deal outside  If n • d < 0 then  Inside Index of refraction  Use –n as normal for calculations η  Use inside η as � i Normal vector  Keep track as you are spawning rays Things to think about Refraction public Vector3f faceForward (Vector3f A Vector3f B)  For sake of checkpoint {  Make one sphere transparent (k t = 0.8) // For acute angles, dot product will  Make other sphere non-transparent // be positive if (A.dot(B) >= 0) return A;  May wish to test first with index of refraction = 1.0 // Obtuse angle, reverse the first vector Vector3f V = new Vector3f (A); V.scale (-1.0f); return V; } Refraction Refraction  Note:  Due date:  If done correctly, you should now have a faithful  Must be posted to Web site by May 2nd reproduction of the target image.  Recall:  Sample parameters  10% penalty per day  Sphere1 – front  Sphere2 – rear  Having trouble?  Color (amb/diffuse)  Color (all) = white (0.7, 0.7, 0.7)  Ka = 0 .0 7 5  Let me know EARLY.  Color (spec) = white  Kd = 0 .0 7 5  Ka = 0 .1 5  Questions?  Ks = 0 .2  Kd = 0 .2 5  Ke = 2 0 .0  Ks = 1 .0  Kr = 0 .0 1  Ke = 2 0 .0  Kt = 0 .8 5  Kr = 0 .7 5  Kt = 0 .0 3

Extra extra  For 5 points:  Adjust shadow ray based upon transparency of objects. 4