demos of ray tracing·DENG Jia (计2 邓嘉)’s DemoPlayVideo: Deng Jia, 2002-2006, Tsinghua University, No1 in GPA. 2006-, Princeton Univetrsity, published apaper on relief in ACM SIGGRAPH 2007DengJia's story in Media computing (late)
demos of ray tracing • DENG Jia (计2 邓嘉)’s Demo Play Video • Deng Jia, 2002-2006, Tsinghua University, No. 1 in GPA. • 2006- , Princeton Univetrsity, published a paper on relief in ACM SIGGRAPH 2007 • Deng Jia’s story in Media computing (late)
Rayintersection（光线求交）. Ray tracing- Ray Representation-Plane intersection- Triangle intersection-Polygon intersection- Sphere intersection- Box intersection
Ray intersection (光线求交) • Ray tracing – Ray Representation – Plane intersection – Triangle intersection – Polygon intersection – Sphere intersection – Box intersection
Ray representation: Parametric representation- P(t)= R。+ t * Rd-- where R,=(xo,Yo,z.) is the original point of the ray ,R,=(Xd,Yd,za) is the direction the ray is going on, usuallythe direction is normalized- t value determines the point the ray arrives at, its valueisalways larger than 0P(t)directionRdoriginA
Ray representation • Parametric representation – P(t) = Ro + t * Rd – where Ro=(xo ,yo ,zo ) is the original point of the ray , Rd=(xd ,yd ,zd ) is the direction the ray is going on, usually the direction is normalized – t value determines the point the ray arrives at, its value is always larger than 0 Rd Ro origin direction P(t)
Plane Intersection. Plane Definition- Explicit: P=(xo,yo,z.), n=(A,B,C)- Implicit: H(P) = Ax+By+Cz+D = 0=n·P+D=0: Point Plane DistanceH(p)= d >0-If n is normalized.OPnormal1the distance is d = H(P)1- But note that, d1PHCis signed distanceOP'H(p)= d< 0
Plane Intersection • Plane Definition – Explicit: Po=(xo ,yo ,zo ), n=(A,B,C) – Implicit: H(P) = Ax+By+Cz+D = 0 = n·P + D = 0 • Point Plane Distance – If n is normalized, the distance is d = H(P) – But note that, d is signed distance Po H normal P P' H(p) = d < 0 H(p) = d > 0
Plane Intersection. Where does the ray intersect this plane?. Given a plane with equation:n·P+D=0;Intersection means satisfy both equations:P(t)= R。+ t * Rdn·P(t)+D = 0;So we havet = -(D+n·R)/(n· Ra)(P(t) Just need to verify if t>0
Plane Intersection • Where does the ray intersect this plane? • Given a plane with equation: n·P + D = 0; • Intersection means satisfy both equations: P(t) = Ro + t * Rd n·P(t)+D = 0; So we have t = -(D+n·Ro )/(n· Rd ) • Just need to verify if t>0 P(t)