CS 4204 Computer Graphics

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1 CS 4204 Computer Graphics Introduction to Ray Tracing Yong Cao Virginia Tech Reference: Ed Angle, Interactive Computer Graphics, University of New Mexico, class notes

2 Raytracing (Picture from Povray.org)

3 Raytracing (Picture from Povray.org)

4 Raytracing (Picture from Povray.org)

5 Raytracing (Picture from Povray.org)

6 Raytracing (Picture from Povray.org)

7 Raytracing (Picture from Povray.org)

8 The Basic Idea Simulate light rays from light source to eye Eye Light Surface

9 Forward Ray-Tracing Trace rays from light Lots of work for little return Light Image Plane Light Rays Eye Object

10 Scene S A shiny, transparent S B,S D S C diffuse, opaque shiny, opaque S C Light S D Eye S A Image Plane S B

11 Three sources of light The light that point P A emits to the eye comes from: light sources other objects (reflection) other objects (refraction) Eye S C Light S D P A S A shiny, transparent S B,S D diffuse,opaque S A S C shiny, opaque S B

12 Directly from light source Local illumination model: I = I a +I diff +I spec S A S B,S D S C shiny, transparent diffuse,opaque shiny, opaque Light Eye S C S D P A S A S B

13 Reflection What is the color that is reflected to P A? The color of P C. What is the color of P C? S A S B,S D S C shiny, transparent diffuse,opaque shiny, opaque Light Eye S C Pc S D n P A S A S B

14 Reflection What is the light that is reflected to P A? The color of P C. as viewed by P A What is the color of P C reflected towards P A? Just like P A : raytrace P C i.e compute the Eye three contributions from 1. Light sources 2. Reflection 3. refraction S A S B,S D S C S C S A shiny, transparent diffuse,opaque shiny, opaque Light S D P A S B

15 Refraction Transparent materials How do you compute the refracted contribution? You raytrace the refracted ray. 1. Lights 2. Reflection 3. Refraction Eye S A S B,S D S C S C S A shiny, transparent diffuse,opaque shiny, opaque Light S D P A S B

16 What are we missing? Diffuse objects do not receive light from other objects.

17 Three sources of light together The color that the pixel is assigned comes from: light sources other objects (reflection) other objects (refraction) It is more convenient to trace the rays from the eye to the scene (backwards) S A S B,S D S C S C shiny, transparent diffuse,opaque shiny, opaque Light S D Eye P A S A S B

18 Backwards Raytracing Algoritm For each pixel construct a ray: eye pixel raytrace( ray ) P = closest intersection color_local = ShadowRay(light1, P)+ + ShadowRay(lightN, P) color_reflect = raytrace(reflected_ray ) color_refract = raytrace(refracted_ray ) color = color_local + k re *color_reflect + k ra *color_refract return( color )

19 How many levels of recursion do we use? The more the better. Infinite reflections at the limit.

20 Stages of raytracing Setting the camera and the image plane Computing a ray from the eye to every pixel and trace it in the scene Object-ray intersections Shadow, reflected and refracted ray at each intersection

21 Setting up the camera

22 Image parameters Width 2W, Height 2H Number of pixels ncols x nrows Camera coordinate system (eye, u,v,n) Image plane at -N

23 Pixel coordinates in camera coordinate system Pixel P(r,c) has coordinates in camera space:

24 Ray through pixel Pixel location Ray through pixel:

25 Triangle Intersection Want to know: at what point (p) does ray intersect triangle? Compute lighting, reflected rays, shadowing from that point p r o r d <?,?,?> (t =???)

26 Triangle Intersection Step 1 : Intersect with plane ( Ax + By + Cz + D = 0 ) Plane normal n = <A, B, C> p r d r o p = -(n. r o + D) / (n. r d )

27 Triangle Intersection Step 2 : Check against triangle edges n V 1 V 0 V 1 E 0 p E i = V i V x i+1 n (plane A, B, C) d i = -A. N (plane D) V 0 V 2 Plug p into (p. E i + d i ) for each edge if signs are all positive or negative, point is inside triangle!

28 Triangle Normals Could use plane normals (flat shading) Better to interpolate from vertices n V1 V 1 Find areas n p n V0 a c b V 0 n V2 V 2 n = an V0 + bn V1 + cn V2 area(v 0 V 1 V 2 )

29 Ray-object intersections Unit sphere at origin - ray intersection: That s a quadratic equation

30 Solving a quadratic equation

31 First intersection? Intersections t= Ray(t) t=0

32 First intersection? t1 < t2 Intersections t= t2 Ray(t) t1 t=0

33 Transformed primitives? Where does S+ct hit the transformed sphere G?

34 Linear transformation

35 Linear transformation

36 Final Intersection Inverse transformed ray Drop 1 and O to get S +c t For each object Inverse transform ray getting S +c t Find intersection t h Use t h in the untransformed ray S+ct to find the intersection

37 Shadow ray For each light intersect shadow ray with all objects. If no intersection is found apply local illumination at intersection Lights If in shadow no contribution

38 Reflected ray Raytrace the reflected ray Ray rf (t) N a Ray(t) a P

39 Refracted ray Raytrace the refracted ray Snell s law N

40 Add all together color(r,c) = color_shadow_ray + Kf*color_rf + Kr*color_rfa

41 Raytracing for each pixel on screen determine ray from eye through pixel find closest intersection of ray with an object cast off reflected and refracted ray, recursively calculate pixel colour, draw pixel end

42 Acceleration 1280x1024 image with 10 rays/pixel 1000 objects (triangle, CSG, NURBS) 3 levels recursion intersection tests tests/second -> 109 days! Must use an acceleration method!

43 Bounding volumes Use simple shape for quick test, keep a hierarchy

44 Space Subdivision Break your space into pieces Search the structure linearly

45 Parallel Processing You can always throw more processors at it.

46 Summary: Raytracing Recursive algorithm Function Main for each pixel (c,r) on screen determine ray r c,r from eye through pixel color(c,r) = raytrace(r c,r ) end for end function raytrace(r) find closest intersection P of ray with objects clocal = Sum(shadowRays(P,Lighti)) c re = raytrace(r re ) c ra = raytrace(r ra ) return c = clocal+k re *c re +k ra *c ra end

47 Advanced concepts Participating media Transculency Sub-surface scattering (e.g. Human skin) Photon mapping

48 Raytracing summary View dependent Computationally expensive Good for refraction and reflection effects

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