CS 428: Fall Introduction to. Raytracing. Andrew Nealen, Rutgers, /18/2009 1

Transcription

1 CS 428: Fall 2009 Introduction to Computer Graphics Raytracing 11/18/2009 1

2 Forward ray tracing From the light sources Simulate light transport one ray at a time Rays start from lights + bounce around the scene Some hit the camera (extremely few!) Very expensive to compute Under-sampling! So: nobody does this 11/18/2009 2

3 Backward ray tracing From the eye Use ray casting from camera to scene Much faster (all rays say something about image) An approximation Use known lighting models (diffuse, specular, etc) No caustics, inter-object reflection (Can be fixed/combined with other techniques ) 11/18/2009 3

4 Raytracing Albrecht Dürer Der zeichner des liegenden weibes, 1538 Impression of Velo von Alberti ( ) Sorry, but thanks to an extremely antiquated and lame attitude w.r.t. male/female nudity, this part of the image is not shown. 11/18/2009 4

5 Recursive raytracing Turner Whitted 1979: Model for Integrating Reflection Refraction Visibility Shadows (Basic) raytracing simulates the light transport and adheres to the rules of ideal reflection and refraction 11/18/2009 5

6 Point light sources Materials Recursive raytracing Assumptions Diffuse mit specular component (Phong model) Light transport Occluding objects (Umbras, but no penumbras) No light attenuation Only specular light transport between surfaces (Rays are only followed along directions of ideal reflection) 11/18/2009 6

7 Recursive raytracing Turner Whitted [1979] 11/18/2009 7

8 Recursive raytracing Examples Raytracing ist extremely suitable for scenes with many mirroring and transparent (refracting) surfaces 11/18/2009 8

9 Recursive raytracing Synthetic camera Defined by an eye point and image (view) plane in world coordinates The image plane is an array of pixels, with the same resolution as the resulting image 11/18/2009 9

10 Recursive raytracing Rays are cast into the scene from the eye point through the pixels 11/18/

11 Recursive raytracing If the ray intersects with more than one object, then the nearest intersection is drawn Otherwise, draw the background color 11/18/

12 Recursive raytracing If a ray intersects with an object, then additional rays are cast from the point of intersection to all light sources 11/18/

13 Recursive raytracing If these shadow feelers intersect with an object, then the first intersection point is in shadow 11/18/

14 Recursive raytracing If the object is reflective, a reflected ray (about the surface normal) is cast into the scene 11/18/

15 Recursive raytracing If the object is transparent, a refracted ray (about the surface normal) is cast into the scene 11/18/

16 Recursive raytracing New rays are generated for reflection, transmission (refraction) and shadow feelers Rays are parameters of a recursive function Detects all visible surfaces intersected by rays, shades them, and returns the result (= color) eye S pixel S S S 11/18/

17 Lighting model Lighting on a surface is combined of Ambient + Diffuse + Specular (highlights and reflection) + Transmitted (refracted) Equivalent to the Phong-model plus contributions from reflected and refracted rays 11/18/

18 Lighting model L sum = L Phong + r r L r + r t L t L r is the luminance of the reflected ray L t is the luminance of the transmitted ray r r is the reflectance (in [0,1]) for ideal reflection r t is the reflectance (in [0,1]) for ideal transmission R = -E+2(N E)N 11/18/

19 Rays Data structure Point of origin p+ direction d Parametric equation If dis normalized, t is distance from pto p+td 11/18/

20 Camera setup 11/18/

21 Camera setup Aspect ratio r = W/H Determine W and H from θand r N n 11/18/

22 Intersecting rays with objects Object representation? Implicit equations make intersections easier Surface is a set of points that satisfy F(x,y,z) = 0 Example: sphere at the origin with radius 1 F(x,y,z) = x 2 + y 2 + z 2-1 As opposed to its explicit representation 11/18/

23 Intersecting rays with objects Normal vector to an implicit surface For the previous example of a sphere F(x,y,z) = x 2 + y 2 + z 2-1 n(x,y,z) = [2x, 2y, 2z] T 11/18/

24 Intersecting rays with objects Given a ray (p,d) Intersection points found by solving F(p+td) = 0 for t Quadratic in t for F(x,y,z) = x 2 + y 2 + z /18/

25 What if object is not at origin? Implicit equation becomes more complex although sphere is still fairly easy Transform the ray with M -1 11/18/

26 What if object is not at origin? Implicit equation becomes more complex although sphere is still fairly easy Transform the ray with M -1 Transform back the intersection point(s) t is the same in both (don t normalize M -1 d) In other words, solve F(M -1 p + t(m -1 d)) = 0 11/18/

27 Transforming intersection Point Normal 11/18/

28 Transforming intersection Why (M -1 ) T for normals? Given a vector v o in the tangent plane then n o v o = 0 (orthogonal) n ot v o = 0 n ot (M -1 M)v o = 0 ((M -1 ) T n o ) T M v o = 0 n T w v w = 0 11/18/

29 Lighting recap 11/18/

30 Shadows Check if anything is between light and intersection point (ip) that would block light Send a ray from ipto each light to check if light illuminates ip Light blocked, tint = 0, otherwise tint = 1 Will modify later for transparency 11/18/

31 Shadows Ray cannot start at ipdue to rounding errors When finding intersections, use a minimum acceptable value of t to be some eps> 0 11/18/

32 Ideal reflection Mirror reflection by law of reflection The incident and reflected ray form the same angle with the surface normal The incident and reflected ray and surface normal all lie in the same plane In polar coordinates: θ = θ and φ = φ + π Forview ray land (normalized) normal n r r = -l + 2 (l n) n i r i 11/18/

33 Ideal reflection Geometry of Reflection law Geometry of refraction law l n r θ 1 Medium 1 θ i θ r Medium 2 θ 2 11/18/

34 Ideal reflection Total reflection Transition from optically dense to less dense material n 2 < n 1 Rays refracted away from the surface normal There exists an incident angle θ T with refraction angle of 90º Once θ T is exceeded All light reflected on the boundary between media Total reflection = 2 1 n sin θ T. n Medium 1 Medium 2 θ T 11/18/