大三05计算机图形学tracing

1、Ray Tracing1Angel: Interactive Computer Graphics 5E Addison-Wesley 2009原著Ed AngelProfessor of Computer Science, Electrical and Computer Engineering, and Media ArtsUniversity of New Mexico编辑 武汉大学计算机学院图形学课程组2Angel: Interactive Computer Graphics 5E Addison-Wesley 2009IntroductionOpenGL is based on a pi

2、peline model in which primitives are rendered one at timeNo shadows (except by tricks or multiple renderings)No multiple reflectionsGlobal approachesRendering equationRay tracingRadiosity3Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Ray TracingFollow rays of light from a point sourceCa

3、n account for reflection and transmission4Angel: Interactive Computer Graphics 5E Addison-Wesley 2009ComputationShould be able to handle all physical interactionsRay tracing paradigm is not computationalMost rays do not affect what we seeScattering produces many (infinite) additional raysAlternative

4、: ray casting5Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Ray CastingOnly rays that reach the eye matterReverse direction and cast raysNeed at least one ray per pixel6Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Ray Casting QuadricsRay casting has e the standard way to v

5、isualize quadrics which are implicit surfaces in CSG systemsConstructive Solid GeometryPrimitives are solidsBuild objects with set operationsUnion, intersection, set difference7Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Ray Casting a SphereRay is parametricSphere is quadricResulting

6、equation is a scalar quadratic equation which gives entry and exit points of ray (or no solution if ray misses)8Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Shadow RaysEven if a point is visible, it will not be lit unless we can see a light source from that pointCast shadow or feeler r

7、ays9Angel: Interactive Computer Graphics 5E Addison-Wesley 2009ReflectionMust follow shadow rays off reflecting or transmitting surfacesProcess is recursive10Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Reflection and Transmission11Angel: Interactive Computer Graphics 5E Addison-Wesley

8、 2009Ray Trees12Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Ray Tree13Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Diffuse SurfacesTheoretically the scattering at each point of intersection generates an infinite number of new rays that should be tracedIn practice, we onl

9、y trace the transmitted and reflected rays but use the Phong model to compute shade at point of intersectionRadiosity works best for perfectly diffuse (Lambertian) surfaces14Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Building a Ray TracerBest expressed recursivelyCan remove recursion

10、 laterImage based approachFor each ray .Find intersection with closest surfaceNeed whole object database availableComplexity of calculation limits object typesCompute lighting at surfaceTrace reflected and transmitted rays15Angel: Interactive Computer Graphics 5E Addison-Wesley 2009When to stopSome

11、light will be absorbed at each intersectionTrack amount leftIgnore rays that go off to infinityPut large sphere around problemCount steps16Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Recursive Ray Tracercolor c = trace(point p, vector d, int step) color local, reflected, transmitted;

12、point q; normal n; if(step max) return(background_color);17Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Recursive Ray Tracerq = intersect(p, d, status);if(status=light_source) return(light_source_color);if(status=no_intersection) return(background_color);n = normal(q);r = reflect(q, n)

13、;t = transmit(q,n);18Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Recursive Ray Tracerlocal = phong(q, n, r);reflected = trace(q, r, step+1);transmitted = trace(q,t, step+1);return(local+reflected+transmitted);19Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Computing Inter

14、sectionsImplicit ObjectsQuadricsPlanesPolyhedraParametric Surfaces20Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Implicit SurfacesRay from p0 in direction d p(t) = p0 +t dGeneral implicit surfacef(p) = 0Solve scalar equation f(p(t) = 0General case requires numerical methods21Angel: Int

15、eractive Computer Graphics 5E Addison-Wesley 2009QuadricsGeneral quadric can be written aspTAp + bTp +c = 0Substitute equation of ray p(t) = p0 +t dto get quadratic equation22Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Sphere(p pc) (p pc) r2 = 0p(t) = p0 +t dp0 p0 t2+ 2 p0 (d p0) t +

16、(d p0) (d p0) r2 = 023Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Planesp n + c = 0p(t) = p0 +t dt = -(p0 n + c)/ d n 24Angel: Interactive Computer Graphics 5E Addison-Wesley 2009PolyhedraGenerally we want to intersect with closed objects such as polygons and polyhedra rather than pla

17、nesHence we have to worry about inside/outside testingFor convex objects such as polyhedra there are some fast tests25Angel: Interactive Computer Graphics 5E Addison-Wesley 2009Ray Tracing PolyhedraIf ray enters an object, it must enter a front facing polygon and leave a back facing polygonPolyhedron is formed by intersection of planesRay enters at furthest intersection with front facing planesRay leaves at closest intersection with back facing planesIf entry is further away than ex