MIT-SCIENCE-Lectures-38emp_empres

本科： SH2701: Thermal-Hydraulic in Nuclear Energy Engineering, 6 ECTS credits SH2702: Nuclear Reactor Technology, 8 ECTS credits SH2703: Reactor Dynamics and Stability, 6 ECTS credits Project Course in Nuclear Energy Technology, as a part of course 4A1609 Undergraduate courses in previous years 研究生 Advanced Course in Thermal Hyቤተ መጻሕፍቲ ባይዱraulics, 9 ECTS credits
Nuclear Power Reactors（核电站反应堆） Thermal-hydraulics for Nuclear Systems（热工水力） Reactor Safety Analysis（反应堆安全分析） Introduction to Plasmas（等离子体导论） Fusion Reactor Technology（聚变反应堆技术） Engineering Principles of Radiation Imaging（辐射成像工程原理） Radiological Health Engineering Fundamentals（放射卫生工程基础） Special Topics in Nuclear Engineering and Radiological Sciences（核工程与放射科学专 题） Research in Nuclear Engineering and Radiological Sciences（核工程与放射科学研究） 500level Quantum Mechanics in Neutron-Nuclear Reactions（中子核反应中的量子力学） Interaction of Radiation and Matter（射线与材料相互做用） Nuclear Measurements Laboratory（核测量实验室） Advanced Radiation Measurements and Imaging（先进辐射测量和成像） Radiation Materials Science I/II/III（辐射材料科学） Nuclear Fuels（核燃料） Nuclear Waste Management（核废料管理） Detection Techniques of Nuclear Non-proliferation（防扩散探测技术） Nuclear Reactor Theory II（核反应堆理论） Monte Carlo Methods（蒙特卡罗方法） Thermal Fluids for Nuclear Reactor Safety Analysis（反应堆安全中的热工流体） Nuclear Reactor Kinetics（反应堆动力学） Radiation Shielding Design（辐射屏蔽设计） Nuclear Core Design and Analysis I/II（堆芯设计分析） Intermediate Plasma Physics I/II（中间等离子体物理） Plasma Engineering（等离子体工程） Plasma Generation and Diagnostics Laboratory（等离子体产生和诊断实验室） Charged Particle Accelerators and Beams（带点粒子加速器和束流） Plasma Spectroscopy（等离子体光谱学） Physical Processes in Plasmas（等离子体中的物理过程）

6.837Introduction to Computer GraphicsAssignment3:Ray Tracing and Phong MaterialsDue Wednesday October1,2003at11:59pm This week,we add local and global illumination to our Ray Caster.Because we cast secondary rays to account for shadows,reflection and refraction,we now call it a Ray Tracer.We clean up and improve shading calculation(local illumination).We define an abstract material class and derive a Phong Material class that implements a diffuse and a specular component(highlight).You will encapsulate the high-level computation in a RayTracer class that will be responsible for sending rays and recursively computing colors along them.To compute cast shadows,you will send rays from the visible point to the light source.If an intersection is reported,the visible point is in shadow and the contribution from that light source is ignored.Note that shadow rays must be sent to all light sources.You will add reflection and refraction effects.For this,you need to send sec­ondary rays in the mirror and transmitted directions,as explained in class.The computation is recursive to account for multiple reflections and or refractions. 1Tasks• Implement an abstract Material class and derive a PhongMaterial class that computes Phong shading.• Update your intersection routines to return the Material of the intersected object,instead of just a simple color.• Create a new class RayTracer that computes radiance(color)along a ray.Update your main function to use this class for the rays through each pixel.• Treat the case of multiple light sources by accumulating shading contri­butions for all light sources.• Compute cast shadows by sending rays toward the light sources.1• Compute perfect mirror reflection by sending rays recursively in the mirror direction.• Compute transparency effects by sending rays recursively in the refracted direction.• Provide a README.txtfile that discusses any problems you encountered, how long it took to complete the assignment,any extra credit work that you did and how we can test the new features.• Extra credit:semi-transparent shadows where the attenuation depends on the distance traveled in the transparent object;nested refracting materials;shadow ray acceleration using early termination and without returning the normal and material;Fresnel reflection term;other BRDF models such as Cook-Torrance or Ward;anisotropic BRDFs;solid textures.2Classes you need to update/writeThe Object3D and Hit classes must now store more detailed information about the properties of the surface,encapsulated in a Material class.You must update your Object3D class(and the constructors of all subclasses)to replace the color by a pointer to a Material.You must also update your intersection routines so that they return a pointer to a Material and not a color in case of an intersection.2.1Material and PhongMaterialThe Material class has a pure virtual method Shade that computes the local interaction of light and the material.It takes as input the viewing ray,the Hit data structure,and light information.virtual Vec3f Material::Shade(const Ray&ray,const Hit&hit,const Vec3f&dirToLight,const Vec3f&lightColor)const=0;In addition to the diffuse object color used in the last assignment,the Material class stores information about transparency and reflection.It must store two colors for the reflection and transparency coefficients,and an index of refraction.You must implement accessor functions for thesefields. Material::Material(const Vec3f&diffuseColor,const Vec3f&transparentColor,const Vec3f&reflectiveColor,float indexOfRefraction);You must derive a subclass PhongMaterial that computes shading using both a diffuse and specular term.The class takes as additional parameters a specular color and a scalar exponent.The constructor expected by the parser is:2PhongMaterial::PhongMaterial(const Vec3f&diffuseColor, const Vec3f&specularColor,float exponent,const Vec3f&transparentColor,const Vec3f&reflectiveColor,float indexOfRefraction);Implement the PhongMaterial::Shade function using the version of the Phong model taught in class based on the angle between the eye ray and the reflected ray.2.2RayTracerThe RayTracer class encapsulates the computation of radiance(color)along rays.It stores a pointer to the SceneParser for access to the geometry and light sources.The constructor is:RayTracer(SceneParser*s,int max_bounces,float min_weight);The main method of this class is traceRay that,given a ray,computes the color seen from the origin along the direction.This computation can be recur­sive because of reflection and refraction.We therefore need a stopping criterion to prevent infinite recursion.traceRay takes as additional parameters the cur­rent number of bounces(recursion depth)and a ray weight that indicates how much the contribution will be dimmed in thefinal image.The corresponding maximum recursion depth and the minimum ray weight arefields of RayTracer, which are passed as command line arguments to the program.Note that the weight is a scalar that corresponds to the magnitude of the color vector.Vec3f traceRay(Ray&ray,float tmin,int bounces,float weight,float indexOfRefraction,Hit&hit)const;First,implement traceRay so that it computes the closest intersection with the scene and performs shading.For ambient lighting,you should use the getDiffuseColor method of the Material pointer stored by Hit and mul­tiply it by the ambient light of the SceneParser.Add the contributions of the light sources in the scene by iterating over the light sources stored by the SceneParser and call the Shade method of the Material.ShadowsNext,you need to implement cast shadows.Modify the code described above to test for each light whether the line segment joining the intersection point and the light source intersects an object.If there is an intersection,then discard the contribution of that light source.Recall that you must displace the ray origin slightly away from the surface,or equivalently set tmin as�.Note that in this ¨naive version,semi-transparent objects still cast opaque shadows.Implement something better for extra credit.3Mirror reflectionYou will then implement mirror reflection.This involves the use of secondary rays in the direction symmetric with respect to the normal.If the material isreflective(getReflectiveColor()>(0,0,0)),then you must create a new ray with origin the current intersection point,and direction the mirror direction. For this,we suggest you write a function:Vec3f mirrorDirection(const Vec3f&normal,const Vec3f&incoming);Trace the secondary ray with a recursive call to traceRay using modified values for the recursion depth and ray weight.The ray weight is simply mul­tiplied by the magnitude of the transparency color.Make sure that traceRay checks these stopping conditions.For the attenuation,check if the magnitude of the color is smaller than the maximum weight.Add the reflected contributionto the color computed for the current ray.Don’t forget to take into account thereflection coefficient of the material.RefractionFinally,you will implement the computation of transmitted rays.For semi­transparent objects,you will trace a new ray in the transmitted direction.We suggest you implement a function transmittedDirection that given an inci­dent vector,a normal and the indices of refraction,returns the transmitted direction.bool transmittedDirection(const Vec3f&normal,const Vec3f&incoming, float index_i,float index_t,Vec3f&transmitted);Be careful about the direction of the vectors and the ratio of indices.We make the simplifying assumption that our transparent objects exist in a vacuum, with no intersecting or nested refracting materials.This allows us to determine the incident and transmitted index of refraction simply by looking at the dot product between the normal and the incoming ray.Indeed,because we now consider transparent objects,we might hit the surface of a primitive from either side,depending on whether we were inside or outside the object.Note that the dot product of the normal and ray direction is negative when we are outside the object,and positive when we are inside.You will use this to detect whether the new index of refraction is1or the index of the hit object.(The index of refraction for the material surrounding the ray origin is passed as an argumentto traceRay.)If you are inside the object,you mustflip the normal before computing the transmitted direction.It is not necessary toflip the normal when computing the direction of the reflected ray(you’ll get the same answer). For shading,use the original normal.4RecapTo summarize,the color returned by traceRay is the sum of the ambient contri­bution,the shading contribution of the visible light sources,the mirror reflection and the transmitted contribution.3Updated Utilities ProvidedHit.hHit has been modified to store the material of the intersection point.We provide you with the updatedfile.Light(light.h)Updated to include point light sources.Also getIllumination()now also provides the distance to the light source,which is important for shadow rays.Parsing inputfiles(scene_parser.h,and scene_parser.C) Thesefiles have been updated to parse the point light sources and Phong materials.The PhongMaterial constructor you will write is called from the parser.Look in the scene_parser.Cfile for details.Command line argumentsIn addition to the parameters used in the previous assignments,your pro­gram should take the maximum number of bounces,and the cutofffor ray weight as command line arguments.Make sure the following example works,as this is how we will test your program:raytracer-input scene.txt-output out.tga-bounces5-weight0.014Hints• You do not need to declare virtual all methods in a class,only the ones which subclasses will override.• Print as much information as you need for debugging.When you get weird results,don’t hesitate to use simple cases,and do the calculations manually to verify your results.Perhaps instead of casting all the rays needed to create an image,just cast a single ray(and its corresponding ray tree).• Modify the test scenes to reduce complexity for debugging:remove ob­jects,remove light sources,change the parameters of the materials so that you can view the contributions of the different components,etc.• Comment your code,we take this into account when grading.5。

pi j m ) pi j p1 p2 ) pi j 1
pn + 1
2
Lecture 13: Lecture Notes
The rst implication follows by substituting the de nition of m. The second follows because pi divides the product p1p2 pn, and so must divide 1 in order to divide the sum. But no prime divides 1, so we have a contradiction. Therefore, there are an in nite number of primes. Proving that the set of primes is in nite is relatively easy, but the next example shows that determining whether a set is nite or in nite can be tricky.
De nition An in nite set S is said to be countably in nite i there exists a bijection f : N 7! S .
A set is countable if it is nite or countably in nite. Many familiar sets are countable: N , the even numbers, primes, integers modulo a constant k, etc. The formal de nition of a countable set is equivalent to the notion of a listable set, since listing the elements of a set gives a bijection with N and vice-versa. If we can list the elements of S as s0 s1 s2 : : : , then we can construct a bijection f : N 7! S de ned by f (i) = si. In the reverse direction, if we have such a bijection, then f (0) f (1) f (2) : : : is a list of all the elements of S . Sometimes we can list the elements of a set S , but the corresponding bijection f : N 7! S is very hard to compute. For example, in principle we could list the elements in any subset of N . However, most of these subsets are bizarre and di cult to describe writing a program to compute f (i) might be di cult or even impossible. The good news is that to prove that S is countable, we must only prove that a bijection f : N 7! S exists we do not have to write f explicitly or to give an algorithm to compute f (i).

Massachusetts Institute of Technology 6.042J/18.062J: Mathematics for Computer Science Professor Tom Leighton
Lecture 1 5 Sep 97
What is a Proof? 1 What is a Proof?
Axiom 1 If a = b and b = c, then a = c.
This seems very reasonable! But sometimes the right choice of axiom is not clear.
Axiom 2 (Euclidean geometry) Given a line l and a point p not on l, there is exactly one line
many lines through p parallel to l.
No one of the three preceding axioms is better than the others all yield equally good proofs. Of course, a di erent choice of axioms makes di erent propositions true. Still, a set of axioms should not be chosen arbitrarily. In particular, there are two basic properties that one would want in any set of axioms it should be consistent and complete.