6.837 Introduction to Computer GraphicsQuiz 1: Ray TracingTuesday October 7, 2003 2:40-4pmOne hand-written sheet allowedTotal is 50 pointsName:1 Ray Tracing [ /14]1.1 Complexity [ /3]We want to render a scene of N objects with one single light source onto an image of M pixels (theimage resolution is√M ∗√M ). Any object can be reflective and refractive, but we enforce a maximumrecursion depth of K.What is the worst-case complexity of ray tracing for the total image?1.2 Light sources [ /2]How is this complexity changed when we have L light sources?1.3 Forward ray tracing [ /3]Give a 1-to-2-sentence explanation of why forward ray tracing is not directly practical.11.4 What is the bug that caused the artifacts in this image? [ /3]1.5 Which sphere has the bigger index of refraction? [ /3]22 Transformations [ /6]2.1 Matrix form [ /3]What is the 4 ×4 matrix in homogeneous coordinate form corresponding to a 3D translation by(a, b, c)?2.2 Normal transform [ /3]In a ray tracer, when an object is transformed by a linear transformation described by matrix M ,how must we transform the surface normal after ray intersection? Give both a one- or two-sentenceexplanation and a formula.3 Local shading [ /8]3.1 Coefficients [ /3]Describe what the image will look like if the scene contains no real light source but the ambient lightcolor is (1,1,1).3.2 Give a one-sentence description of the Fresnel effect. [ /3]3.3 Dimensionality of BRDFs [ /2]How many dimensions does an anisotropic BRDF have?How many dimensions does an isotropic BRDF have?34 Ray-Cylinder Intersection [ /22]yxzrRD4.1 Implicit cylinder [ /2]Give the implicit equation for an infinite cylinder centered on the z axis and with radius r.4.2 Explicit ray [ /2]Give the explicit (parametric) equation for a ray with origin R and direction D.4.3 Ray-cylinder intersection equation [ /4]Write the quadratic equation for the intersection of a ray with an infinite cylinder centered on the zaxis. Solve your equation for t.44.4 Ray-cylinder intersection pseudo code [ /8]Using the result from the previous question, write the pseudocode for the intersection methodbool Cylinder::intersect(const Ray &r, Hit &h, float tmin);Don’t forget to compute the surface normal, but don’t worry about the material.54.5 General cylinder [ /3]In your ray tracer, without writing additional code, how would you use the code from question 4.4 torender arbitrary infinite cylinders (arbitrary position and arbitrary orientation)?4.6 Non-infinite cylinders [ /3]How would you modify the code from question 4.4 to render non-infinite cylinders. That is, thecylinder only goes from z1to z2. You do not need to render the caps of the cylinder. You can assumethat z2≥
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