QuestionAnswered step-by-stepDescribe the code you would generate for the JARGON virtual machine…Describe the code you would generate for the JARGON virtual machine for the body of the function sum defined above. If you need to extend the virtual machine with new instructions, then define their semantics. Give a detailed explanation of how in general GBB decides where to make its first backjump. Illustrate your answer using the example above, assuming that it is not possible to make a consistent assignment at V8.(d) In the example illustrated, assume the first backjump made is from V8 as in part (c). We find after the first backjump that the variable we have arrived at has no further consistent assignments. Give a detailed explanation of how GBB decides what to do next, including in your answer a description of the set of induced ancestors that are relevant in making the decision. Computer Graphics and Image Processing Consider the transformations used in the construction and rendering of a threedimensional model on a screen. (a) List the three principal transformations in the processing pipeline and explain their roles. (b) Why is it convenient to represent the transformations as matrices? [2 marks] (c) What are homogeneous coordinates? Explain how they are used in modelling these transformations as matrices. [2 marks] (d) Derive the matrix to represent a perspective transformation for a viewer at the origin of a point in three dimensions to a point on a screen in the plane z = d. [5 marks] (e) Perspective in classical art has vanishing points towards which parallel lines converge. Explain mathematically why this is the case and show how to calculate the location on the screen of the vanishing point for lines in a particular direction. [5 marks] [Hint: It may be helpful to represent lines parametrically in vector form as P(s) = A + sV where V is a direction and A is any point on the line.] 4 Computer Graphics and Image Processing Consider a curve defined by polynomial parametric segments Pi(s) for i = 1, 2, . . . m that interpolates a set of points {Ai}0=i=m in three dimensions. (a) What is meant by Ck continuity at the junction of two segments? [3 marks] (b) What is the least order of the polynomials that must be used to achieve Ck continuity at the junctions? [2 marks] (c) Derive the Overhauser formulation for a set of weighting functions w-2(s), w-1(s), w0(s) and w1(s) so that the cubic curve segment joining Ai-1 and Ai can be expressed as Pi(s) = w-2(s)Ai-2 + w-1(s)Ai-1 + w0(s)Ai + w1(s)Ai+1 for 1 < i < m. [10 marks] (d) Extend this formulation to give a set of paerametric patches Pi,j (s, t) for 1 < i < m and 1 < j < n interpolating a surface through an array of points {Ai,j}0=i=m,0=j=n. [5 marks] 4 CST.2015.4.5 5 Databases (a) The relational schema R(A, B, C, D, E) has the following functional dependencies. A ? E B ? D A, B ? C Decompose this into a set of relations in BCNF. Show your working. [5 marks] (b) By inspecting your answer to (a), describe a possible interpretation in the language of Entity-Relationship modelling. [5 marks] (c) Heath's Rule tells us that if R(A, B, C) is a relational schema with functional dependency A ? B, then R = pA,B(R) ?A pA,C(R). This rule is often applied in the relational decomposition process that seeks to arrive at relations in a particular normal form. For example, we might decompose R into two implemented relations R1(A, B) and R2(A, C). Some people have been very critical of this approach since it ignores the fact that the implementation of such a decomposition is normally associated with foreign key constraints between tables. What is missing? Can you express, in the relational algebra, what such a missing constraint might look like for the decomposition described above using Heath's rule? Justify your answer. [5 marks] (d) Using your answer to (c), discuss which constraints might be missing from your decomposition in question (a). package edu.ser222.m02_02;* @author Lewis et al., Acuna* @version 4.0* @param

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