8/14/2019 Aml710 Major Sem2 08

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AML 710 Computer Aided DesignMajorExamination SemesterII- Session2007-08Marks: 60

Note: Answer all questions.

(3+4)

1. a) Derive a general transformation matrix for rotation about a point P(x,y).b) Determine the matrix for reflection with respect to the plane passing through theorigin and having a normal vector n=i+j+k

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(2+6)5. a) Define a graph and distinguish it from a tree. What is a binary tree? Explain the treetraversal methods.b) Discuss the salient features of Warnock algorithm for visible lines and surfaces.

(4+4)6. Consider the solid shown in the figure below. Discuss representations of the solid. using a) Half spaces b) Hyper patches (ASM).

2.a) A ',iaogle with verti,e, (2 .0)(.02) ,"d (-.2.0) ;",,",f"'med by [1'1 ~ [~1 ~]. Findthe area of the transformed triangle and verifyyour answer.

b) A surface is mapped trom parametric to xyz space using the following relations:x(u, w) = (u - W)2 y(u, w) = u - W2 z(u, w) = uw.; 0::; u ::;1;0::; w::; 1Determine the boundary curves and a point at u = w = 0,25,

3. a) What is a sweep representation? What are its advantages and }imitations?b) Discuss 2D clipping and simple visibility algorithm.I II,,----

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a) is a convenient user defined coordinate system that facilitatesgeometricconstruction,andthe softwaredoesthe necessary- beforestoring the data.b) In set theory, c(cP)= and c(PnQ) =c) The mathematical definition of cylindrical half-space isconical half space isd) In B-rep the complementary operation ofMME is -ESQUEEZE ise) The indegree and autdegree oftheroot node in an inverted binary tree arerespectively and .f) In a CSG tree with n primitives, there are Boolean operations for atotal of nodes.g) The two essential parts of floating horizon algorithm areh) The computational complexity in object space algorithms grows as

and the same in images space grows asi) initializes the database in Euler operations and its complement isj) Topologically, a I-manifold curve ishomeomorhpic to ~ and a 2~manifold surface is homeomorphic tok) Sweep representation is called~modeling shceme.I) In 2D clipping the end point coding identifiesneighboring regions whereas in 3D case this becomesm) Thefour typesof cubic splineendconditionsare-andn) For knot values within the knot vector athe basis functions.

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