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AML 710 Computer Aided DesignMinor I Semester I- Session 2008-09

Time: 1 hr - Marks: 25

Note: Answer all the questions

1. Write the most appropriate answers-that fill the blanks of the following statements.a) Scaling W.r.t causes apparent translation while that W.r.t causes

pure scaling.b) about the line x=y actually interchanges the coordinates.c) Given a point P(2,4,8), its transformed coordinates after applying translation.

d=3i-4j-5k and a uniform scaling s=1.5 are ( , -~, ).~The standard !GE~tands for~ A primitive is generally represented using - coordinate system while the

- computer display uses coordinate system.

f) If [Rj is a transformation matrix that rotates apoint by-60° then we'know that[RT rotates the point by and [R] [RTf = .

g) The 2D transformation matrices to cause translation of k units along x-axis andreflection about the liney = -x are respectively and

h) For a pure rotation matrix the can be shown to be its transpose.i) The t1Y~jn?,.q?categories of parallel projections are and -

j) In a ~rojection the angle between the projected x-axis and the. horizontal is -

k) Three properties that identify a curve generally are ,_and

(20xO,5= 10)

~ Derive transformation matrix for rotation about the origin. Extend it to the case ofrotation about an arbitrary point.

Q!Show tha~the parametric equations:: rc?sBand v = r<;ine!e.pr-~~ a o~in centeredcIrcle ofradms r. -

~ (4+3)3. Outline the procedure to obtain the perspective transformation and projection of a lineparallel to any of the coordinate axis. Define vanishing points and trace points.

(4)~ Show that the transformed area At of a polygon is related to its original area AiasAt=Ajdet[T]where the [T] is the transformation matrix.b) A triangle with vertices [2 0], [0 2] and [-2 0] is transformed by a transformationmatrix [T]=[3 2; -1 2]. Find its transformed area and verify the answer.

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