Q 1(b) Explain the following concepts with examples and illustrations:i) Parametric respresentation:Curves and surfaces can have explicit, implicit, and parametric representations. Parametric representations are the most common in computer graphics.Example: Parametric representation of Line: L(t) = C + btwhere parameter t distinguishes one point on the line L from another point. Also b = B C as this straight line is defined by points B and C. ii) 3D wireframe model:The lowest level of realism is wireframe model in which only edges of each object is drawn and we can see right through an object.Example: Following is a wireframe model of a cube:

Q2 (a) Derive any TWO transformation matrices:i) Matrix representing Reflection about arbitrary line:Consider a line through the origin that makes an angle with x-axis, point A reflects into point B. We want to develop the transformation that reflects any point P about this axis, to produce point Q.To show that it is affine, we build it out of three parts:* A rotation through angle - (so that rotation axis coincides with the x-axis)* A reflection about x-axis* A rotation back through that restores the axisEach of these is represented by a transformation matrix, so this is an affine transformation & overall transformation is give by product of these three matrices:

cs0100c-s0c2 s2 -2cs 0-sc00-10sc0=-2cs s2 c2 0001001001 0 0 1

where c stands for cos() and s stands for sin().Using trigonometric identities, the final matrix for reflection about arbitrary point is given as:

cos ( 2 )sin ( 2 )0sin ( 2 )-cos ( 2 )00 01