UNIT III

1. Explain reflection and shear?

Reflection

• It is a mirror image of an object

• Rotating about 180 degree

• Flat object moving in the xy plane

• Reflection about y axis flips x coordinates

• Reflection point as pivot point is same as above

• To obtain the transformation matrix for reflection diagonal

is y = -x

• Sequence

• Clockwise rotation by 45 degree

• Reflection about y axis

• Counter wise rotation by 45 degree

Shear

• Internal layer cause to slide over each other called shear

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• Transforms coordinate position as

X ‘= x + shx . y’ , Y’ = y

• Shift in the position of objects relative to shearing reference

lines are equivalent to translations

2. Explain Liang Barsky line clipping

• Faster line clipper of the parametric equation of a line

segment

• Line parallel to one of the clipping boundaries

• Line intersects the extension of boundary k

• If u1 > u2 line is outside the clipping window

• Else inside the clipping window

• Clipping is done using the reflection in the clip window

3. Explain Sutherland Hodgeman polygon clipping

• Clipping polygon which lies inside the clipping window

• Four possible cases

• If the first vertex is outside the window

boundary and the second vertex inside

• If the first vertex is inside the window

boundary and the second vertex outside

• If both are outside

• If both are inside

• Repeat the process of algorithm

• Convex polygon are correctly clipped using this clipping

• Concave and convex polygon are also used

4. Explain about clipping operations

• Clip a picture from either outside or inside a region known

as clipping

• Also called as clipping algorithm

• The region against the object is known as clip window

• Clipping operations on different types of objects

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• Point clipping

• Polygon clipping

• Area clipping

• Line clipping

• Curve clipping

• Text clipping

• Polygon and line clipping are the standard clipping

components

UNIT IV

1. Explain the three dimensional display methods?

• Parallel projection

• The production of the 2D display of the 3D scene is

called projection

• Project points on the object surface along the parallel

lines on to the display plane

• Different 2D views of objects can be produced by

projecting the visible points

• Perspective projection

• Done by the projecting points to the display plane

along the converging points

• Causes the objects farther from the viewing point

should be smaller of the same sized object present here.

• Depth CUEING

• Basic problem for visualization techniques is called

depth cueing

• Some 3D objects are without depth information

• Visible line and surface identification

• To highlight the visible lines

• Display visible lines as dashed lines

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• Removing the invisible lines

• Surface rendering

• Lightening conditions in the screen

• Assigned characteristics

• Degree of transparency

• How rough or smooth the surfaces are to be

• Exploded and cutaway views

• Three dimensional and stereoscopic views

2. Explain spline representation

• It is referred to a curve drawn in a different manner

• Interpolation and approximation splines

• Set of coordinate points called control points

• Curve can be translated , rotated and scaled

• Enclosing a set of points called convex hull

• Set of connected points is often called control graph

• Parametric continuity condition

• Geometric continuity condition

• Spline specification

3. Explain Bezier curves and surfaces

• Have number of properties

• Can be fitted to any number of control points

• Polynomial functions between p0 and pn

n

P(u) = Σ pk BEZ k,n(u)

K = 0

• Calculated x(u), y(u), z(u)

• Properties of Bezier curves

• Cubic Bezier curves

• Design techniques in Bezier curves

• Bezier surfaces

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4. Explain general three dimensional rotations

• Transformation sequences

• P’ = T’.Rx (θ) .T.P

• Rotation in five steps

• Translate the object that rotates in parallel coordinate

axis

• Rotate the object with one coordinate axis

• Apply inverse rotation to its original position

• Apply inverse translation to its original position

• V = p2 – p1

• After rotation to original position

R( θ ) = T’.M.T

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