## Computer Graphics

#### Answers for End Term Question Paper (2014)

Question: What do you understand by window port and view port? Briefly describe the steps to transform an object from window port to view conversion.
Answer:
Window port:Window port is nothing but a rectangle area in the world defining the region to be displayed.

Viewport: In the interface window there is a rectangular poryion which defines that where the image will actually appear or we can say that the entire interface window but in some cases modified to be a portion of the interface window.

#### Window to Viewport mapping:

Window to viewport mapping is a process of transforming a two-dimensional world coordinate view to a particular device coordinates.The objects inside the clipped window are mapped or transformed into the viewport. The interface window on the screen displays the viewport.It is done by some formula which are derived from mathematical calculations using the coordinates of windowport and the viewport. A point at position (Xw,Yw) in the window is mapped into position (Xv,Yv) in the associated viewport to maintain the same relative placement in the viewport as in window.

Question: Scan convert the straight line using Mid point line algorithm whose end points are (0,0) and (5.5).

Answer
Question: Consider a square A(1,0) B(0,0) C (0,1) D(1,1). Rotate the square ABCD by 60 degree clockwise about the point A(1,0). Also draw the transformed square.

Answer: See answer in blog post on Problems on Transformations

Question: Prove that two successive 2-D rotations are additive in nature i.e. R(α) R(β)= R (α+β).

Answer:

Question: Reflect a diamond shaped polygon whose vertices are A(-1,0), B(0,-2), C(1,0) and D (0,2) about
(i) the horizontal line y=2 and
(ii) the vertical line x=2.

Answer:

Question: Write the properties of Bezier Curves.

Answer:

Properties Of Bezier Curve:
1. Bezier curves follow the shape of the control polygon, which have segments joining the control points.
2. They always pass through the first and the last control point.
3. A convex hull is generated which contains these control points.
4. The degree of polynomial defining the polygon is one less than the number of control points used to generate the curve. Like: for 4 control points, the degree of polynomial is 3, i.e., it would be a cubic curve.
5. The curve usually follow the shape of the defining polygon.
6. The tangent vector of Bezier Curve is always in the same direction as it is in the first and the last segment.
7. The convex hull property for Bezier Curves ensures that the polynomial smoothly follows the control points.
8. There are no such straight lines that intersect the Bezier Curves more number of times than it intersects its control polygon.
9. In these curves, moving a control point means altering the shape of the entire curve.
10. A given Bezier curve can be subdivided at a point t=t0 into two Bezier segments which join together at the point corresponding to the parameter value t=t0.
Question: Define Vanishing point.

Answer: Vanishing Point: After projection in perspective projection, a certain set of parallel lines appear to meet at some point on the projection plane. These points are called vanishing points.

The vanishing point for any set of lines that are parallel to one of the principal axis is referred to as principal Vanishing point.

We can control the number of vanishing points(one, two or three) with an orientation of the projection plane.

A vanishing point is where parallel lines that move off into the distance seem to converge. It's an artifact of perspective. For example- If you are standing on the road and the two edges/sides of the road appear to converge at a very far distance and the road appears to vanish, at that point where it seems to converge and vanish, could be called as the vanishing point.

Question: Define Primitive Instancing

Answer:
Primitive Instancing: In Primitive instancing, the modelling system defines a set of primitive 3D solid shapes that are relevant to the application area.
Primitive Instancing is often used for relatively complex objects, such as gears in bolts, that are tedious to define in terms of Boolean combinations of simpler objects.

Question: Define projections.

Answer:  Projections: A projection is a transformation from n-dimensional space to an m-dimensional space, where m < n. E.g. from 3D to 2D.

Projection of a 3D object is defined by straight projection rays, called projectors emitted from a centre of projection, passing through each point of the object, and intersecting a projection plane to form the projection.

These are known as planar geometric projections because the projection is onto a plane rather than some curved surfaces.

Projections can be divided into categories like:
• Perspective
1. One Point
2. Two Point
3. Three Point
• Parallel
1. Orthographic (projectors perpendicular to view plane)
• MultiView (Viewplane parallel to principal axis)
• Axonometric (viewplane not parallel to principal axis)
1. Isometric
2. Dimetric
3. Trimetric
2. Oblique (projectors not perpendicular to view plane)
• Cavalier
• Cabinet

A planar geometric projection constructed using parallel projectors is called a parallel projection.
If the projectors intersect at the COP, the projection is called a perspective projection.