BCA Semester 5 – Computer Graphics and Animation – Unit 2: Two dimensional and three dimensional transformations (7Hrs)

Explain 3D basic geometric transformation with an example.

Derive the formula for windows to viewport transformation. Given a window bordered by (0,0) at the lower left and (4,4) at the upper right. Similarly, a viewport bordered by (0,0) at the lower left and (2,2) at the upper right. If a window at position (2,4) is mapped into the viewport. What will be the position of viewport to maintain same relative placement as in window.

Define scaling transformation? Prove that two successive scaling are multiplicative.

Define window and view port. Explain 2D viewing transformation pipeline.

Reflect a prism A(0,0,0), B(1,1,0), C(1,2,2) and (0,2,0) about yz-plane which has been rotated previously with +90 degree about y-axis.

What do you mean by window to viewport transformation? Explain 2D viewing pipeline.

Define reflection transformation and derive the 2D reflection matrix along x-axis and y-axis in homogeneous coordinate.

What is the need of homogeneous coordinate system in geometric transformation system? Find the new co-ordinate of rectangle ABCD whose center is at (4, 2) is reduced to half of its size and center will remain same. The co-ordinate of ABCD are A(0, 0), B(0, 4), C(8, 4) and D(8, 0).

What is a viewport? Consider a window with lower left corner at (2, 2) and upper right corner (5, 10) and a viewport with left lower corner at (3, 5) and upper right corner at (8, 8). What will be the value of the point in the viewport after the window to viewport transformation if the point is (4, 4) in the window?

Derive the transformation matrices for 3D rotation and reflections.

Differentiate between boundary fill algorithm and flood fill algorithm in detail. Find the composite transformation matrix for anti-clockwise rotation of 60° about a point (2, 3). Use it to rotate a triangle ABC with vertices A (4, 3), (5, 5) and (8, 9).

Given a triangle with vertices A(2,3), B(5,5), C(4,3) by rotating 90 degree about the origin and then translating two unit in each direction. Use homogenous transformation matrix to find the new vertices of the triangle.