Cpsc 591/691 Rendering




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CPSC 591/691 Rendering





Assignment 4 handed out: March 27

Assignment 4 due: April 15




  1. Show that the one-dimensional triangular “hat” function is the convolution of two identical box functions (see textbook figure 4.11 a) and b).




  1. What is the relationship between the convolution in the question 1 and B-splines?




  1. Interpolate in the plane between (1, 1), (2, 1) and (3, 2) using a) Lagrange interpolation b) Bezier curves c) B-splines.




  1. List the pros and cons of each of the following shadow algorithms: integration of shadow polygons with a scan line hidden surface removal algorithm, shadow generation based on transformations and clipping, shadow volumes, shadow computation with a shadow buffer, shadow computation in a recursive ray tracer, and shadow computation by the radiosity method.




  1. An object should be moved as follows: a) First, translate by 3 in X. b) Then rotate by 45 degrees clockwise about the origin. c) Then translate by 2 in Y. d) Finally rotate by another 45 degrees clockwise about the origin.

Show that these operations could be simplified into one translation followed by one rotation about the origin.


Alternatively, show that the operations could be simplified into one rotation about the origin followed by one translation.


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