Tutorial 2

1. In the table that shows the comparative costs of the various interpolation techniques (see Lecture notes 3 & 4 (ppt), page 22), the figures there have not included the cost required for computing the weights.
   Consider interpolations using the bilinear kernel.
   1. How many multiplications would be required for computing the weights? How many multiplications would therefore be required in total for bilinear interpolation (including the weight computation)?
   2. If the operation is decomposed into linear interpolations in 1-dimension, would the number of multiplications required be fewer? if so, how many multiplications would be saved?
   
   
   
2. Consider the sixteen combinations that a contour intersects a square cell as shown in Figure 6-5 (see attachment or Lecture notes 5 & 6 (ppt), page 17).  How many distinct cases are there?
   
   
3. Sketch the contour cases for marching triangles.  How many distinct cases are there?
   
   
4. Isoline contours of different values are typically shown together (as different colours) in one image.  Describe the advantages and disadvantages of displaying isoline contours simultaneously.
   
   
5. The Marching cubes algorithm visits each cell during algorithm execution.  Many of these cells do not contain the isosurface.  Describe a technique to improve the performance of isosurface extraction by eliminating visits to cells not containing the isosurface. (Hint:  Use a preprocessing step to analyse data.  Assume that many isosurfaces will be extracted and that the preprocessing step will not count against execution time.)