Please submit all your work as a PDF electronically on the blackboard website.  Please include all your code in the PDF.

Problem 1. (4pt) Use marching cubes algorithm to generate (1) Sphere, (2) Cylinder. A good resource is the isosurface function of Matlab, or skimage.measure.marching_cube function in Python. Report a screenshot, # of triangles and # vertices, # edges for each of them (sphere, cylinder) (3pt). Compute normal for each triangle using cross product (1pt) and display them. function in Python. Report a screenshot, # of triangles and # vertices, # edges for each of them (sphere, cylinder) (3pt). Compute normal for each triangle using cross product (1pt) and display them.

Problem 2. (1pt) Compute surface areas of the four surfaces by computing the areas of each triangle and sum over all triangles.

Problem 3. (4pt) Download a surface mesh model of your choice from the Shape Repository: http://visionair.ge.imati.cnr.it/ontologies/shapes/. Display it. Apply 45 degree rotation w.r.t z-axis and display it (1pt). Apply 2x scaling in x direction and display it (1pt). Report the number of triangles, number of faces and number of unique edges and the Euler number (2pt).