Summer Session 12
August 10
Construct the VRML files associated with all models in this exercise.
Location of the Cosmo Player:
 http://poncelet.math.nthu.edu.tw/software/cosmoplayerinstall.exe

HTML	MWS	WRL
12-1.Construct a surface which appears as a triangle along the x-axis,appears as a triangle along the y-axis,apprears as an astroid along the z-axisand whose z-cross section are formed by ellipses.
12-2.Construct a solid which appears as an equilateral triangle along the x-axis, appears as a half-ellipse along the y-axis, appears as a circle along the z-axis.
12-3.Construct the Klein bottle with parametric equations x=(a+cos(u/2) sin(v)- sin(u/2) sin(2v))cos(u) y=(a+cos(u/2) sin(v) - sin(u/2) sin(2v))sin(u) z = sin(u/2) sin(v) + cos(u/2) sin(2v)
12-4.Construct the hyperboloid of two sheets given by the equation x2 - y2 - z2 = 1.
12-5.Construct the smallest sphere that contains the six circles each of which is inscribed in a face of a cube.
12-6.Construct the part of the sphere x2 + y2 + z2 =1 lying outside the cylinder (x - 0.5)2 + y2 = 0.25.
12-7.Construct three tori of the same size each enclosing the other two.
12-8.Show that a certain section of a cube consists of a hexagon.
12-9.Construct the surface given by the equation (x2 + y2 + z2)2 = 2z(x2+ y2)
12-10.Construct the surface given by the equation over the square [-2, 2] x [-2,2].
12-11.Construct the same surface located above the disc
12-12.Construct the graph of the function as (x,y) ranges over the unit disc.
12-13.Construct the solid enclosed by the paraboloids z = 5x2 + 5y2 and z = 6 - 7x2 -y2.