parametric

# parametric - 4 BASIC EXAMPLES(THESE ARE THE ONES TO KNOW...

This preview shows page 1. Sign up to view the full content.

PARAMETRIC SURFACES Math21a, O. Knill HW A) Parametrize the upper half of the ellipsoid x 2 + y 2 + z 2 / 4 = 1 in three different ways: as a graph vector r ( x, y ) = ( x, y, f ( x, y )) (Euclidean coordinates), as a surface of revolution vector r ( θ, z ) = ( g ( z ) cos( θ ) , g ( z ) sin( θ ) , z ) (cylindrical coordinates) and as a deformed sphere vector r ( φ, θ ) = ( x ( φ, θ ) , y ( φ, θ ) , z ( φ, θ )) (spherical coordinates). B) The curve vector r ( t ) = ( t cos( t ) , t sin( t ) , t ) is on a surface. Find a parametrization vector r ( t, s ) of this surface. C) Parametrize the surface which has distance 1 from the unit circle in the xy plane. This is a doughnut. Use two angles θ , a rotation angle around the z axes and φ a rotation angle around the circle. D) Parametrize the paraboloid x 2 + y 2 = z in two different ways: as a graph or as a surface of revolution. E) Upload a picture for a gallery of marbles. PARAMETRIC SURFACES. The image of a map vector r ( u, v ) = ( x ( u, v ) , y ( u, v ) , z ( u, v )) defines a surface . r is called the parametrisation of the surface. The surface is defined by three functions x ( u, v )
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern