List of surfaces

Table of contents

1. Surfaces of revolution
2. Remainder

Surfaces of revolution

Sphere (Surface of a ball)

x = r*cos(u)sin(v)
y = r*sin(u)sin(v)
z = r*cos(v)
u in [0,2pi)
v in [0,pi]
r^2 = x^2+y^2+z^2

u: longitude
v: colatitude
r: radius

Torus

x = r*cos(u)sin(v)+R*cos(u)
y = r*sin(u)sin(v)+R*sin(u)
z = r*cos(v)
u in [0,2pi), v in [0,2pi)
r^2 = (R-sqrt(x^2+y^2))^2+z^2
4R^2(x^2+y^2) = (x^2+y^2+z^2+R^2-r^2)^2

R: radius of the center line
r: radius of the cross section of the tube
u: arc of vector R
v: arc of vector r

Remainder

Dini's surface

x = a*cos(u)sin(v)
y = a*sin(u)sin(v)
z = a*(cos(v)+ln(tan(v/2)))+b*u
a=1, b=1/10
u in [0,2k*pi), v in (0,pi/2]