capsule | catenoid | infinite cone | closed cone | finite cone | conical frustum | infinite cylinder | closed cylinder | finite cylinder | ding-dong surface | double sphere | eight surface | elliptic torus | football surface | first funnel surface | Gabriel's horn | hemisphere | horn torus | one-sheeted hyperboloid | two-sheeted hyperboloid | ... (total: 37)

double cone | Kegel surface

doubled sphere

8-dong surface | octdong surface

Toricelli's trumpet

Dullo surface

spaghetti bundle | Spindel surface

UFO surface

Hershey's chocolate kiss surface

Pilzchen surface

Gupf surface

| parametric equations catenoid | x(u, v) = a cos(u) cosh(v/a) y(u, v) = a sin(u) cosh(v/a) z(u, v) = v infinite cone | x(u, v) = a u cos(v) y(u, v) = a u sin(v) z(u, v) = u finite cone | x(u, v) = (a (h - u) cos(v))/h y(u, v) = (a (h - u) sin(v))/h z(u, v) = u conical frustum | x(u, v) = (cos(v) (a (h - u) + b u))/h y(u, v) = (sin(v) (a (h - u) + b u))/h z(u, v) = u infinite cylinder | x(u, v) = a cos(u) y(u, v) = a sin(u) z(u, v) = v finite cylinder | x(u, v) = a cos(u) y(u, v) = a sin(u) z(u, v) = v ding-dong surface | x(u, v) = a sqrt(1 - v) v cos(u) y(u, v) = a sqrt(1 - v) v sin(u) z(u, v) = a v double sphere | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = a cos(v) eight surface | x(u, v) = a cos(u) sin(2 v) y(u, v) = a sin(u) sin(2 v) z(u, v) = a sin(v) elliptic torus | x(u, v) = cos(u) (a cos(v) + c) y(u, v) = sin(u) (a cos(v) + c) z(u, v) = b sin(v) football surface | x(u, v) = (a sqrt(1 - v^2/c^2) cos(u) (b - v^4/c^4 - v^2/c^2))/b y(u, v) = (a sqrt(1 - v^2/c^2) sin(u) (b - v^4/c^4 - v^2/c^2))/b z(u, v) = v first funnel surface | x(u, v) = a u cos(v) y(u, v) = a u sin(v) z(u, v) = log(u) Gabriel's horn | x(u, v) = v y(u, v) = (a cos(u))/v z(u, v) = (a sin(u))/v hemisphere | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = a cos(v) horn torus | x(u, v) = a cos(u) (cos(v) + 1) y(u, v) = a sin(u) (cos(v) + 1) z(u, v) = a sin(v) one-sheeted hyperboloid | x(u, v) = a sqrt(u^2 + 1) cos(v) y(u, v) = a sqrt(u^2 + 1) sin(v) z(u, v) = c u two-sheeted hyperboloid | x(u, v) = a sinh(u) cos(v) y(u, v) = a sinh(u) sin(v) z(u, v) = (c u cosh(u))/sqrt(u^2) kiss surface | x(u, v) = (a sqrt(1 - v) v^2 cos(u))/sqrt(2) y(u, v) = (a sqrt(1 - v) v^2 sin(u))/sqrt(2) z(u, v) = a v lemon surface | x(u, v) = cos(u) (sqrt(R^2 - v^2) - r) y(u, v) = sin(u) (sqrt(R^2 - v^2) - r) z(u, v) = v oblate spheroid | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = c cos(v) infinite paraboloid | x(u, v) = a u cos(v) y(u, v) = a u sin(v) z(u, v) = u^2 paraboloidal segment | x(u, v) = a sqrt(u/h) cos(v) y(u, v) = a sqrt(u/h) sin(v) z(u, v) = u prolate spheroid | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = c cos(v) pseudosphere | x(u, v) = a sech(u) cos(v) y(u, v) = a sech(u) sin(v) z(u, v) = a (u - tanh(u)) pumpkin surface | x(θ, ϕ) = (a sin(ϕ) ((n + 1) cos(θ) - cos(θ (n + 1))))/n y(θ, ϕ) = (a sin(ϕ) ((n + 1) sin(θ) - sin(θ (n + 1))))/n z(θ, ϕ) = h cos(ϕ) sphere | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = a cos(v) spherical cap | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = a cos(v) spheroid | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = c cos(v) torus | x(u, v) = cos(u) (a cos(v) + c) y(u, v) = sin(u) (a cos(v) + c) z(u, v) = a sin(v) zone | x(u, v) = a cos(u) sin(v) y(u, v) = a sin(u) sin(v) z(u, v) = a cos(v) | Cartesian equation | semialgebraic description capsule | | (z - h/2)^2 + x^2 + y^2 = r^2 and z>h/2 or (h/2 + z)^2 + x^2 + y^2 = r^2 and z<-h/2 or -h/2<=z<=h/2 and x^2 + y^2 = r^2 infinite cone | z^2 = (x^2 + y^2)/a^2 | closed cone | | x^2 + y^2 = (a^2 (h - z)^2)/h^2 and 0<=z<=h or z = 0 and x^2 + y^2<=a^2 finite cone | | x^2 + y^2 = (a^2 (h - z)^2)/h^2 and 0<=z<=h conical frustum | | x^2 + y^2 = (a (h - z) + b z)^2/h^2 and 0<=z<=h infinite cylinder | x^2 + y^2 = a^2 | closed cylinder | abs(sqrt(x^2 + y^2) - a ((2 z)/h - 1)) + abs(a ((2 z)/h - 1) + sqrt(x^2 + y^2)) = 2 a | x^2 + y^2 = a^2 and 0<=z<=h or x^2 + y^2<=a^2 and z = 0 or z = h finite cylinder | | x^2 + y^2 = a^2 and 0<=z<=h ding-dong surface | x^2 + y^2 = (1 - z) z^2 | double sphere | (-a^2 + x^2 + y^2 + z^2)^2 = 0 | eight surface | a^2 (x^2 + y^2 - 4 z^2) + 4 z^4 = 0 | elliptic torus | (a^2 (z^2/b^2 - 1) - c^2 + x^2 + y^2)^2 = 4 a^2 c^2 (1 - z^2/b^2) | football surface | x^2 + y^2 = (a^2 (1 - z^2/c^2) (b - z^4/c^4 - z^2/c^2)^2)/b^2 | Gabriel's horn | y^2 + z^2 = a^2/x^2 | hemisphere | | x^2 + y^2 + z^2 = a^2 and z>=0 horn torus | (x^2 + y^2 + z^2)^2 = 4 a^2 (x^2 + y^2) | one-sheeted hyperboloid | (x^2 + y^2)/a^2 - z^2/c^2 = 1 | two-sheeted hyperboloid | (x^2 + y^2)/a^2 - z^2/c^2 = -1 | kiss surface | x^2 + y^2 = 1/2 (1 - z) z^4 | lemon surface | (r^2 - R^2 + x^2 + y^2 + z^2)^2 = 4 r^2 (x^2 + y^2) | mushroom surface | (z^3 - a^3)^2 + (-a^2 + x^2 + y^2)^3 = 0 | oblate spheroid | (x^2 + y^2)/a^2 + z^2/c^2 = 1 | infinite paraboloid | z = (x^2 + y^2)/a^2 | paraboloidal segment | | z = (h (x^2 + y^2))/a^2 and 0<=z<=h piriform surface | a^2 (y^2 + z^2) - a x^3 + x^4 = 0 | prolate spheroid | (x^2 + y^2)/a^2 + z^2/c^2 = 1 | pseudosphere | z^2 = (a sech^(-1)(sqrt(x^2 + y^2)/a) - sqrt(a^2 - x^2 - y^2))^2 | sphere | x^2 + y^2 + z^2 = a^2 | spherical cap | | x^2 + y^2 + z^2 = a^2 and z<=a - h and 0c^2 (a/(R - a) + 1)^2 and (c - sqrt(x^2 + y^2))^2sqrt((a - c - R) (a + c - R)) torus | (c - sqrt(x^2 + y^2))^2 + z^2 = a^2 | zone | | x^2 + y^2 + z^2 = a^2 and d<=z<=d + h