Funny Scalar Fields (Heat Maps) on a Surface

Heat Map on a Torus

Heat Map on a Torus

Scalar Field on a Torus

Scalar Field on a Möbius Strip

Scalar Field on a Möbius Strip

( Mathematical software used: gnuplot )

Funny Inequalities on a Torus

(1)

(2-1)

(2-2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

(10)

(11)

(12)

( Mathematical software used: gnuplot )

Rounded Cuboid with Superquadric Corners

The corners of the rounded cuboids on my previous post are spherical corners.

We can generalize the spherical corners (power = 2) to superquadric corners (power > 0).

Equation 1.

The equation for a rounded cuboid with superquadric corners can be given by:

       max(|x| - a, 0)^p + max(|y| - b, 0)^p + max(|z| - c, 0)^p = d^p,

where a, b, c, d ＞ 0, and p ≧ 1.

p = 1

p = 1.5

p = 2

p = 4

p = 10

Equation 2.

Furthermore, the above equation can be generalized as follows:

       max(|x| - a, 0)^p + max(|y| - b, 0)^q + max(|z| - c, 0)^r = d,

where a, b, c ≧ 0, d ＞ 0, and p, q, r ＞ 0.

Related posts:

• Equation of a Rounded Rectangle

Funny Equations - 3D surfaces

( Softwares used: MathGL - UDAV, gnuplot )