Sfäärikoordinaatistossa

Sfäärikoordinaatistossa, also known as spherical coordinates, is a three-dimensional coordinate system that uses a distance from a point, an angle from the positive z-axis, and an angle from the positive x-axis to describe the position of a point in space. This system is particularly useful in fields such as physics, engineering, and computer graphics.

The coordinates in a spherical coordinate system are typically denoted as (ρ, θ, φ), where:

ρ (rho) is the radial distance from the origin to the point,

θ (theta) is the polar angle, measured from the positive z-axis down to the point,

φ (phi) is the azimuthal angle, measured from the positive x-axis to the projection of the point onto the xy-plane.

The conversion between spherical coordinates (ρ, θ, φ) and Cartesian coordinates (x, y, z) is given by the following formulas:

x = ρ sin(θ) cos(φ)

y = ρ sin(θ) sin(φ)

z = ρ cos(θ)

Spherical coordinates are often used in problems involving symmetry, such as those found in physics and engineering. They are also useful in computer graphics for tasks like texture mapping and lighting calculations. However, they can be less intuitive to work with compared to Cartesian coordinates, especially for those not familiar with the underlying trigonometric relationships.