Coordinates

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Overview

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Coordinate Systems

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Coordinate

Coordinate(name, cs=None)

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Parameters

• name (str): Name of the coordinate
• cs (CoordinateSystem, optional): Parent coordinate system

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Attributes

• dim (int): Dimension (always 1 for Coordinate)
• curvilinear (bool): Whether coordinate is curvilinear (default: False)
• coords (tuple): Tuple containing self

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Example

import dedalus.public as d3

# Create a coordinate
x = d3.Coordinate('x')

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CartesianCoordinates

CartesianCoordinates(*names, right_handed=True)

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Parameters

• names (str): Names for each coordinate axis
• right_handed (bool, optional): Whether 3D system is right-handed (default: True)

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Attributes

• dim (int): Number of dimensions
• coords (tuple): Tuple of Coordinate objects
• curvilinear (bool): Always False for Cartesian

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Example

import dedalus.public as d3

# 2D Cartesian coordinates
coords = d3.CartesianCoordinates('x', 'y')

# 3D Cartesian coordinates
coords = d3.CartesianCoordinates('x', 'y', 'z')

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SphericalCoordinates

SphericalCoordinates(azimuth, colatitude, radius)

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Parameters

• azimuth (str): Name of azimuthal coordinate (φ)
• colatitude (str): Name of colatitude coordinate (θ)
• radius (str): Name of radial coordinate (r)

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Attributes

• dim (int): Always 3
• curvilinear (bool): Always True
• spin_ordering (tuple): Component ordering (-1, +1, 0)
• right_handed (bool): Always False

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Methods

x, y, z = SphericalCoordinates.cartesian(phi, theta, r)
# x = r * sin(θ) * cos(φ)
# y = r * sin(θ) * sin(φ)  
# z = r * cos(θ)

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Example

import dedalus.public as d3
import numpy as np

# Create spherical coordinates
coords = d3.SphericalCoordinates('phi', 'theta', 'r')

# Use in a domain
basis = d3.SphereBasis(coords, (32, 64), radius=1)

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S2Coordinates

S2Coordinates(azimuth, colatitude)

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Parameters

• azimuth (str): Name of azimuthal coordinate
• colatitude (str): Name of colatitude coordinate

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Attributes

• dim (int): Always 2
• curvilinear (bool): Always True
• spin_ordering (tuple): Component ordering (-1, +1)

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Example

import dedalus.public as d3

coords = d3.S2Coordinates('phi', 'theta')

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PolarCoordinates

PolarCoordinates(azimuth, radius)

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Parameters

• azimuth (str): Name of azimuthal coordinate
• radius (str): Name of radial coordinate

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Attributes

• dim (int): Always 2
• curvilinear (bool): Always True
• spin_ordering (tuple): Component ordering (-1, +1)

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Methods

x, y = PolarCoordinates.cartesian(phi, r)
# x = r * cos(φ)
# y = r * sin(φ)

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Example

import dedalus.public as d3

coords = d3.PolarCoordinates('phi', 'r')
basis = d3.DiskBasis(coords, (32, 64), radius=1)

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DirectProduct

DirectProduct(*coordsystems, right_handed=None)

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Parameters

• coordsystems: Coordinate system objects to combine
• right_handed (bool, optional): For 3D systems, whether right-handed

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Attributes

• dim (int): Sum of component system dimensions
• coords (tuple): Flattened tuple of all coordinates
• coordsystems (tuple): Component coordinate systems

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Example

import dedalus.public as d3

# Combine Cartesian and radial
cart = d3.CartesianCoordinates('x', 'y')
radial = d3.Coordinate('z')
coords = d3.DirectProduct(cart, radial)

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See Also

• Basis - Spectral bases on coordinate systems
• Field - Fields defined on coordinate systems
• Operators - Differential operators in various coordinate systems