Points

All docstrings from Mantis.Points

Mantis.Points Module

module Points

Contains all definitions of points used to evaluate geometries, function spaces, forms and any other objects.

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Mantis.Points.AbstractPoints Type

AbstractPoints{manifold_dim}

Supertype for all evaluable points.

Type parameters

• manifold_dim: Dimension of the manifold where the points are evaluated.

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Mantis.Points.CartesianPoints Type

CartesianPoints{manifold_dim, T, CI, LI} <: AbstractPoints{manifold_dim}

Represents a set of points constructed from manifold_dim lists of uni-dimensional points. Conceptually, this structure combines the functionalities of CartesianIndices and Iterators.product.

Fields

• constituent_points::NTuple{manifold_dim, T}: The set of points per manifold dimension.

• cart_num_points::CI: The CartesianIndices used to convert from linear to cartesian indexing.

• lin_num_points::LI: The LinearIndices used to convert from cartesian to linear indexing.

• iteration_order::NTuple{manifold_dim, Int}: Used to determine the iteration order over

`cart_num_points`. If the `dim`-th entry has value `i`, then dimension `dim` will be the
`i`-th fastest changing index.

• permuted_cart_num_points::CI: A permuted version of cart_num_points as given by

`iteration_order`.

Example

julia> points = Points.CartesianPoints(([1,2], [1,2,3]), (1,2));

julia> for point in points
           display(point)
       end
(1, 1)
(2, 1)
(1, 2)
(2, 2)
(1, 3)
(2, 3)

julia> points = Points.CartesianPoints(([1,2], [1,2,3]), (2,1));

julia> for point in points
           display(point)
       end
(1, 1)
(1, 2)
(1, 3)
(2, 1)
(2, 2)
(2, 3)

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Mantis.Points.PointSet Type

PointSet{manifold_dim, T} <: AbstractPoints{manifold_dim}

Represents a set of points in manifold_dim dimensions.

Fields

• constituent_points::NTuple{manifold_dim, T}: The set of points per manifold dimension.

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Mantis.Points.get_cart_num_points Method

get_cart_num_points(points::CartesianPoints)

Returns the CartesianIndices used to convert from linear to cartesian indexing.

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Mantis.Points.get_constituent_num_points Method

get_constituent_num_points(
  points::CartesianPoints{manifold_dim}
) where {manifold_dim}

Returns the number of constituent points per manifold dimension.

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Mantis.Points.get_constituent_points Method

get_constituent_points(points::P) where {P <: AbstractPoints}

Returns the constituent points of points per manifold dimension.

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Mantis.Points.get_iteration_order Method

get_iteration_order(points::CartesianPoints)

Returns the iteration_order order used to index points.

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Mantis.Points.get_lin_num_points Method

get_cart_num_points(points::CartesianPoints)

Returns the LinearIndices used to convert from cartesian to linear indexing.

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Mantis.Points.get_manifold_dim Method

get_manifold_dim(points::AbstractPoints{manifold_dim}) where {manifold_dim}

Returns the manifold dimension of the evaluable points.

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Mantis.Points.get_num_points Method

get_num_points(points::P) where {manifold_dim, P <: AbstractPoints{manifold_dim}}

Returns the number of of evaluable points in the given point structure.

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Mantis.Points.get_permuted_cart_num_points Method

get_permuted_cart_num_points(points::CartesianPoints)

Returns the permuted cart_num_points used to index points, as given by iteration_order.

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Mantis.Points.scale_and_shift_points Method

scale_and_shift_points(
    points::P, scalings::S, translations::T
) where {
    manifold_dim,
    P <: AbstractPoints{manifold_dim},
    S <: NTuple{manifold_dim, Real},
    T <: NTuple{manifold_dim, Real},
}

Applies an affine map defined by scalings and translations to each point in points.

Arguments

• points::P: The set of points.

• scalings::S: The scaling of the affine map.

• translations::T: The translation of the affine map.

Returns

• transformed_points::P: The set of transformed points of the same type as the original

`points`.

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