Transforms

GeometricTransform

A method to transform the geometry (e.g. coordinates) of objects. See https://en.wikipedia.org/wiki/Geometric_transformation.

CoordinateTransform

A method to transform the coordinates of objects. See https://en.wikipedia.org/wiki/List_of_common_coordinate_transformations.

inverse(transform)

Returns the inverse transform of the transform.

See also isinvertible.

isinvertible(transform)

Tells whether or not the transform is invertible, i.e. whether it implements the inverse function. Defaults to false for new transform types.

Transforms can be invertible in the mathematical sense, i.e., there exists a one-to-one mapping between input and output spaces.

See also inverse, isrevertible.

Rotate(R)

Rotate geometry or domain with rotation R from Rotations.jl.

Rotate(u, v)

Rotation mapping the axis directed by u to the axis directed by v. More precisely, it maps the plane passing through the origin with normal vector u to the plane passing through the origin with normal vector v.

Rotate(θ)

Rotate the 2D geometry or domain by angle θ, in radians, using the Angle2d rotation.

Examples

Rotate(one(RotXYZ{Float64})) # identity rotation
Rotate(AngleAxis(0.2, 1.0, 0.0, 0.0)) # rotate 0.2 radians around X axis
Rotate(rand(QuatRotation{Float64})) # random rotation
Rotate(Vec(1, 0, 0), Vec(1, 1, 1)) # rotation from (1, 0, 0) to (1, 1, 1)
Rotate(π / 2) # 2D rotation with angle in radians

Translate(o₁, o₂, ...)

Translate coordinates of geometry or mesh by given offsets o₁, o₂, ....

Scale(s₁, s₂, ...)

Scale geometry or domain with strictly positive scaling factors s₁, s₂, ....

Examples

Scale(1.0, 2.0, 3.0)

Affine(A, b)

Affine transform Ax + b with matrix A and vector b.

Examples

Affine(AngleAxis(0.2, 1.0, 0.0, 0.0), [-2, 2, 2])
Affine(Angle2d(π / 2), SVector(2, -2))
Affine([0 -1; 1 0], [-2, 2])

Stretch(s₁, s₂, ...)

Stretch geometry or domain outwards with strictly positive scaling factors s₁, s₂, ....

Examples

Stretch(1.0, 2.0, 3.0)

StdCoords()

Standardize coordinates of all geometries to the interval [-0.5, 0.5].

Examples

julia> CartesianGrid(10, 10) |> StdCoords()
10×10 CartesianGrid{2,Float64}
  minimum: Point(-0.5, -0.5)
  maximum: Point(0.5, 0.5)
  spacing: (0.1, 0.1)

Proj(CRS)
Proj(code)

Convert the coordinates of geometry or domain to a given coordinate reference system CRS or EPSG/ESRI code.

Optionally, the transform samples the boundary of polytopes, if this option is true, to handle distortions that occur in manifold conversions.

Examples

Proj(Polar)
Proj(WebMercator)
Proj(Mercator{WGS84Latest})
Proj(EPSG{3395})
Proj(ESRI{54017})

Notes

• By default, only the vertices of the polytopes are transformed, disregarding distortions that occur in manifold conversions. To handle this case, use TransformedGeometry.

Morphological(fun)

Morphological transform given by a function fun that maps the coordinates of a geometry or a domain to new coordinates (coords -> newcoords).

Examples

ball = Ball((0, 0), 1)
ball |> Morphological(c -> Cartesian(c.x + c.y, c.y, c.x - c.y))

triangle = Triangle(Point(LatLon(0, 0)), Point(LatLon(0, 45)), Point(LatLon(45, 0)))
triangle |> Morphological(c -> LatLonAlt(c.lat, c.lon, 0.0m))

Notes

• By default, only the vertices of the polytopes are transformed, disregarding distortions that occur in manifold conversions. To handle this case, use TransformedGeometry.

LengthUnit(unit)

Convert the length unit of coordinates of a geometry or domain to unit.

Examples

LengthUnit(u"cm")
LengthUnit(u"km")

Shadow(dims)

Project the geometry or domain onto the given dims, producing a "shadow" of the original object.

Examples

Shadow(:xy)
Shadow("xz")
Shadow(1, 2)
Shadow((1, 3))

Slice(x=(xmin, xmax), y=(ymin, ymax), z=(zmin, zmax))
Slice(lat=(latmin, latmax), lon=(lonmin, lonmax))

Retain the domain elements within x limits [xmax,xmax], y limits [ymax,ymax] and z limits [zmin,zmax] in length units (default to meters), or within lat limits [latmin,latmax] and lon limits [lonmin,lonmax] in degree units.

Examples

Slice(x=(1000km, 3000km))
Slice(x=(1000km, 2000km), y=(2000km, 5000km))
Slice(lon=(0°, 90°))
Slice(lon=(0°, 45°), lat=(0°, 45°))

Repair(K)

Perform repairing operation with code K.

Available operations

• K = 0: duplicated vertices and faces are removed
• K = 1: unused vertices are removed
• K = 2: non-manifold faces are removed
• K = 3: degenerate faces are removed
• K = 4: non-manifold vertices are removed
• K = 5: non-manifold vertices are split by threshold
• K = 6: close vertices are merged (given a radius)
• K = 7: faces are coherently oriented
• K = 8: zero-area ears are removed
• K = 9: rings of polygon are sorted
• K = 10: outer rings of polygon are expanded
• K = 11: rings of polygon are coherently oriented
• K = 12: degenerate rings of polygon are removed

Examples

# remove duplicates and degenerates
mesh |> Repair(0) |> Repair(3)

Bridge(δ=0)

Transform polygon with holes into a single outer ring via bridges of given width δ as described in Held 1998.

References

• Held. 1998. FIST: Fast Industrial-Strength Triangulation of Polygons

LambdaMuSmoothing(n, λ, μ)

Perform n smoothing iterations with parameters λ and μ.

See also LaplaceSmoothing, TaubinSmoothing.

References

• Taubin, G. 1995. Curve and Surface Smoothing without Shrinkage

LaplaceSmoothing(n, λ=0.5)

Perform n iterations of Laplace smoothing with parameter λ.

References

• Sorkine, O. 2005. Laplacian Mesh Processing

TaubinSmoothing(n, λ=0.5)

Perform n iterations of Taubin smoothing with parameter 0 < λ < 1.

References

• Taubin, G. 1995. Curve and Surface Smoothing without Shrinkage