surface_poly_fit.core.MongeJetFitter¶

class surface_poly_fit.core.MongeJetFitter[source]¶

Bases: MongeJetFitter

Fits Monge polynomial to PolyhedralSurface patch vertices.

FittingBasisType Descriptions¶

The MongeJetFitter.fit_at_vertex() and MongeJetFitter.fit_all() methods take a fit_basis_type argument which specifies how the polynomial fitting coordinate system (fitting-basis) is calculated for a polyhedral-surface-patch:

MongeJetFitter.PCA: Uses Principal Component Analysis of the patch coordinates with the smallest component assigned to the \(z\) direction and the largest component the \(x\) direction.
MongeJetFitter.VERTEX_NORMAL: Use the vertex-normal as the polynomial fitting coordinate system \(z\) direction.
MongeJetFitter.RING_NORMAL_MEAN: Use mean of all surface-patch vertex-normals as the polynomial fitting coordinate system \(z\) direction.
MongeJetFitter.RING_NORMAL_GAUSSIAN_WEIGHTED_MEAN: Use a Gaussian-weighted-mean of all surface-patch vertex-normals as the polynomial fitting coordinate system \(z\) direction. The sigma used for calculating the Gaussian weights is num_rings / 3.0.
MongeJetFitter.RING_NORMAL_GAUSSIAN_WEIGHTED_MEAN_SIGMA: Use a Gaussian-weighted-mean of all surface-patch vertex-normals as the polynomial fitting coordinate system \(z\) direction. The sigma used for calculating the Gaussian weights is MongeJetFitter.ring_normal_gaussian_sigma.

Fitting Result Array Field Definitions¶

The MongeJetFitter.fit_at_vertex() and MongeJetFitter.fit_all() return a numpy structured array with fields:

“vertex_index” (numpy.int64): The index of the vertex at which polynomial fitting was performed.
“degree_monge” (numpy.uint8): The degree of the Monge polynomial (converted from the fitting polynomial).
“degree_poly_fit” (numpy.uint8): The degree of the fitting polynomial.
“num_rings” (numpy.int64): The number of ring neighbours defining the polynomial fitting coordinates.
“num_fitting_points” (numpy.int64): The number of neighbour coordinates (neighbours) in the “num_rings” neighbourhood. This is the number of coordinates used to fit the polynomial.
“poly_fit_condition_number” (numpy.float64): The polynomial fitting matrix condition number.
“pca_eigenvalues” (numpy.float64): A (3,) shaped array. If MongeJetFitter.PCA is used for the fitting basis determination, then these are the eigenvalues of the principal component analysis (otherwise all values are numpy.nan).
“poly_fit_basis” (numpy.float64): A (3, 3) shaped rotation matrix, indicating the orientation of the polynomial fitting coordinate-system (basis).
“poly_fit_residual_stats” (numpy.dtype): A struct containing statistics on the polynomial fitting residual values. See residual stats description.
“poly_fit_bounding_area” (numpy.dtype): A struct containing info about 2D bounding areas of the fitting coordinates. See bounding area description.
“origin” (numpy.float64): A (3,) shaped array indicating the Monge polynomial origin coordinate. The Monge polynomial intersects this coordinate. Note that the “vertex_index” coordinate is the origin of the fitting-coordinate-system.
“direction” (numpy.float64): A (3, 3) shaped rotation matrix R, where columns R[:, 0] and R[:, 1] are the principal curvature directions, and where R[:, 2] is outward facing and orthogonal to R[:, 0] and R[:, 1].
“k” (numpy.float64): A (2,) shaped array of the principal curvature magnitudes.
“b” (numpy.float64): A (4,) shaped array, b[0] and b[3] are the directional derivatives of k[0] and k[1] along their respective curvature line. b[1] and b[2] are the directional derivatives of k[0] and k[1] along the other curvature lines.
“c” (numpy.float64): A (5,) shaped array of higher order derivatives of curvature.

The “poly_fit_residual_stats” structure contains residual statistics and has fields:

“min” (numpy.float64): Minimum residual value.
“max” (numpy.float64): Maximum residual value.
“mean” (numpy.float64): Mean residual value.
“median” (numpy.float64): Median residual value.
“min_abs” (numpy.float64): Minimum absolute residual value.
“max_abs” (numpy.float64): Maximum absolute residual value.
“mean_abs” (numpy.float64): Mean absolute residual value.
“median_abs” (numpy.float64): Median absolute residual value.
“stdd” (numpy.float64): Standard deviation residual value.

The “poly_fit_bounding_area” structure has 2D bounding area info in fields:

“rectangle_min_side_length” (numpy.float64): Minimum oriented bounding rectangle smallest side length.
“rectangle_max_side_length” (numpy.float64): Minimum oriented bounding rectangle largest side length.
“circle_radius” (numpy.float64): Minimum bounding circle radius.
“ellipse_min_radius” (numpy.float64): Minimum oriented bounding ellipse smallest radius.
“ellipse_max_radius” (numpy.float64): Minimum oriented bounding ellipse largest radius.

Methods

`__init__`(self, poly_surface[, ...])	Construct.
`convert_result_to_point_data`(result_array)	Convert the `result_array` record array to a point-data `dict` suitable for `meshio.Mesh.point_data`.
`fit_all`(self, num_rings, fit_basis_type)	Fits a polynomial surface to the neigbourhoods of all vertices.
`fit_at_vertex`(self, vertex_index, num_rings, ...)	Fits a polynomial surface to the neigbourhood of vertices of vertex with index `vertex_index`.
`get_field_data`(result_array)	Returns a `dict` which can be used as `meshio.Mesh.field_data`.
`to_meshio_mesh`(result_array)	Return a `meshio.Mesh` version of the surface with point-data assigned from the `result_array`.

Attributes

`PCA`
`RING_NORMAL_GAUSSIAN_WEIGHTED_MEAN`
`RING_NORMAL_GAUSSIAN_WEIGHTED_MEAN_SIGMA`
`RING_NORMAL_MEAN`
`VERTEX_NORMAL`
`degree_monge`	An `int` indicating the degree of the Monge polynomial.
`degree_poly_fit`	An `int` indicating the degree of the fitting polynomial.
`min_num_fit_points`	An `int` indicating the minimum number of points (vertex coordinates) required to fit a polynomial of degree `degree_poly_fit`.
`poly_surface`	Polynomial patch vertex fitting performed on this `PolyhedralSurface` .
`ring_normal_gaussian_sigma`	The sigma `float` value used to calculate Gaussian weights when determining the polynomial fitting basis \(z\) direction.