Signed Distance Fields¶

Sdf3D¶

class meshpy.Sdf3D(sdf_data, origin, resolution, use_abs=True, T_sdf_world=RigidTransform(rotation=[[ 1. 0. 0.] [ 0. 1. 0.] [ 0. 0. 1.]], translation=[ 0. 0. 0.], from_frame=sdf, to_frame=world))¶

Bases: meshpy.sdf.Sdf

transform(delta_T)¶

Creates a new SDF with a given pose with respect to world coordinates.

Parameters:	delta_T (`autolab_core.RigidTransform`) – transform from cur sdf to transformed sdf coords

__getitem__(coords)¶

Returns the signed distance at the given coordinates.

Parameters:	coords (`numpy.ndarray` of int) – A or 3-dimensional ndarray that indicates the desired coordinates in the grid.
Returns:	The signed distance at the given coords (interpolated).
Return type:	float
Raises:	`IndexError` – If the coords vector does not have three entries.

gradient(coords)¶

Returns the SDF gradient at the given coordinates, interpolating if necessary

Parameters:	coords (`numpy.ndarray` of int) – A 3-dimensional ndarray that indicates the desired coordinates in the grid.
Returns:	The gradient at the given coords (interpolated).
Return type:	float
Raises:	`IndexError` – If the coords vector does not have three entries.

curvature(coords, delta=0.001)¶

Returns an approximation to the local SDF curvature (Hessian) at the given coordinate in grid basis.

Parameters:	coords (numpy 3-vector) – the grid coordinates at which to get the curvature
Returns:	curvature
Return type:	3x3 ndarray of the curvature at the surface points

surface_normal(coords, delta=1.5)¶

Returns the sdf surface normal at the given coordinates by computing the tangent plane using SDF interpolation.

Parameters:	coords (`numpy.ndarray` of int) – A 3-dimensional ndarray that indicates the desired coordinates in the grid. delta (float) – A radius for collecting surface points near the target coords for calculating the surface normal.
Returns:	The 3-dimensional ndarray that represents the surface normal.
Return type:	`numpy.ndarray` of float
Raises:	`IndexError` – If the coords vector does not have three entries.

surface_points(grid_basis=True)¶

Returns the points on the surface.

Parameters:	grid_basis (bool) – If False, the surface points are transformed to the world frame. If True (default), the surface points are left in grid coordinates.
Returns:	The points on the surface and the signed distances at those points.
Return type:	`tuple` of `numpy.ndarray` of int, `numpy.ndarray` of float

rescale(scale)¶

Rescale an SDF by a given scale factor.

Parameters:	scale (float) – the amount to scale the SDF
Returns:	new sdf with given scale
Return type:	`Sdf3D`

transform_dense(delta_T, detailed=False)¶

Transform the grid by pose T and scale with canonical reference frame at the SDF center with axis alignment.

Parameters:	delta_T (SimilarityTransform) – the transformation from the current frame of reference to the new frame of reference detailed (bool) – whether or not to use interpolation
Returns:	new sdf with grid warped by T
Return type:	`Sdf3D`

transform_pt_obj_to_grid(x_sdf, direction=False)¶

Converts a point in sdf coords to the grid basis. If direction then don’t translate.

Parameters:	x_sdf (numpy 3xN ndarray or numeric scalar) – points to transform from sdf basis in meters to grid basis
Returns:	x_grid – points in grid basis
Return type:	numpy 3xN ndarray or scalar

transform_pt_grid_to_obj(x_grid, direction=False)¶

Converts a point in grid coords to the world basis. If direction then don’t translate.

Parameters:	x_grid (numpy 3xN ndarray or numeric scalar) – points to transform from grid basis to sdf basis in meters
Returns:	x_sdf – points in sdf basis (meters)
Return type:	numpy 3xN ndarray

static find_zero_crossing_linear(x1, y1, x2, y2)¶: Find zero crossing using linear approximation

static find_zero_crossing_quadratic(x1, y1, x2, y2, x3, y3, eps=1.0)¶: Find zero crossing using quadratic approximation along 1d line

Sdf¶

class meshpy.Sdf¶

Bases: object

Abstract class for signed distance fields.

dimensions¶

SDF dimension information.

Returns:	The ndarray that contains the dimensions of the sdf.
Return type:	`numpy.ndarray` of int

origin¶

The location of the origin in the SDF grid.

Returns:	The 2- or 3-ndarray that contains the location of the origin of the mesh grid in real space.
Return type:	`numpy.ndarray` of float

resolution¶

The grid resolution (how wide each grid cell is).

Returns:	The width of each grid cell.
Return type:	float

center¶

Center of grid.

This basically transforms the world frame to grid center.

Returns:
Return type:	`numpy.ndarray`

gradients¶

Gradients of the SDF.

Returns:	A list of ndarrays of the same dimension as the SDF. The arrays are in axis order and specify the gradients for that axis at each point.
Return type:	`list` of `numpy.ndarray` of float

data¶

The SDF data.

Returns:	The 2- or 3-dimensional ndarray that holds the grid of signed distances.
Return type:	`numpy.ndarray` of float

transform(tf)¶: Returns a new SDF transformed by similarity tf.

transform_pt_obj_to_grid(x_world, direction=False)¶: Transforms points from world frame to grid frame

transform_pt_grid_to_obj(x_grid, direction=False)¶: Transforms points from grid frame to world frame

surface_points()¶

Returns the points on the surface.

Returns:	The points on the surface and the signed distances at those points.
Return type:	`tuple` of `numpy.ndarray` of int, `numpy.ndarray` of float

__getitem__(coords)¶

Returns the signed distance at the given coordinates.

Parameters:	coords (`numpy.ndarray` of int) – A 2- or 3-dimensional ndarray that indicates the desired coordinates in the grid.
Returns:	The signed distance at the given coords (interpolated).
Return type:	float

transform_to_world()¶: Returns an sdf object with center in the world frame of reference.

center_world()¶: Center of grid (basically transforms world frame to grid center)

on_surface(coords)¶

Determines whether or not a point is on the object surface.

Parameters:	coords (`numpy.ndarray` of int) – A 2- or 3-dimensional ndarray that indicates the desired coordinates in the grid.
Returns:	Is the point on the object’s surface, and what is the signed distance at that point?
Return type:	`tuple` of bool, float

is_out_of_bounds(coords)¶

Returns True if coords is an out of bounds access.

Parameters:	coords (`numpy.ndarray` of int) – A 2- or 3-dimensional ndarray that indicates the desired coordinates in the grid.
Returns:	Are the coordinates in coords out of bounds?
Return type:	bool