Mesh Utilities

Utilities.meshutils.area_AABB(points, **kwargs)

Marks points that are inside the specified AABB in the plan.

Parameters

• points (torch.Tensor) – Point tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• aabb (Utilities.AABB) – The AABB that marks the area.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is inside the shape.

Return type

torch.BoolTensor

Utilities.meshutils.area_convex_hull(points, **kwargs)

Marks points inside a computed convex hull.

Returns a torch.BoolTensor marking points that are inside the convex hull of scatter.

Parameters

• points (torch.Tensor) – Points tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• scatter (torch.Tensor) – Points tensor of dimension ($M$, 2), with $M$ number of points, from which the convex hull will be computed.

• intersect (bool, default=False) – Set this to True if points on the line should be accounted inside the marking region.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is inside the convex hull.

Return type

torch.BoolTensor

Utilities.meshutils.area_convex_shape(points, **kwargs)

Marks points inside a convex shape.

Returns a torch.BoolTensor marking points that are inside the convex shape shape.

Parameters

• points (torch.Tensor) – Point tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• shape (torch.Tensor) – Point tensor of dimension ($M$, 2), with $M$ number of points, that defines the convex shape.

• side (either +1 or -1, default=1) – If set to +1/-1 shape is defined as CW/CCW.

• intersect (bool, default=False) – Set this to True if points on the line should be accounted inside the marking region.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is inside the convex hull.

Return type

torch.BoolTensor

Utilities.meshutils.area_disc(points, **kwargs)

Marks points that are inside the specified disc in the plan.

Returns a boolean tensor.

Parameters

• points (torch.Tensor) – Point tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• center (torch.Tensor) – Point tensor of dimension (2) that defines the center of the disc.

• radius (float) – Radius of the disc.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is inside the shape.

Return type

torch.BoolTensor

Utilities.meshutils.area_polyline_outline(points, **kwargs)

Marks points that are in the neighborhood of a polyline.

Parameters

• points (torch.Tensor) – Point tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• polyline (torch.Tensor) – Point tensor of dimension ($M$, 2), with $M$ number of vertices, that defines the polyline.

• width (float, default=0.) – Width of the polyline.

• close (bool, default=False) – Set to True in order to close the polyline.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is inside the shape.

Return type

torch.BoolTensor

Utilities.meshutils.area_segment(points, **kwargs)

Marks points that are inside the neighborhood of the specified segment in the plan.

Parameters

• points (torch.Tensor) – Point tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• p0 (torch.Tensor) – First point defining the separation line.

• p1 (torch.Tensor) – Second point defining the separation line and thus its direction.

• origin (torch.Tensor) – Origin vector.

• direction (torch.Tensor) – Direction vector.

• width (torch.Tensor) – Width of the segment.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is inside the shape.

Return type

torch.BoolTensor

Utilities.meshutils.area_shape(points, **kwargs)

Marks points inside a shape.

Returns a torch.BoolTensor marking points that are inside the shape shape. Shape does not need to be convex and can overlap itself.

Parameters

• points (torch.Tensor) – Point tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• shape (torch.Tensor) – Shape.

• side (either +1 or -1, default=1) – If set to +1/-1 shape is defined as CW/CCW.

• intersect (bool, default=False) – Set this to True if points on the line should be accounted inside the marking region.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is inside the shape.

Return type

torch.BoolTensor

Utilities.meshutils.area_side(points, **kwargs)

Marks points that are on one side of the specified separation line on the plan.

Returns a torch.BoolTensor marking points that are in side side. The seperation line can either be specified by two points p0 and p1, or by origin and direction.

Parameters

• points (torch.Tensor) – Point tensor of dimension ($N$, 2), with $N$ number of points, that will be marked.

• p0 (torch.Tensor) – First point tensor of dimension (2) defining the separation line.

• p1 (torch.Tensor) – Second point tensor of dimension (2) defining the separation line and thus its direction.

• origin (torch.Tensor) – Origin vector of dimension (2).

• direction (torch.Tensor) – Direction vector of dimension (2).

• side (int, either +1 or -1, default=1) – +1/-1 to select points to the left/right of the separation line.

• intersect (bool, default=False) – Set this to True if points on the line should be accounted inside the marking region.

Returns

Bool tensor of dimension $N$, with $i$ True if point $i$ is at side side of the defined separation line.

Return type

torch.BoolTensor

Utilities.meshutils.close_shape(shape)

Returns the closed shape.

Parameters

shape (torch.Tensor) – Shape tensor of dimension ($N$), with $N$ number of vertices, that will be closed.

Returns

The closed shape.

Return type

torch.Tensor

Utilities.meshutils.compute_centers_normals_lengths(vertices, faces)

Utilities.meshutils.distance_segment(point, p0, p1)

Returns the minimal distance between a point and a segment.

Parameters

• point (torch.Tensor) – Point tensor of dimension (2) from which distance is computed.

• p0 (torch.Tensor) – First point defining the segment.

• p1 (torch.Tensor) – Second point defining the segment.

Returns

The minimal distance between the point and the segment.

Return type

float

Utilities.meshutils.extract_convex_hull(points)

Extracts a convex hull from a set of points.

Notes

The output shape in 2D is CCW defined. In 3D outputs a tuple of points and triangle list forming the convex hull. Uses Scipy internaly.

Parameters

points (torch.Tensor) – Points tensor of dimension ($N$, d), with $N$ the number of points and $d$ the dimension, from which the convex hull will be computed.

Returns

If in 2D, the resulting convex hull, of dimension ($M$, 2), with $M$ the number of points the convex hull contains. If in 3D, a 2-tuple with first element representing the points of the convex hull of dimension ($M$, 3), with $M$ the number of points the convex hull contains and a list of 3-tuple representing the faces of the hull.

Return type

torch.Tensor

Utilities.meshutils.fill_area_random(area, aabb, N, **kwargs)

Randomly fill a 2D area enclosed by aabb given by the area function.

The random process follows a Poisson distribution. Sampling is done using a rejection sampling algorithm.

Parameters

• area (callable) – Callable defining the area that will be filled.

• enclosing_aabb (Utilities.AABB) – Bounding box enclosing the area callable function.

• N (int) – Number of points to generate.

• kwargs (dictpp) – Arguments passed to the area function.

Returns

Points tensor of dimension ($N$, 2), with $N$ the number of points.

Return type

torch.Tensor

Utilities.meshutils.fill_area_random_density(area, aabb, density, **kwargs)

Randomly fill a 2D area enclosed by aabb given by the area function.

The random process follows a Poisson distribution. Sampling is done using a rejection sampling algorithm.

Parameters

• area (callable) – Callable defining the area that will be filled.

• enclosing_aabb (Utilities.AABB) – Bounding box enclosing the area callable function.

• density (int) – Density of points to generate.

• kwargs (dict) – Arguments passed to the area function.

Returns

Points tensor of dimension ($N$, 2), with $N$ the number of points.

Return type

torch.Tensor

Utilities.meshutils.fill_area_uniform(area, enclosing_aabb, spacing, **kwargs)

Uniformly fills a 2D area enclosed given by a callable.

The area callable should have the following signature:

Parameters

• area (callable) – Callable defining the area that will be filled.

• enclosing_aabb (Utilities.AABB) – Bounding box enclosing the area callable function.

• spacing (float) – Distance between points.

• kwargs (dict) – Arguments passed to the area callable function.

Returns

Points tensor of dimension ($N$, 2), with $N$ the number of points.

Return type

torch.Tensor

Utilities.meshutils.fill_area_uniform_density(area, enclosing_aabb, density, **kwargs)

Fill a 2D area enclosed by aabb given by the area function uniformly.

Parameters

• area (callable) – Callable defining the area that will be filled.

• enclosing_aabb (Utilities.AABB) – AABB.

• density (float) – Density of points.

• kwargs (dict) – Arguments passed to the area function.

Returns

Points tensor of dimension ($N$, 2), with $N$ the number of points.

Return type

torch.Tensor

Utilities.meshutils.gaussian_kernel_smooth(points, sigma)

Utilities.meshutils.is_shape_closed(shape)

Returns True if the input shape is closed.

Parameters

shape (torch.Tensor) – Shape tensor of dimension ($N$, 2), with $N$ number of vertices, that will be closed.

Returns

True if shape is closed, False otherwise.

Return type

bool

Utilities.meshutils.kernel_smooth(points, kernel)

Utilities.meshutils.point_side(point, p0, p1)

Returns the side of a point relative to a line.

Parameters

• point (torch.Tensor) – Point tensor of dimension (2) from which side will be computed.

• p0 (torch.Tensor) – First point defining the line.

• p1 (torch.Tensor) – Second point defining the line, and thus it’s direction.

Returns

-1/+1 if the point is on the left/right. 0 if the point is exactly on the line.

Return type

int

Utilities.meshutils.resample_curve(curve, density)

Utilities.meshutils.winding_order(point, shape, side)

Returns the winding order of a point relative to a shape.

Notes

This function assumes the shape is closed.

Parameters

• point (torch.Tensor) – Point tensor of dimension (2) around which the winding order will be computed.

• shape (torch.Tensor) – Shape tensor of dimension ($N$), with $N$ number of vertices, from which the winding order will be computed.

• side (int, either +1 or -1) – Set to +1/-1 if shape is defined CCW/CW.

Returns

The computed winding order.

Return type

int