Intersect
The Intersect module computes geometric intersections between meshes and scalar fields. All intersection computations are geometrically and topologically exact, using exact arithmetic.
import trueform as tf
Overview
The Intersect module computes intersection geometry without modifying the input meshes:
- Mesh-mesh intersections: Curves where two or more meshes intersect
- Self-intersections: Curves where a mesh intersects itself
- Scalar field intersections: Contour curves at threshold values
Curves are returned as (paths, points) tuples where paths is an OffsetBlockedArray of index sequences and points is a numpy array of coordinates.
Supported Input
Intersection computation supports a wide range of input geometry:
- Open and closed meshes — boundaries are handled correctly
- Non-manifold edges — edges shared by 3 or more faces
- Coplanar faces — overlapping faces from the same or different meshes
- Self-intersecting geometry — meshes that intersect themselves are detected and curves are extracted
- Crossing intersection curves — where curves from different mesh pairs meet on a face, crossings can be resolved by splitting curves at the crossing point. Controlled via
modeandresolve_crossings/resolve_self_crossingsparameters.
tf.self_intersection_curves.Intersection Modes
The mode parameter selects the base intersection strategy:
| Mode | Description |
|---|---|
"sos" | SoS (Simulation of Simplicity) perturbation. Fast, no degenerate cases. |
"primitives" | Full 5-type classification. Handles shared edges, shared vertices, and coplanar faces. |
Contour crossing resolution is controlled by two additional keyword arguments:
| Parameter | Description |
|---|---|
resolve_crossings | Resolve crossings between different contours on the same face. A contour is defined by a mesh pair — e.g. contour (A,B) and contour (A,C) can cross on a face of mesh A. |
resolve_self_crossings | Resolve self-crossings within a single contour. Needed when edges from different face pairs of the same contour cross on a face. |
Each function sets appropriate defaults — see the individual function documentation below and in Cut.
Intersection Curves
Between Two Meshes
mesh0 = tf.Mesh(*tf.read_stl("mesh0.stl"))
mesh1 = tf.Mesh(*tf.read_stl("mesh1.stl"))
paths, points = tf.intersection_curves(mesh0, mesh1)
paths, points = tf.intersection_curves(mesh0, mesh1, mode="primitives")
Default: mode="sos", resolve_crossings=False, resolve_self_crossings=False. With two meshes only one contour exists, so crossing resolution flags have no effect.
N-Mesh Intersection Curves
Compute all pairwise intersection curves from a list of meshes:
paths, points = tf.intersection_curves([mesh0, mesh1, mesh2])
paths, points = tf.intersection_curves(
[mesh0, mesh1, mesh2], mode="primitives", resolve_crossings=True)
Default: mode="sos", resolve_crossings=True (for 3+ meshes), resolve_self_crossings=False.
Self-Intersection Curves
Find where a mesh intersects itself:
paths, points = tf.self_intersection_curves(mesh)
paths, points = tf.self_intersection_curves(mesh, mode="primitives")
Default: mode="sos", resolve_crossings=True, resolve_self_crossings=True.
tf.embedded_self_intersection_curves from the Cut module.With Transformations
import numpy as np
mesh1.transformation = np.eye(4, dtype=np.float32)
mesh1.transformation[:3, 3] = [5, 0, 0]
paths, points = tf.intersection_curves(mesh0, mesh1)
Using Curves
for path_ids in paths:
curve_points = points[path_ids]
# Process curve
Isocontours
Extract isocontour curves from scalar fields on meshes.
tf.isobands from the Cut module.Single Isocontour
scalar_field = tf.distance(tf.Point(mesh.points), plane)
paths, points = tf.isocontours(mesh, scalar_field, 0.0)
Multiple Isocontours
thresholds = np.array([0.0, 0.5, 1.0], dtype=np.float32)
paths, points = tf.isocontours(mesh, scalar_field, thresholds)