`pycanha.gmm` — Geometric Mathematical Model#

Geometric primitives for defining thermal surface elements.

Primitives#

class pycanha.gmm.Triangle(p1, p2, p3)[source]#

Bases: Triangle

Triangular flat surface defined by three 3D vertices.

Parameters:

p1 (npt.ArrayLike)
p2 (npt.ArrayLike)
p3 (npt.ArrayLike)

is_valid(self) → bool#: Whether the primitive geometry is valid.

normal_at_uv(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Outward surface normal at a 2D parametric (uv) point.

property p1#: First vertex.

property p2#: Second vertex.

property p3#: Third vertex.

surface_area(self) → float#: Total surface area.

to_cartesian(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Map a 2D parametric (uv) point back to 3D space.

to_uv(self, point: numpy.ndarray[dtype=float64, shape=(3), order='C']) → numpy.ndarray[dtype=float64, shape=(2), order='C']#: Project a 3D point onto the primitive’s 2D parametric (uv) space.

class pycanha.gmm.Rectangle(p1, p2, p3)[source]#

Bases: Rectangle

Rectangular flat surface: p1->p2 is one edge, p1->p3 the adjacent edge.

Parameters:

p1 (npt.ArrayLike)
p2 (npt.ArrayLike)
p3 (npt.ArrayLike)

is_valid(self) → bool#: Whether the primitive geometry is valid.

normal_at_uv(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Outward surface normal at a 2D parametric (uv) point.

property p1#: Origin vertex.

property p2#: Second vertex (first edge from p1).

property p3#: Third vertex (second edge from p1).

surface_area(self) → float#: Total surface area.

to_cartesian(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Map a 2D parametric (uv) point back to 3D space.

to_uv(self, point: numpy.ndarray[dtype=float64, shape=(3), order='C']) → numpy.ndarray[dtype=float64, shape=(2), order='C']#: Project a 3D point onto the primitive’s 2D parametric (uv) space.

class pycanha.gmm.Quadrilateral(p1, p2, p3, p4)[source]#

Bases: Quadrilateral

General quadrilateral surface defined by four vertices.

Parameters:

p1 (npt.ArrayLike)
p2 (npt.ArrayLike)
p3 (npt.ArrayLike)
p4 (npt.ArrayLike)

is_valid(self) → bool#: Whether the primitive geometry is valid.

normal_at_uv(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Outward surface normal at a 2D parametric (uv) point.

property p1#: First vertex.

property p2#: Second vertex.

property p3#: Third vertex.

property p4#: Fourth vertex.

surface_area(self) → float#: Total surface area.

to_cartesian(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Map a 2D parametric (uv) point back to 3D space.

to_uv(self, point: numpy.ndarray[dtype=float64, shape=(3), order='C']) → numpy.ndarray[dtype=float64, shape=(2), order='C']#: Project a 3D point onto the primitive’s 2D parametric (uv) space.

class pycanha.gmm.Cylinder(p1, p2, p3, radius, start_angle, end_angle)[source]#

Bases: Cylinder

Cylindrical surface segment defined by axis, radius and angular extent.

Parameters:

p1 (npt.ArrayLike)
p2 (npt.ArrayLike)
p3 (npt.ArrayLike)
radius (float)
start_angle (float)
end_angle (float)

property end_angle#: End angle [rad].

is_valid(self) → bool#: Whether the primitive geometry is valid.

normal_at_uv(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Outward surface normal at a 2D parametric (uv) point.

property p1#: Base center position.

property p2#: Top center position.

property p3#: Reference point for the angle origin.

property radius#: Cylinder radius.

property start_angle#: Start angle [rad].

surface_area(self) → float#: Total surface area.

to_cartesian(self, uv: numpy.ndarray[dtype=float64, shape=(2), order='C']) → numpy.ndarray[dtype=float64, shape=(3), order='C']#: Map a 2D parametric (uv) point back to 3D space.

to_uv(self, point: numpy.ndarray[dtype=float64, shape=(3), order='C']) → numpy.ndarray[dtype=float64, shape=(2), order='C']#: Project a 3D point onto the primitive’s 2D parametric (uv) space.