Cone Ply Piece Optimization Tool (desicos.cppot)

Please, refer to the CPPOT tutorial for more details about how to use this module.

Cone Virtual Material Model (desicos.cppot.core)

CPPOT-geometry (desicos.cppot.core.geom)

Classes and functions to help with 2D geometrical operations.

class desicos.cppot.core.geom.ConeGeometry(H, rbot, alpharad, extra_height)

ConeGeometry object

Carries all the information about the geometry of a cone, plus some read-only accessors to calculate often-needed cone properties. These are all calculated on-the-fly, so no rebuild()-ing is necessary.

Attribute	Description
H	float, height of the free area of the cone.
rbot	float, bottom radius of the cone
alpharad	float, semi-vertex angle of the cone, in radians. Must be between 0 and pi/2.
extra_height	float, extra (support) height. A section with this height is added along both the top and bottom edge of the free cone. This represents the extra material that is present during manufacturing.

Attributes

L

Read-only property: Meridional length.

cone_area

Read-only property: Surface area of the free cone (supports excluded).

cos_alpha

Read-only property: Cosine of the semi-vertex angle.

rtop

Read-only property: Top radius of the cone.

s1

Read-only property: Radius of top (support) edge in unfolded coordinates.

s2

Read-only property: Radius of top edge of the free cone in unfolded coordinates.

s3

Read-only property: Radius of bottom edge of the free cone in unfolded coordinates.

s4

Read-only property: Radius of bottom (support) edge in unfolded coordinates.

sin_alpha

Read-only property: Sine of the semi-vertex angle.

tan_alpha

Read-only property: Tangent of the semi-vertex angle.

Methods

from_conecyl(cc, extra_height)

Construct a ConeGeometry object based on an existing ConeCyl

property L

Read-only property: Meridional length.

property cone_area

Read-only property: Surface area of the free cone (supports excluded).

property cos_alpha

Read-only property: Cosine of the semi-vertex angle.

classmethod from_conecyl(cc, extra_height)

Construct a ConeGeometry object based on an existing ConeCyl

Parameters

ccConeCyl

Existing cone to use. Must be a cone, i.e. alpha > 0.

extra_heightfloat

Extra support height for this model.

Returns

cgConeGeometry

The constructed ConeGeometry object

property rtop

Read-only property: Top radius of the cone.

property s1

Read-only property: Radius of top (support) edge in unfolded coordinates.

property s2

Read-only property: Radius of top edge of the free cone in unfolded coordinates.

property s3

Read-only property: Radius of bottom edge of the free cone in unfolded coordinates.

property s4

Read-only property: Radius of bottom (support) edge in unfolded coordinates.

property sin_alpha

Read-only property: Sine of the semi-vertex angle.

property tan_alpha

Read-only property: Tangent of the semi-vertex angle.

class desicos.cppot.core.geom.Line2D(a, b, c)

Class representing a line on a two-dimensional plane It is based on namedtuple, which allows both named attribute access (line.a) and iteration / indexing. Line2D instances are immutable after construction.

The line is defined based on two equations: a*x + b*y = c a**2 + b**2 = 1 The latter normalization constraint is enforced in __new__

Attribute	Description
a	float, Line parameter in equation (a*x + b*y = c)
b	float, Line parameter in equation (a*x + b*y = c)
c	float, Line parameter in equation (a*x + b*y = c)

Attributes

a

Alias for field number 0

b

Alias for field number 1

c

Alias for field number 2

Methods

all_intersections_circle(radius)	Get all intersection points of a line with a circle The center of the circle is presumed to be at the origin
angle()	Calculate the angle of this line with respect to the x-axis
count(value, /)	Return number of occurrences of value.
direction()	Obtain a point representing a unit direction vector parallel to the line.
distance_point(point)	Get the shortest Euclidean distance between this line and a point
from_point_angle(point, angle)	Class method, constructs a line based on a point and an angle
from_points(point1, point2)	Class method, constructs a line based on two points
index(value[, start, stop])	Return first index of value.
intersection_circle_near(radius, near_point)	Get the intersection of a line with a circle If there is more than one intersection point, it returns the intersection closest to near_point.
intersection_line(other)	Get the intersection point of this line and another line
point_on_right(point)	Check on which side of this line a point lies
rotate(angle)	Created a new line, rotated with respect to the origin.

all_intersections_circle(radius)

Get all intersection points of a line with a circle The center of the circle is presumed to be at the origin

Parameters

radiusfloat

Radius of circle

Returns

intersection_pointslist of Point2D

List containing either 0, 1 or 2 intersection points

Notes

See also: http://en.wikipedia.org/wiki/Intersection_(Euclidean_geometry)#A_line_and_a_circle

angle()

Calculate the angle of this line with respect to the x-axis

Returns

anglefloat

The counterclockwise angle (in radians) from the positive x-axis

direction()

Obtain a point representing a unit direction vector parallel to the line.

Returns

directionPoint2D

The requested unit direction vector

distance_point(point)

Get the shortest Euclidean distance between this line and a point

Parameters

pointPoint2D

Point to find the distance to

Returns

distancefloat

The shortest distance from this line to the given point.

classmethod from_point_angle(point, angle)

Class method, constructs a line based on a point and an angle

Parameters

pointPoint2D

Point that the line should go through

anglefloat

The counterclockwise angle (in radians) between the line and the positive x-axis

Returns

lineLine2D

The constructed line

classmethod from_points(point1, point2)

Class method, constructs a line based on two points

Parameters

point1Point2D

First point that the line should go through

point2Point2D

Second point that the line should go through

Returns

lineLine2D

The constructed line

Notes

If no line can be constructed, a ValueError is raised. This happens when the points are identical.

See also: http://math.stackexchange.com/questions/422602/convert-two-points-to-line-eq-ax-by-c-0

intersection_circle_near(radius, near_point)

Get the intersection of a line with a circle If there is more than one intersection point, it returns the intersection closest to near_point. If there is no intersection, a ValueError is raised.

Parameters

radiusfloat

Radius of circle

nearby_pointPoint2D

The intersection nearest to this point will be returned

Returns

intersection_pointPoint2D

The found intersection point

intersection_line(other)

Get the intersection point of this line and another line

Parameters

otherLine2D

Other line to find intersection point with

Returns

intersection_pointPoint2D

The found intersection point

Notes

If no intersection point could be found, a ValueError is raised. This can happen when the lines are parallel.

See also: http://en.wikipedia.org/wiki/Intersection_(Euclidean_geometry)#Two_lines

point_on_right(point)

Check on which side of this line a point lies

Parameters

pointPoint2D

Point to check

Returns

on_right_sidebool

True if the point is on the right side of this line (looking into the direction of self.direction()), False otherwise.

rotate(angle)

Created a new line, rotated with respect to the origin. The original line remains untouched.

Parameters

anglefloat

Angle (in radians) with which the line is to be rotated

Returns

new_lineLine2D

The newly constructed rotated line

class desicos.cppot.core.geom.Point2D(x, y)

Class representing a point on a two-dimensional plane It is based on namedtuple, which allows both named attribute access (point.x) and iteration / indexing. Point2D instances are immutable after construction. Addition / subtraction operators are overloaded, as wel as pre-multiplying by a scalar.

Attribute	Description
x	float, Cartesian x-coordinate
y	float, Cartesian y-coordinate

Attributes

x

Alias for field number 0

y

Alias for field number 1

Methods

angle()	Calculate the angle of this point in polar coordinates
count(value, /)	Return number of occurrences of value.
distance(other)	Calculate Euclidean distance between two points.
from_polar(norm, angle)	Class method, creates a point from polar coordinates
index(value[, start, stop])	Return first index of value.
norm()	Calculate distance of this point with respect to the origin.
rotate(angle)	Created a new point, rotated with respect to the origin.

angle()

Calculate the angle of this point in polar coordinates

Returns

anglefloat

The counterclockwise angle (in radians) from the positive x-axis

distance(other)

Calculate Euclidean distance between two points.

classmethod from_polar(norm, angle)

Class method, creates a point from polar coordinates

Parameters

normfloat

Distance from the origin

anglefloat

The counterclockwise angle (in radians) from the positive x-axis

Returns

pointPoint2D

The newly constructed point

norm()

Calculate distance of this point with respect to the origin.

rotate(angle)

Created a new point, rotated with respect to the origin. The original point remains untouched.

Parameters

anglefloat

Angle (in radians) with which the point is to be rotated

Returns

new_pointPoint2D

The newly constructed rotated point

class desicos.cppot.core.geom.Polygon2D(iterable=(), /)

Class representing a polygon on a two-dimensional plane. It is assumed that polygons do not self-intersect

Pass an iterable of Point2D-objects to the constructor. Polygon2D instances are immutable after construction.

Notes

Even though this object if (currently) a tuple of its points, it is recommended to not rely on this. This to allow possible future changes to the underlying implementation.

Methods

area()	Calculate the area enclosed by this polygon.
contains_point(point)	Determine if a point is inside or outside the polygon
count(value, /)	Return number of occurrences of value.
get_closed_line([num_points])	Get a closed line that can be used to plot this polygon.
index(value[, start, stop])	Return first index of value.
points()	Get an iterator over all corner points in this polygon
rotate(rotate_angle)	Create a new polygon, idential to this one but rotated around the origin by a certain angle.
slice_line(line)	Slice this polygon, returning only the section on the right side of the given line.

area()

Calculate the area enclosed by this polygon.

See also: http://en.wikipedia.org/wiki/Shoelace_formula

contains_point(point)

Determine if a point is inside or outside the polygon

Parameters

pointPoint2D

Point to test

Returns

inside_polygonbool

True if the point is inside the polygon, False otherwise

Notes

The ‘Ray casting’ algorithm is used, since the ‘interior angle’ algorithm was found to be very slow.

This method has not been verified to work correctly for special cases, such as the point being (almost) exactly on a vertex or line.

get_closed_line(num_points=1)

Get a closed line that can be used to plot this polygon.

Parameters

num_pointsint

The number of points to use per edge. Default value is 1.

Returns

outtuple

out[0] contains a numpy array of x-coordinates, out[1] an array of y-coordinates. The first point in the polygon is repeated, such that plot(x, y) results in a closed polygon.

points()

Get an iterator over all corner points in this polygon

rotate(rotate_angle)

Create a new polygon, idential to this one but rotated around the origin by a certain angle.

Parameters

rotate_anglefloat

Rotation angle to use, in radians

Returns

new_polyPolygon2D

The (newly created) rotated polygon.

slice_line(line)

Slice this polygon, returning only the section on the right side of the given line.

Parameters

lineLine2D

Line to be used for slicing.

Returns

new_polyPolygon2D

The (newly created) sliced polygon.

desicos.cppot.core.geom.angle_in_range(angle, angle_min, angle_max)

Check if an angle is within the specified range (min..max) While taking care of all the (mod 2pi)-issues.

Parameters

anglefloat

The angle to check

min_anglefloat

The lower limit of the range

max_anglefloat

The upper limit of the range

Returns

in_rangebool

True iff the given angle is in range min_angle…max_angle

desicos.cppot.core.geom.circle_segment_area(radius, angle)

Calculate the area of a circle segment, which is a region bound by an arc (less than 180 deg) and a straight line connecting the end points of that arc.

Parameters

radiusfloat

Radius of the arc

anglefloat

Angle (in radians) of the arc

Returns

areafloat

The calculated area

Notes

See http://en.wikipedia.org/wiki/Circular_segment

desicos.cppot.core.geom.wrap_to_pi(angle)

Wrap an angle to within the range [-pi, pi), by adding multiples of 2*pi

Parameters

anglefloat

The angle to wrap

Returns

new_anglefloat

Wrapped angle within the range [-pi, pi)

Virtual Ply Model (desicos.cppot.core.ply_model)

Classes to create a virtual model of the ply pieces on an actual cone.

class desicos.cppot.core.ply_model.PlyPiece(polygon, phi_nom, phi_nom_min, phi_nom_max, phi_limit_min=None, phi_limit_max=None)

PlyPiece object

Carries all the information about a single piece of ply in the layup of a cone, with a defined size and orientation.

Attributes	Description
polygon	Polygon2D, containing the geometry of the ply piece.
phi_nom	float, angle at which the origin line (L0) of the ply piece intersects the circle with radius starting_position
phi_nom_min	float, smallest angle phi that is contained within this ply piece at radius starting_position
phi_nom_max	float, largest angle phi that is contained within this ply piece at radius starting_position
phi_limit_min	float, minimum value of phi for any of the points in polygon. Optional, will be calculated if not supplied to the constructor.
phi_limit_max	float, minimum value of phi for any of the points in polygon. Optional, will be calculated if not supplied to the constructor.

Notes

On the nominal circle (radius starting_position), this ply piece occupies the range phi_nom_min…``phi_nom_max``.

For all points in this ply piece, the inequality phi_limit_min <= phi <= phi_limit_max should hold.

Methods

angle_deviation(point)	Get the deviation between the local and nominal fiber angle at a certain point
contains_point(point[, phi])	Check if a point is contained in this ply piece
copy_rotated(rotate_angle)	Create a copy of this ply piece, which is rotated by a certain angle.

angle_deviation(point)

Get the deviation between the local and nominal fiber angle at a certain point

Parameters

pointPoint2D

Cartesian coordinates of the point. These are in the coordinate system of the unfolded cone, so (eta, zeta) (as floats).

Returns

angle_difffloat

Local minus nominal fiber angle at this point, in degrees

contains_point(point, phi=None)

Check if a point is contained in this ply piece

Parameters

pointPoint2D

The point to check. This is in the coordinate system of the unfolded cone, so (eta, zeta).

phifloat

Angle corresponding to point. Parameter is optional, but passing it from the caller can help performance.

Returns

cointains_pointbool

True if the point is in this ply piece, false otherwise. For points exactly on the edge of the ply piece, resuls are undefined.

copy_rotated(rotate_angle)

Create a copy of this ply piece, which is rotated by a certain angle.

Parameters

rotate_anglefloat

Angle of new ply piece with respect to this one, in radians

Returns

new_piecePlyPiece

Rotated ply piece

class desicos.cppot.core.ply_model.PlyPieceModel(cg, fiber_angle, starting_position, max_width, rel_ang_offset=0.0, eccentricity=None)

Abstract base class for all ply piece models

This class encapsulates all functionality to create a virtual ply model based on the given parameters. Various methods are available to subsequently extract information about this virtual ply model.

For the different ply piece shapes, subclasses should be made that define at least the method construct_single_ply_piece and possibly others.

Methods

all_local_orientations(eta, zeta)	Determine the local fiber orientations of all plies at a point.
construct_single_ply_piece([fraction])	Construct a single ply piece.
corner_orientations()	Get the fiber orientations at all corners of the useful area, which is the area between radii s2 and s3.
edge_lengths()	Get the lengths of the edges of the (base) ply piece.
effective_area([ply_piece, max_angle_dev])	Get the effective area of a single ply piece.
local_num_pieces(eta, zeta)	Determine the local number of overlapping pieces at a given point.
local_orientation(eta, zeta)	Determine the local fiber orientation at a given point.
num_pieces()	Determine the total number of pieces needed to fully cover the cone.
ply_piece_area()	Get the area of a single ply piece that is on the free cone area, i.e.
ratio_continuous_fibers()	Get the ratio of continuous fibers, i.e.
rebuild()	Rebuild the model, actually constructing all ply pieces

all_local_orientations(eta, zeta)

Determine the local fiber orientations of all plies at a point.

Parameters

etafloat

Horizontal coordinate of point, in the coordinate system of the unfolded cone.

zetafloat

Vertical coordinate of point, in the coordinate system of the unfolded cone.

Returns

local_angleslist

Lists of floats representing the local fiber angle of each (possibly overlapping) ply piece at this point, in degrees.

construct_single_ply_piece(fraction=1.0)

Construct a single ply piece.

Parameters

fractionfloat

Optional, range (0, 1], default is 1. The newly constructed ply piece will normally span an angle delta_phi on the nominal circle (radius s_theta_nom) from phi_nom_min to phi_nom_max. When this parameter is set unequal to 1, delta_phi of the resulting ply piece will be the indicated fraction of the value it would normally have. This functionality is used to construct rest-pieces.

Returns

ply_piecePlyPiece

The newly constructed ply piece.

Notes

This method is just to define the interface, implementation should be provided by a derived class.

corner_orientations()

Get the fiber orientations at all corners of the useful area, which is the area between radii s2 and s3.

Returns

corner_orientationslist

Fiber angles (in degrees) at the four useful corner points of the base ply piece. The order of values matches P1, P2, P3, P4.

edge_lengths()

Get the lengths of the edges of the (base) ply piece.

Returns

edge_lengthslist

List of edge lengths (L1 to L4)

effective_area(ply_piece=None, max_angle_dev=2.0)

Get the effective area of a single ply piece. This is the area on useful section of the cone, where the deviation of the fiber angle is less than a given maximum.

Parameters

ply_piecePlyPiece, optional

Ply piece to get the effective area for. If not set, the base piece is used.

max_angle_devfloat, optional

Maximum deviation from the nominal fiber angle to consider the material ‘effective’. In degrees.

Returns

outtuple

2-tuple, where out[0] is the effective surface area and out[1] is the corresponding polygon.

Notes

Note that the polygon has straight edges, while the calculation of the effective area takes into account that some edges of the effective area may be arc sections.

local_num_pieces(eta, zeta)

Determine the local number of overlapping pieces at a given point.

Parameters

etafloat

Horizontal coordinate of point, in the coordinate system of the unfolded cone.

zetafloat

Vertical coordinate of point, in the coordinate system of the unfolded cone.

Returns

num_piecesint

Number of overlapping pieces at the given point in the ply

local_orientation(eta, zeta)

Determine the local fiber orientation at a given point. If the given point is not inside any ply piece, NaN is returned. If there are multiple overlapping ply pieces, the orientation belonging to one of them (the first in the ply piece list) is returned.

Parameters

etafloat

Horizontal coordinate of point, in the coordinate system of the unfolded cone.

zetafloat

Vertical coordinate of point, in the coordinate system of the unfolded cone.

Returns

local_anglefloat

Local fiber angle at the given point in the given ply, in degrees.

num_pieces()

Determine the total number of pieces needed to fully cover the cone.

Returns

num_piecesfloat

The number of needed pieces, as a float. The fractional part indicates the size of the ‘rest piece’ that is needed.

ply_piece_area()

Get the area of a single ply piece that is on the free cone area, i.e. between radii s2 and s3.

Returns

areafloat

The aforementioned area

ratio_continuous_fibers()

Get the ratio of continuous fibers, i.e. the fraction of the fibers at the bottom edge (radius s3) that reach the top edge (radius s2).

Returns

ratiofloat

The ratio of continuous fibers

rebuild()

Rebuild the model, actually constructing all ply pieces

class desicos.cppot.core.ply_model.RectPlyPieceModel(cg, fiber_angle, starting_position, max_width, rel_ang_offset=0.0, eccentricity=None)

Sub-class of PlyPieceModel, for shape C (rectangle)

Methods

all_local_orientations(eta, zeta)	Determine the local fiber orientations of all plies at a point.
construct_single_ply_piece([fraction])	Construct a ply piece for shape C (rectangle)
corner_orientations()	Get the fiber orientations at all corners of the useful area, which is the area between radii s2 and s3.
edge_lengths()	Get the lengths of the edges of the (base) ply piece.
effective_area([ply_piece, max_angle_dev])	Get the effective area of a single ply piece.
local_num_pieces(eta, zeta)	Determine the local number of overlapping pieces at a given point.
local_orientation(eta, zeta)	Determine the local fiber orientation at a given point.
num_pieces()	Determine the total number of pieces needed to fully cover the cone.
ply_piece_area()	Get the area of a single ply piece that is on the free cone area, i.e.
ratio_continuous_fibers()	Get the ratio of continuous fibers, i.e.
rebuild()	Rebuild the model, actually constructing all ply pieces

construct_single_ply_piece(fraction=1.0)

Construct a ply piece for shape C (rectangle)

class desicos.cppot.core.ply_model.Trapez2PlyPieceModel(cg, fiber_angle, starting_position, max_width, rel_ang_offset=0.0, eccentricity=None)

Sub-class of PlyPieceModel, for shape B (trapezium with one overlap)

Methods

all_local_orientations(eta, zeta)	Determine the local fiber orientations of all plies at a point.
construct_single_ply_piece([fraction])	Construct a ply piece for shape A (trapezium)
corner_orientations()	Get the fiber orientations at all corners of the useful area, which is the area between radii s2 and s3.
edge_lengths()	Get the lengths of the edges of the (base) ply piece.
effective_area([ply_piece, max_angle_dev])	Get the effective area of a single ply piece.
local_num_pieces(eta, zeta)	Determine the local number of overlapping pieces at a given point.
local_orientation(eta, zeta)	Determine the local fiber orientation at a given point.
num_pieces()	Determine the total number of pieces needed to fully cover the cone.
ply_piece_area()	Get the area of a single ply piece that is on the free cone area, i.e.
ratio_continuous_fibers()	Get the ratio of continuous fibers, i.e.
rebuild()	Rebuild the model, actually constructing all ply pieces

construct_single_ply_piece(fraction=1.0)

Construct a ply piece for shape A (trapezium)

class desicos.cppot.core.ply_model.TrapezPlyPieceModel(cg, fiber_angle, starting_position, max_width, rel_ang_offset=0.0, eccentricity=None)

Sub-class of PlyPieceModel, for shape A (trapezium)

Methods

all_local_orientations(eta, zeta)	Determine the local fiber orientations of all plies at a point.
construct_single_ply_piece([fraction])	Construct a ply piece for shape A (trapezium)
corner_orientations()	Get the fiber orientations at all corners of the useful area, which is the area between radii s2 and s3.
edge_lengths()	Get the lengths of the edges of the (base) ply piece.
effective_area([ply_piece, max_angle_dev])	Get the effective area of a single ply piece.
local_num_pieces(eta, zeta)	Determine the local number of overlapping pieces at a given point.
local_orientation(eta, zeta)	Determine the local fiber orientation at a given point.
num_pieces()	Determine the total number of pieces needed to fully cover the cone.
ply_piece_area()	Get the area of a single ply piece that is on the free cone area, i.e.
ratio_continuous_fibers()	Get the ratio of continuous fibers, i.e.
rebuild()	Rebuild the model, actually constructing all ply pieces

construct_single_ply_piece(fraction=1.0)

Construct a ply piece for shape A (trapezium)

CPPOT GUI (desicos.cppot.gui)

All the functionalities of the Graphic User Interface will be started by clicking on the Click_me.pyw file.