Curve

Class Name

Curve

Description

A parametric curve has one free parameter, u, and three associated functions f(u), g(u) and h(u). For every value, u=u*, f(u*), g(u*), and h(u*) represent the coordinates of a point in space. As u is swept from its minimum to maximum value, a curve in 3D space is generated. For additional information on the definition of Curve, please see the Description and the Comments section of Reference_ParamCurve.

Attribute Summary

Name	Property	Modifiable by command?	Designable?
id	Int ()
label	Str ()
matrix	Reference ("Matrix")	Yes	FD Only
xyx	Nodes (None, count=0)
curve_points	Bool ()	Yes
closed	Bool (False)	Yes
minpar	Double (-1.0)
maxpar	Double (1.0)
function	Function ("CURSUB")		FD Only
routine	Routine () or Str ()		FD Only
script	Script ()

Usage

Curves are available in the following forms:

#1: Curve data provided in a Matrix
Curve(matrix=objMatrix, optional_attributes)

#2. Curve data provided as xyz points
Curve(xyz=xyz_points, optional_attributes)

#3. Curve specified in a compiled user-written subroutine
Curve(function=userString, routine=string, optional_attributes)

#4. Curve specified in a Python function
Curve(function=userString, routine=functionPointer, curve_points=boolean, optional_attributes)

Attributes

Curve data provided in a Matrix.

matrix: Reference to an existing matrix object.; Specifies the Matrix that contains the curve data. The matrix should contain only the x-, y-, and z- data for the individual curve points. For example: [x1,y1,z1,x2,y2,z2,…].
Note: For a closed curve, the first and last data points must be the same.

Curve data provided as xyz points.

xyz: Nodes; List of [x,y,z] points used by the curve. For example: [[x1,y1,z1],[x2,y2,z2],…]
Note: For a closed curve, the first and last data points must be the same.

Curve specified in a compiled user-written subroutine.

function: String; The list of parameters that are passed from the data file to the user-defined subroutine.
routine: String; Specifies an alternative name for the user subroutine. The name consists of two pieces of information, separated by "::". The first is the pathname to the shared library containing the function that computes the response of the user-defined Surface. The second is the name of the function in the shared library that does the computation.; An example is: routine="/staff/Altair/engine.dll::myCurve"

"/staff/Altair/engine.dll is the DLL.

"myCurve" is the function within this DLL that performs the calculations.; The attribute routine is optional.; When not specified, routine defaults to CURSUB.
minpar: Double; Specifies the minimum value of the curve parameter.; The minpar attribute is optional. When not specified, it defaults to -1.
Note: When specified, minpar < maxpar.
maxpar: Double; Specifies the maximum value of the curve parameter.; The maxpar attribute is optional. When not specified, it defaults +1.
Note: When specified, minpar < maxpar.

Curve specified in a Python function.

function: String; The list of parameters that are passed from the data file to the user-defined function.
routine: Callable function in Python or string.; An example is: routine=myCurve or routine=”myCurve”.

If script is not used, then myCurve is a Python function or method defined within the namespace.

If script is used, then “myCurve” is a string that names the function in an external written script.; The attribute routine is optional.; When not specified, routine defaults to CURSUB.
script: Specifies the path and name of the user-written script that contains the function specified by routine.; The attribute script is optional.; When not specified, MotionSolve looks for a function within the namespace.
minpar: Double; Specifies the minimum value of the curve parameter.; The minpar attribute is optional. When not specified, it defaults to -1.
Note: When specified, minpar < maxpar.
maxpar: Double; Specifies the maximum value of the curve parameter.; The maxpar attribute is optional. When not specified, it defaults +1.
Note: When specified, minpar < maxpar.

Optional attributes: Available to all description methods.

id: Integer; Specifies the element identification number. This number must be unique among all the Surface objects in the model.; This attribute is optional. MotionSolve automatically creates an ID when one is not specified.; Range of values: id > 0
label: String; Specifies the name of the Surface object.; This attribute is optional. When not specified, MotionSolve will create a label for you.
closed: String; Select from "OPEN" or "CLOSED".
Note: For a closed curve, the first and last data points must be the same.; The type attribute is mandatory.
curve_points: Boolean; Select from TRUE or FALSE.

TRUE means that the curve passes through the points.

FALSE means that the curve (B-spline) stays close to the points, but does not pass through them in general.; When not specified, curve_points defaults to False.

Example

A cycloid is defined in parametric space as:

x = a * (t - sin(t))
y = a * (1-cos(t))

"t" is the independent parameter. The cycloid is shown in the image below.

Figure 1. A parametrically defined cycloid curve

Define a parametric curve using a matrix.
The statement defining the cycloid described above has the following curve attributes:
- The Curve is open
- The independent parameter t starts at zero
- The independent parameter t ends at 5
- The curve points are specified in the Matrix object mat23
The corresponding MotionSolve Python specification is:
```
# Note, since curve_points=True, MINPAR=-1 and MAXPAR=+1. 
# This range in u will accommodate all the data provided in the matrix.
curve1 = Curve (type="OPEN", curve_points=True, matrix=mat23)
```

Define a parametric curve in a python function.

This example shows how to specify exactly the same for implementation in a user-defined subroutine written in Python:

# The cycloid function saved in file: cycloid.py
from msolve import sin, cos
def cycloid (id, par, npar, t, iord, iflag):
   a = par[0]  
   if iord == 0:
      x = a * (t - sin(t))
      y = a * (1 - cos(t))
      z = 0.0
   elif iord == 1:
      x = a * (1 - cos(t))
      y = a * sin(t)
      z = 0.0
   else:
      x = a * sin(t)
      y = a * cos(t)
      z = 0.0
   
   return [x, y, z]

The corresponding MotionSolve Python specification is:

curve2 = Curve(function="USER(1)", routine=cycloid, type="OPEN", minpar=0, maxpar=6)

Comments

See Properties for an explanation about what properties are, why they are used, and how you can extend these.
For a more detailed explanation about Curve, see Reference: ParamCurve.