Plot 3D Parametric Curve

Plot 3D Parametric Curve

File: Shape_Generation_Scripts/Plot_3D_Parametric_Curve.py
Version: 1.0
Document Type: Part

---

Description

Evaluates three user-entered mathematical expressions x(t), y(t), z(t) over a parameter range and creates the resulting 3D curve in the active CATPart as a GSD point set and spline. All functions from Python's math module are available. If the first and last points coincide (within 0.001 mm) the spline is automatically closed.

Settings are saved between sessions.

---

Requirements

Requirement	Value
Python	>= 3.10
pycatia	>= 0.8.3
wxPython	Required
Open document	Part

---

Usage

1. Open a CATPart document
2. Run the script
3. Enter the three component expressions, parameter range, and number of points in the dialog
4. Click OK — all expressions are validated then a progress bar shows while geometry is created
5. A new geometric set is added to the part containing the point set and spline

---

Parameters

Parameter	Description	Default
x(t) =	X coordinate as a function of t (mm)	cos(t) * 50
y(t) =	Y coordinate as a function of t (mm)	sin(t) * 50
z(t) =	Z coordinate as a function of t (mm)	t * 5
t start	Start value of the parameter range. May use pi and e.	0.0
t end	End value of the parameter range. Must be greater than t start.	2 * pi
Points	Number of sample points. Minimum 2.	100

Expression Syntax

Each expression is a Python math expression using t as the parameter. Available functions:

Category	Functions
Trigonometric	sin, cos, tan, asin, acos, atan, atan2
Hyperbolic	sinh, cosh, tanh
Power / log	sqrt, exp, log, log2, log10
Rounding	floor, ceil, fabs
Constants	pi, e
Other	abs, round

You can also use pi and e directly in the t start and t end fields (e.g. 2*pi, -pi).

Example Curves

Curve	x(t)	y(t)	z(t)	t range
Circle (XY, r=50)	cos(t)*50	sin(t)*50	0	0 to 2*pi
Helix	cos(t)*50	sin(t)*50	t*10	0 to 2*pi
Lissajous	sin(3*t)*50	sin(2*t)*50	0	0 to 2*pi

---

Dialog Buttons

Button	Action
OK	Validates all expressions and inputs, then generates the curve
Cancel	Exits without generating
Reset Defaults	Restores factory default values
Clear Saved	Deletes the saved user presets file
Help	Opens the full in-script user manual

---

Output

A geometric set named Parametric_x(t)_<expr> is created at the top level of the part tree containing:

Parametric_x(t)_cos(t)x50
├── Points
│   ├── Pt_0001
│   ├── Pt_0002
│   │   ...
│   └── Pt_0100
└── Parametric_Spline  (open or closed)

The spline is automatically closed if the distance between the first and last points is less than 0.001 mm. For a closed curve, the last point is dropped from the point set before building the spline so the geometry is not duplicated.

---

Settings Persistence

Settings are saved automatically to:

%APPDATA%\pycatia_scripts\Plot_3D_Parametric_Curve\user_presets.json

The next time the script runs, your last-used values are pre-filled in the dialog.

---

Notes

• All coordinates produced by the expressions are treated as mm
• Each expression is validated at t = 1 during dialog validation to catch syntax errors before touching CATIA
• The geo set name is a sanitised, truncated version of the x(t) expression
• t start and t end support Python math expressions using pi and e only; full math module not available in those fields