NURBS-Python Custom Format¶
NURBS-Python provides import_txt() function for reading control points of curves and surfaces from a
text file. For saving the control points export_txt() function may be used.
The format of the text file depends on the type of the geometric element, i.e. curve or surface. The following sections explain this custom format.
2D Curves¶
To generate a 2D B-Spline Curve, you need a list of (x, y) coordinates representing the control points (P), where
- x: value representing the x-coordinate
- y: value representing the y-coordinate
The format of the control points file for generating 2D B-Spline curves is as follows:
| x | y |
|---|---|
| x1 | y1 |
| x2 | y2 |
| x3 | y3 |
The control points file format of the NURBS curves are very similar to B-Spline ones with the difference of weights. To generate a 2D NURBS curve, you need a list of (x*w, y*w, w) coordinates representing the weighted control points (Pw) where,
- x: value representing the x-coordinate
- y: value representing the y-coordinate
- w: value representing the weight
The format of the control points file for generating 2D NURBS curves is as follows:
| x*w | y*w | w |
|---|---|---|
| x1*w1 | y1*w1 | w1 |
| x2*w2 | y2*w2 | w2 |
| x3*w3 | y3*w3 | w3 |
Note
compatibility module provides several functions to manipulate & convert control point arrays into NURBS-Python compatible ones and more.
3D Curves¶
To generate a 3D B-Spline curve, you need a list of (x, y, z) coordinates representing the control points (P), where
- x: value representing the x-coordinate
- y: value representing the y-coordinate
- z: value representing the z-coordinate
The format of the control points file for generating 3D B-Spline curves is as follows:
| x | y | z |
|---|---|---|
| x1 | y1 | z1 |
| x2 | y2 | z2 |
| x3 | y3 | z3 |
To generate a 3D NURBS curve, you need a list of (x*w, y*w, z*w, w) coordinates representing the weighted control points (Pw) where,
- x: value representing the x-coordinate
- y: value representing the y-coordinate
- z: value representing the z-coordinate
- w: value representing the weight
The format of the control points file for generating 3D NURBS curves is as follows:
| x*w | y*w | z*w | w |
|---|---|---|---|
| x1*w1 | y1*w1 | z1*w1 | w1 |
| x2*w2 | y2*w2 | z2*w2 | w2 |
| x3*w3 | y3*w3 | z3*w3 | w3 |
Note
compatibility module provides several functions to manipulate & convert control point arrays into NURBS-Python compatible ones and more.
Surfaces¶
Control points file for generating B-Spline and NURBS has 2 options:
First option is very similar to the curve control points files with one noticeable difference to process u and v indices. In this list, the v index varies first. That is, a row of v control points for the first u value is found first. Then, the row of v control points for the next u value.
The second option sets the rows as v and columns as u. To generate a B-Spline surface using this option, you need a list of (x, y, z) coordinates representing the control points (P) where,
- x: value representing the x-coordinate
- y: value representing the y-coordinate
- z: value representing the z-coordinate
The format of the control points file for generating B-Spline surfaces is as follows:
| v0 | v1 | v2 | v3 | v4 | |
|---|---|---|---|---|---|
| u0 | (x, y, z) | (x, y, z) | (x, y, z) | (x, y, z) | (x, y, z) |
| u1 | (x, y, z) | (x, y, z) | (x, y, z) | (x, y, z) | (x, y, z) |
| u2 | (x, y, z) | (x, y, z) | (x, y, z) | (x, y, z) | (x, y, z) |
To generate a NURBS surface using the 2nd option, you need a list of (x*w, y*w, z*w, w) coordinates representing the weighted control points (Pw) where,
- x: value representing the x-coordinate
- y: value representing the y-coordinate
- z: value representing the z-coordinate
- w: value representing the weight
The format of the control points file for generating NURBS surfaces is as follows:
| v0 | v1 | v2 | v3 | |
|---|---|---|---|---|
| u0 | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) |
| u1 | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) |
| u2 | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) | (x*w, y*w, z*w, w) |
Note
compatibility module provides several functions to manipulate & convert control point arrays into NURBS-Python compatible ones and more.
Volumes¶
Parametric volumes can be considered as a stacked surfaces, which means that w-parametric axis comes the first and then other parametric axes come.