Name
CG_NurbsCurveApproximate — Creates an approximating NURBS curve fitting data points within a tolerance
Synopsis
geometry CG_NurbsCurveApproximate(geometry data_points, integer degree, float8 tolerance, integer max_control_points=100);
Description
Creates a NURBS curve that approximates the given data points within the specified tolerance. Unlike interpolation, the curve does not necessarily pass through all points but provides a smooth fit with fewer control points.
Parameters:
-
data_points- A LINESTRING geometry containing the points to approximate. -
degree- Polynomial degree of the NURBS curve. -
tolerance- Maximum allowed distance between the curve and data points. -
max_control_points- Optional maximum number of control points (default: 100). Limits curve complexity.
Availability: 3.7.0 - requires SFCGAL >= 2.3.0.
This method needs SFCGAL backend.
This function supports 3d and will not drop the z-index.
Examples
Approximate noisy 2D data with a degree-2 curve and a tolerance of 0.5.
WITH data AS (
SELECT 'LINESTRING(0 0,1 2.1,2 1.9,3 3.2,4 2.8,5 1)'::geometry AS input_points
)
SELECT input_points AS input_points,
CG_NurbsCurveApproximate(input_points, 2, 0.5) AS approximated_curve
FROM data;
LINESTRING(0 0,1 2.1,2 1.9,3 3.2,4 2.8,5 1) | NURBSCURVE(DEGREE 2, CONTROLPOINTS(NURBSPOINT(WEIGHTEDPOINT(0 0),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(-0.05 2.64),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(2.24 1.65),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(2.79 3.48),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(4.84 2.43),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(5 1),WEIGHT 1)),KNOTS (KNOT(0,3), KNOT(0.35,1), KNOT(0.51,1), KNOT(0.68,1), KNOT(1,3)))
Approximate a 3D point set while preserving the Z dimension in the fitted curve.
WITH data AS (
SELECT 'LINESTRING Z (0 0 0,1 2 1,2 3 2,3 2 1,4 1 0,5 0 0)'::geometry AS input_points
)
SELECT input_points AS input_points,
CG_NurbsCurveApproximate(input_points, 3, 0.1) AS approximated_curve
FROM data;
LINESTRING Z (0 0 0,1 2 1,2 3 2,3 2 1,4 1 0,5 0 0) | NURBSCURVE Z (DEGREE 3,CONTROLPOINTS Z (NURBSPOINT(WEIGHTEDPOINT Z (0 0 0),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT Z (0.18 -0.15 -1.29),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT Z (1.49 4.36 3.35),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT Z (3.33 1.33 0.38),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT Z (4.34 0.83 -0.44),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT Z (5 0 0),WEIGHT 1)),KNOTS (KNOT(0,4), KNOT(0.46,1), KNOT(0.64,1), KNOT(1,4)))