Name
CG_NurbsCurveDerivative — Computes the derivative (tangent, curvature) of a NURBS curve at a given parameter
Synopsis
geometry CG_NurbsCurveDerivative(geometry nurbscurve, float8 parameter, integer derivative_order);
Description
Computes the derivative of a NURBS curve at a specific parameter value. The derivative represents the rate of change at that point:
-
Order 1: Tangent vector (direction and speed)
-
Order 2: Curvature vector (how the tangent changes)
-
Order 3: Third-order derivative (supported maximum)
Parameters:
-
nurbscurve- A NURBS curve geometry. -
parameter- Parameter value for evaluation (typically 0.0 to 1.0). -
derivative_order- Order of derivative to compute (1, 2, or 3).
Returns a POINT geometry representing the derivative vector at the specified parameter.
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
The first derivative gives the tangent vector at the evaluation parameter.
WITH data AS (
SELECT 'NURBSCURVE (2, (0.00 0.00, 5.00 10.00, 10.00 0.00))'::geometry AS input_curve
)
SELECT input_curve AS input_curve,
CG_NurbsCurveDerivative(input_curve, 0.5, 1) AS tangent
FROM data;
NURBSCURVE(DEGREE 2, CONTROLPOINTS(NURBSPOINT(WEIGHTEDPOINT(0 0),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(5 10),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(10 0),WEIGHT 1)),KNOTS (KNOT(0,3), KNOT(1,3))) | POINT Z (10 0 0)
The second derivative exposes curvature change for a higher-degree curve.
WITH data AS (
SELECT 'NURBSCURVE (3, (0.00 0.00, 2.00 8.00, 5.00 5.00, 8.00 2.00, 10.00 0.00))'::geometry AS input_curve
)
SELECT input_curve AS input_curve,
CG_NurbsCurveDerivative(input_curve, 0.5, 2) AS curvature
FROM data;
NURBSCURVE(DEGREE 3, CONTROLPOINTS(NURBSPOINT(WEIGHTEDPOINT(0 0),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(2 8),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(5 5),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(8 2),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT(10 0),WEIGHT 1)),KNOTS (KNOT(0,4), KNOT(0.5,1), KNOT(1,4))) | POINT Z (9 -9 0)
The same derivative call also works for 3D NURBS curves.
WITH data AS (
SELECT 'NURBSCURVE Z (2, (0.00 0.00 0.00, 5.00 10.00 5.00, 10.00 0.00 0.00))'::geometry AS input_curve
)
SELECT input_curve AS input_curve,
CG_NurbsCurveDerivative(input_curve, 0.5, 1) AS tangent
FROM data;
NURBSCURVE Z (DEGREE 2,CONTROLPOINTS Z (NURBSPOINT(WEIGHTEDPOINT Z (0 0 0),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT Z (5 10 5),WEIGHT 1), NURBSPOINT(WEIGHTEDPOINT Z (10 0 0),WEIGHT 1)),KNOTS (KNOT(0,3), KNOT(1,3))) | POINT Z (10 0 0)