Nom
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.
Cette méthode nécessite le backend SFCGAL.
Cette fonction prend en charge la 3D et ne supprime pas l'indice z.
Exemples
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)