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);
Descrição
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.
Exemplos
-- Get tangent vector at curve midpoint
WITH nurbs AS (
SELECT ST_MakeNurbsCurve(2, 'LINESTRING(0 0, 5 10, 10 0)'::geometry) AS geom
)
SELECT CG_NurbsCurveDerivative(geom, 0.5, 1) FROM nurbs;
-- Get curvature at start of curve
WITH nurbs AS (
SELECT ST_MakeNurbsCurve(3, 'LINESTRING(0 0, 2 5, 5 5, 8 2, 10 0)'::geometry) AS geom
)
SELECT CG_NurbsCurveDerivative(geom, 0.0, 2) FROM nurbs;
-- Analyze tangent at multiple points
WITH nurbs AS (
SELECT ST_MakeNurbsCurve(2, 'LINESTRING(0 0, 5 10, 10 0)'::geometry) AS geom
)
SELECT
t.param,
CG_NurbsCurveDerivative(n.geom, t.param, 1) AS tangent
FROM nurbs n
CROSS JOIN (VALUES (0.0), (0.25), (0.5), (0.75), (1.0)) AS t(param);