Fitting curves and surfaces to point clouds in the presence of obstacles

Robust fitting of Zernike polynomials to noisy point clouds defined over connected domains of arbitrary shape

“…The robust and accurate fitting of a noisy cloud of 3D points to an analytical surface is a problem of paramount importance in fields such as computer aided design, virtual reality, computer vision and production engineering [1][2][3]. This problem was addressed first by Hayes and Hallyday [4] who presented a method for fitting a cloud of points to a B-Spline surface based on least-squares minimization of a functional defined as the Euclidean distance between the B-Splines control points and the measured cloud points.…”

Aproximación de perfiles discretos en elementos de contacto de ensambles mecánicos

“…En la práctica es complicado especificar una curva inicial a priori con un número adecuado de puntos de control, de forma que se pueda obtener una aproximación satisfactoria a un perfil de superficie dado (Yang et al, 2004). Un tópico de interés para reducir el gasto computacional es reducir la cantidad de información representada por el número de datos de los puntos medidos (Flöry, 2009;Flöry y Hofer, 2010), y sustituirla por una aproximación de las superficies. Para representar superficies de contacto en FEM se usan elementos discretos, cuyo proceso en sí mismo tiene problemas inherentes a la discretización, que se manifiestan en desviaciones de los ajustes de perfiles continuos mediante elementos discretos.…”

Automatic fitting of conical envelopes to free-form surfaces for flank CNC machining

“…The result is a nearly straight curve that is approximated by a single linear segment, see e.g. [10,23,30] for curve fitting algorithms.…”