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Bézier surfaces are a species of mathematical spline used in computer graphics, computer-aided design, and finite element modeling. As with Bézier curves, a Bézier surface is defined by a set of control points. Similar to interpolation in many respects, a key difference is that the surface does not, in general, pass through the central ...
Freeform surface modelling is a technique for engineering freeform surfaces with a CAD or CAID system.. The technology has encompassed two main fields. Either creating aesthetic surfaces (class A surfaces) that also perform a function; for example, car bodies and consumer product outer forms, or technical surfaces for components such as gas turbine blades and other fluid dynamic engineering ...
Thin plate splines (TPS) are a spline-based technique for data interpolation and smoothing. "A spline is a function defined by polynomials in a piecewise manner." [1] [2] They were introduced to geometric design by Duchon. [3] They are an important special case of a polyharmonic spline. Robust Point Matching (RPM) is a common extension and ...
A NURBS curve represents a 1D perfectly smooth curve in 2D or 3D space. To represent a three-dimensional solid object, or a patch of one, B-Spline or NURBS curves are extended to surfaces. These surfaces consist of a rectangular grid of control points, called a control grid or control net, and two knot vectors, commonly called U and V.
In geometric modelling and in computer graphics, a composite Bézier curve or Bézier spline is a spline made out of Bézier curves that is at least continuous. In other words, a composite Bézier curve is a series of Bézier curves joined end to end where the last point of one curve coincides with the starting point of the next curve.
In solid modeling and computer-aided design, boundary representation (often abbreviated B-rep or BREP) is a method for representing a 3D shape [1] by defining the limits of its volume. A solid is represented as a collection of connected surface elements, which define the boundary between interior and exterior points.
Bicubic interpolation can be accomplished using either Lagrange polynomials, cubic splines, or cubic convolution algorithm. In image processing , bicubic interpolation is often chosen over bilinear or nearest-neighbor interpolation in image resampling , when speed is not an issue.
In computer-aided geometric design a control point is a member of a set of points used to determine the shape of a spline curve or, more generally, a surface or higher-dimensional object.