Computer Aided Geometric Design

For prescribed values of a function and its partial derivatives of orders 1 and 2 at the vertices of a square, we fit an interpolating surface. We investigate two families of solutions provided by two Hermite subdivision schemes, denoted HD^2 and HR^2. ...

Starting with a given planar cubic curve [x(t),y(t)]^T, we construct Pythagorean hodograph (PH) space curves of the form [x(t),y(t),z(t)]^T in Euclidean and in Minkowski space, which interpolate the tangent vector at a given point. We prove the ...

Laser range-scanners are used in fields as diverse as product design, reverse engineering, and rapid prototyping to quickly acquire geometric surface data of parts and models. This data is often in the form of a dense, noisy surface mesh that must be ...

We present a new method for interpolation by a shape-preserving space curve with third-order geometric continuity. The curve is represented by a discrete sequence of vertices along with first, second, and third derivative vectors at each vertex, where ...

For prescribed values of a function and its partial derivatives of orders 1 and 2 at the vertices of a square, we fit an interpolating surface. We investigate two families of solutions provided by two Hermite subdivision schemes, denoted H D² and H R². ...

We present a new method for interpolation by a shape-preserving space curve with third-order geometric continuity. The curve is represented by a discrete sequence of vertices along with first, second, and third derivative vectors at each vertex, where ...