Sep 1, 2017 · We introduce the new framework of Patchwork B-splines (PB-splines), which alleviates these constraints and therefore increases the flexibility of the representations that are available in different parts of a geometric model.

Sep 19, 2019 · We adopt the framework of Patchwork B-splines, which supports very flexible refinement strategies, and apply it to the construction of lofting surfaces. This approach not only reduces the resulting data volume but also limits the propagation of derivative discontinuities.

U is the neighborhood in |K| of x . A regular parameterization π is one that is continuously differentiable, one‐to‐one, and has a Jacobi matrix of maximum rank. How can we prove properties of a subdivision scheme? Prove properties (convergence, continuity, affine invariance, etc.) using eigen‐analysis. Matrix.

the B-spline surface defined by these information is the following: where N i,p ( u ) and N j,q ( v ) are B-spline basis functions of degree p and q , respectively. Note that the fundamental identities , one for each direction, must hold: h = m + p + 1 and k = n + q + 1.

We present a new interpolatory subdivision scheme based on PB-splines (Point-Based B-splines), over trian-gular meshes. Using the stencil of the interpolatory 3-subdivision scheme, we propose...

The surface analogue of the B-spline curve is the B-spline surface (patch). This is a tensor product surface defined by a topologically rectangular set of control points , , and two knot vectors and associated with each parameter , . The corresponding integral B-spline surface is given by.

Sep 27, 2023 · This document facilitates understanding of core concepts about uniform B-spline and its matrix representation.

Jul 29, 2010 · This work considers the fitting of data points organized in a rectangular array to parametric spline surfaces. Point Based (PB) splines, a generalization

Theorem The PB-splines span the patchwork spline space Pif both SCA and CBA are satisfied. Thus, we have two different characterizations of the patchwork spline space: P= ff2Cs(): fj ˇ ‘2V ‘j ˇ 8‘= 1;:::;Ng; (“implicit” definition: space defined by properties of functions) P= span [N ‘=1 f ‘2B‘: ‘j ˇ ‘6= 0 and ‘j = 0g

B-Spline Surfaces. B-Spline surface - tensor product surface of B-Spline curves. Building blocks: Control net, m + 1 rows, n + 1 columns: P. ij. Knot vectors . U = { u. 0, u. 1, …, u. h }, V = { v. 0, v. 1, …, v. k} The degrees . p. and . q. for the . u. and . v. directions