approximating subdivision surfaces

Catmull–Clark subdivision surface

The Catmull–Clark algorithm is a technique used in 3D computer graphics to create smooth surfaces by using a type of subdivision surface modeling It was devised by Edwin Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline surfaces to arbitrary topology In 2005 Edwin Catmull received an Academy Award for Technical Achievement together with Tony DeRose and Jos

Approximating subdivision surfaces with Gregory patches

We present a new method for approximating subdivision surfaces with hardware accelerated parametric patches Our method improves the memory bandwidth requirements for patch control points translating into superior performance compared to existing methods

Six

Subdivision is an efficient method for generating curves and surfaces in computer aided geometric design In general subdivision schemes can be divided into two categories: interpolatory schemes and approximating schemes Li and Zheng constructed interpolatory subdivision from primal approximating subdivision with a new observation of the

Lecture 17: Scheduling the Graphics Pipeline on a GPU

Approximating Subdivision Surfaces with Gregory Patches for Hardware Tessellation Charles Loop Microsoft Research Scott Schaefer Texas AM University Tianyun Ni NVIDIA IgnacioCastan˜o NVIDIA Figure 1: The first image (far left) illustrates an input control mesh regular (gold) faces do not have an incident extraordinary v ertex

Methods for Approximating Loop Subdivision Using

Jul 16 2012The availability of tessellation supported hardware presents an opportunity to develop algorithms that can render subdivision surfaces in realtime We discuss the performance of approximating Loop Subdivision surfaces using tessellation-enabled GPUs in terms of speed and quality of rendering for these methods as well as the implementation strategy

Approximating Catmull

We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a minimal set of bicubic patches For each quadrilateral face of the control mesh we construct a geometry patch and a pair of tangent patches The geometry patches approximate the shape and silhouette of the Catmull-Clark surface and are smooth everywhere []

Approximating Catmull

8 Approximating Catmull-Clark Subdivision Surfaces with Bicubic Patches CHARLES LOOP Microsoft Research and SCOTT SCHAEFER Texas AM University We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a

G2 Bezier Crust on Quad Subdivision Surfaces

Figure 1: Two examples of Bezier crust applied on Catmull-Clark subdivision surfaces Abstract Subdivision surfaces have been widely used in computer graphics and can be classified into two categories ap-proximating and interpolatory Representative approximating schemes are Catmull-Clark (quad) and Loop (trian-gular)

A Method for Constructing Interpolatory Subdivision

May 21 2007In addition a family of subdivision surfaces varying from the given approximatory scheme to its associated interpolatory scheme namely the blending subdivisions can also be established Based on the proposed method variants of several known interpolatory subdivision schemes are constructed

Approximation of Subdivision Surfaces for Interactive

of subdivision surfaces which offers a very close appearance com-pared to the true subdivision surface while being at least one order of magnitude faster than true subdivision rendering Our technique approximating subdivision Alternatively the Modified Butterfly

Loop Subdivision Surface Based Progressive Interpolation

On the other hand even though subdivision surfaces generated by approximating subdivision schemes do not interpolate their control meshes it is possible to use this approach to generate a subdivision surface to interpo-late the vertices of a given mesh One method called global optimization does the work by building a global

Catmull–Clark subdivision surface

The Catmull–Clark algorithm is a technique used in 3D computer graphics to create smooth surfaces by using a type of subdivision surface modeling It was devised by Edwin Catmull and Jim Clark in 1978 as a generalization of bi-cubic uniform B-spline surfaces to arbitrary topology In 2005 Edwin Catmull received an Academy Award for Technical Achievement together with Tony DeRose and Jos

Subdivision surface

We propose an algorithm for visually approximating Catmull-Clark subdivision surfaces possibly with boundaries using a collection of bicubic patches (one for each face of a quad-mesh) We contend approximating the surface with patches that are in one-to-one correspondence with the faces of the coarsest base mesh is best

G2 Bezier Crust on Quad Subdivision Surfaces

Figure 1: Two examples of Bezier crust applied on Catmull-Clark subdivision surfaces Abstract Subdivision surfaces have been widely used in computer graphics and can be classified into two categories ap-proximating and interpolatory Representative approximating schemes are Catmull-Clark (quad) and Loop (trian-gular)

US6950099B2

The surface approximating the original subdivision surface face is given by the standard formula for a cubic Bezier surface: a ⁡ (u v) = [(1-u) 3 3 ⁢ u ⁡ (1-u) 2 3 ⁢ u 2 ⁡ (1-u) u 3] T ⁡ [b 11 b 12 b 13 b 14 b 21 b 22 b 23 b 24 b 31 b 32 b 33 b 34 b 41 b 42 b 43 b 44] ⁡ [(1-v) 3 3 ⁢ v ⁡ (1-v) 2 3 ⁢ v 2 ⁡ (1-v) v 3]

Research

Approximating Catmull-Clark Subdivision Surfaces with Bicubic Patches Loop C and Schaefer S ACM Transactions on Graphics Vol 27 No 1 (2008) pages 8:1-8:11 slides movie Abstract: We present a simple and computationally efficient algorithm for approximating Catmull-Clark subdivision surfaces using a minimal set of bicubic patches

CGAL 5 0 2

Subdivision methods recursively refine a control mesh and generate points approximating the limit surface This package consists of four popular subdivision methods and their refinement hosts Supported subdivision methods include Catmull-Clark Loop Doo-Sabin and ( sqrt{3}) subdivisions

Tangents and curvatures of matrix

Subdivision provides an e cient method to generate smooth curves and surfaces Recently matrix-valued subdivision schemes were introduced to provide more exibility and smaller subdivision templates for curve and surface design For matrix-valued subdivision

A New 4

The approximation order of a convergent subdivision scheme which is exact for (set of polynomials at most degree n) is 3 Smoothness Analysis of Proposed Scheme This section is devoted for analysis of 4-point quaternary approximating subdivision scheme by using Laurent polynomial method The following result shows that scheme is continuous

CGAL 5 0 2

Subdivision methods recursively refine a control mesh and generate points approximating the limit surface This package consists of four popular subdivision methods and their refinement hosts Supported subdivision methods include Catmull-Clark Loop Doo-Sabin and ( sqrt{3}) subdivisions

Building Interpolating and Approximating Implicit Surfaces

This dissertation addresses the problems of building interpolating or approximating im-plicit surfaces from a heterogeneous collection of geometric primitives like points polygons and spline/subdivision surface patches The user can choose to generate a surface that

Subdivision Schemes for Thin Plate Splines

ational problems using approximating subdivision schemes has been presented in 22 The work presented here is distinguished from previous work on variational subdivision for surfaces by the use of an approximating subdivision basis The use of approximating basis functions leads just as for B-splinesin the one dimen-

Assessment of an isogeometric approach with Catmull–Clark

Jul 15 2020Cirak et al implemented Loop subdivision surfaces for solving the Kirchhoff–Love shell formulation This was the first application of subdivision surfaces to engineering problems Subdivision surfaces have subsequently been used in electromagnetics shape optimisation [6 7] acoustics [15 38] and lattice-skin structures

Real

Catmull-Clark subdivision surfaces are the dominant higher-order surface type used in feature films particularly in the area of char-acter modeling [Catmull and Clark 1978] [DeRose et al 1998] Modeling with Catmull-Clark surfaces is familiar and intuitive to artists and the limit surface behaves well when the control mesh is animated

Adaptive fitting algorithm of progressive interpolation

A subdivision scheme is called an interpolating one if the limit surface interpolates the given control mesh such as Butterfly and Kobbelt schemes 13 14 Otherwise it is called an approximating scheme such as Catmull–Clark Doo–Sabin and Loop schemes 15 –17 Approximating subdivision surface usually has better quality than that of