Midpoint subdivision generalizes the Lane-Riesenfeld algorithm for uniform tensor product splines and can also be applied to non regular meshes. For example, midpoint subdivision of degree 2 is a specific Doo-Sabin algorithm and midpoint subdivision of degree 3 is a specific Catmull-Clark algorithm. In 2001, Zorin and Schröder were able to prove C1-continuity for midpoint subdivision surfaces a...

These course notes will attempt to answer the following questions: What is subdivision? How can the rules for subdivision schemes be derived in a systematic manner? How can these rules be extended to handle special topological features such as extraordinary points or creases? We will argue that most subdivision schemes correspond to a special type of multigrid method that generates shapes which...

We introduce the RGB Subdivision: an adaptive subdivision scheme for triangle meshes, which is based on the iterative application of local refinement and coarsening operators, and generates the same limit surface of the Loop subdivision, independently on the order of application of local operators. Our scheme supports dynamic selective refinement, as in Continuous Level Of Detail models, and it...

This paper presents approaches of incorporating subdivision techniques in the rendering process for computer-generated line drawings. A new method for accelerating silhouette detection is introduced. This “silhouette propagation” method gains its strength from being intertwined with the 3D subdivision process. Another technique reduces the number of 3D subdivision steps necessary for high-quali...

Hierarchical subdivision techniques remove the need for a-priori meshing of surfaces when approximating global illumination. In addition they allow progressive re nement of the solution. However, when subdivision is based upon Monte Carlo methods, due to the stochastic nature of such techniques, subdivision decisions cannot be made unless a su ciently large number of samples have been considere...

Effective conservation of biological diversity on private lands will require changes in land-use policy and development practice. Conservation development (CD) is an alternative form of residential development in which homes are built on smaller lots and clustered together and the remainder of the property is permanently protected for conservation purposes. We assessed the degree to which CD is...

This work is about the implementation of a MPEG-4 decoder for subdivision surfaces, which are powerful 3D paradigms allowing to compactly represent piecewise smooth surfaces. This ‘study’ will take place in the framework of MPEG-4 AFX, the extension of the MPEG-4 standard including the subdivision surfaces. This document will introduce, with some details, the ‘theory’ of subdivision surfaces in...

The Falkland Islands (Long 57-62°W; Lat51-53°S), land area 12,200km have a cool temperate (2.2°C.9.4°C), oceanic climate. Rainfall varies between 400-800mm and is lowest in spring. The islands were glaciated only on the highest ground with surrounding land affected by a periglacial environment. During the Post-glacial period acid, organic soils have formed mainly because of low temperature and ...

We derive necessary and sufficient conditions for tangent plane and C-continuity of stationary subdivision schemes near extraordinary vertices. Our criteria generalize most previously known conditions. We introduce a new approach to analysis of subdivision surfaces based on the idea of the universal surface. Any subdivision surface can be locally represented as a projection of the universal sur...