This document has two objectives: decomposition of a given trimmed surface into several four-sided subregions and creation of a diffeomorphism from the unit square onto each subregion. We aim at having a diffeomorphism which is easy and fast to evaluate. Throughout this paper one of our objectives is to keep the shape of the curves delineating the boundaries of the trimmed surfaces unchanged. The approach that is used invokes the use of transfinite interpolations. We will describe an automatic manner to specify internal cubic Bezier-spline curves that are to be subsequently interpolated by a Gordon patch. Some theoretical criterion pertaining to the control points of the internal curves is proposed and proved so as to ensure that the resulting Gordon patch is a diffeomorphism. Numerical results are reported to illustrate the approaches. Our benchmarks include CAD objects which come directly from IGES files.

Many computer graphic API’s, including OpenGL, emphasize modeling with rectangular patches, which are especially useful in Computer Aided Geomeric Design (CAGD). However, not all shapes are rectangular; some are triangular or more complex. This paper extends the OpenGL library to support the modeling of triangular patches, Coons patches, and Box-splines patches. Compared with the triangular patch created from degenerate rectangular Bezier patch with the existing functions provided by OpenGL, the triangular Bezier patches can be used in certain design situations and allow designers to achieve high-quality results that are less CPU intense and require less storage space. The addition of Coons patches and Box splines to the OpenGL library also give it more functionality. Both patch types give CAGD users more flexibility in designing surfaces. A library for all three patch types was developed as an addition to OpenGL.

This document has two objectives: decomposition of a given trimmed surface into several four-sided subregions and creation of a diffeomorphism from the unit square onto each subregion. We aim at having a diffeomorphism which is easy and fast to evaluate. Throughout this paper one of our objectives is to keep the shape of the curves delineating the boundaries of the trimmed surfaces unchanged. The approach that is used invokes the use of transfinite interpolations. We will describe an automatic manner to specify internal cubic Bezier-spline curves that are to be subsequently interpolated by a Gordon patch. Some theoretical criterion pertaining to the control points of the internal curves is proposed and proved so as to ensure that the resulting Gordon patch is a diffeomorphism. Numerical results are reported to illustrate the approaches. Our benchmarks include CAD objects which come directly from IGES files.