Smooth parametric surfaces and n-sided patches

The theory of 'geometric continuity' within the subject of CAGD is reviewed. In particular, we are concerned with how parametric surface patches for CAGD can be pieced together to form a smooth Ck surface. The theory is applied to the problem of filling an n-sided hole occurring within a smooth rectangular patch complex. A number of solutions to this problem are surveyed

Blending techniques in Curve and Surface constructions

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Discrete B-splines and subdivision techniques in compter-aided geometric design and computer graphics

Journal ArticleThe relevant theory of discrete 5-sphnes with associated new algorithms is extended to provide a framework for understanding and implementing general subdivision schemes for nonuniform B-splines. The new derived polygon corresponding to an arbitrary refinement of the knot vector for an existing .B-spline curve, including multiplicities, is shown to be formed by successive evaluations of the discrete B-spline defined by the original vertices, the original knot vector, and the new refined knot vector. Existing subdivision algorithms can be seen as proper special cases. General subdivision has widespread applications in computer-aided geometric design, computer graphics, and numerical analysis. The new algorithms resulting from the new theory lead to a unification of the display model, the analysis model, and other needed models into a single geometric model from which other necessary models are easily derived. New sample algorithms for interference calculation, contouring, surface rendering, and other important calculations are presented

Extensions to OpenGL for CAGD.

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

VGRIDSG: An unstructured surface grid generation program

This report contains an overview of the VGRIDSG unstructured surface grid generation program. The VGRIDSG program was created from the VGRID3D unstructured grid generation program developed by Vigyan, Inc. The purpose of this report is to document the changes from the original VGRID3D program and to describe the capabilities of the new program

Semantic definition of a subset of the structured query language (SQL)

Journal ArticleSQL is a relational database definition and manipulation language. Portions of the manipulation language are readily described in terms of relational algebra. The semantics of a subset of the SQL select statement is described. The select statement allows the user to query the database. The select statement is shown to be equivalent to a series of relational and set operations. The semantics are described in terms of abstract data types for relation schemes, tuples, and relations. Certain forms of the union or intersection of two select statements are shown to have equivalent single select statement forms

The Computer Graphics Scene in the United States

We briefly survey the major thrusts of computer graphics activities, examining trends and topics rather than offering a comprehensive survey of all that is happening. The directions of professional activities, hardware, software, and algorithms are outlined. Within hardware we examine workstations, personal graphics systems, high performance systems, and low level VLSI chips; within software, standards and interactive system design; within algorithms, visible surface rendering and shading, three-dimensional modeling techniques, and animation. Note: This paper was presented at Eurographics\u2784 in Copenhagen, Denmark