Practical quality control tools for curves and surfaces

Curves (geometry) and surfaces created by Computer Aided Geometric Design systems in the engineering environment must satisfy two basic quality criteria: the geometric shape must have the desired engineering properties; and the objects must be parameterized in a way which does not cause computational difficulty for geometric processing and engineering analysis. Interactive techniques are described which are in use at Boeing to evaluate the quality of aircraft geometry prior to Computational Fluid Dynamic analysis, including newly developed methods for examining surface parameterization and its effects

Algoritma Subbahagian Dalam Cagd

CAGD adalah singkatan untuk "Computer Aided Geometric Design" atau di dalam Bahasa Melayu ialah Rekabentuk Geometri Bantuan Komputer iaitu RGBK. Membina dan mengawal lengkung menjadi keutamaan di dalam rekabentuk berbantukan komputero Teknik pe~anaan lengkung dan permukaan menggunakan polinomial Bernstein dalam CAGD ini mula diperkenalkan oleh Paul de Casteljau dan Pierre Benero Projek ini membincangkan dua algoritma subbahagian yang digunakan dalam proses untuk menghasilkan lengkung dan permukaan iaitu algoritma de Casteljau dan algoritma Chaikin. Algoritma de Casteljau menghasilkan lengkung dengan carn menginterpolasi titik kawalan pertama dan titik kawalan terakhir manakala algoritma Chaikin menjana lengkung dengan cara memotong setiap penjuru poligon kawalan asalo Lengkung dan permukaan Bezier kini digunakan secara meluas sebagai asas matematik dalam sistem CAD dan menjadi alat utama dalam perkembangan kaedah-kaedah bam untuk keperluan lengkung dan permukaan dalam CAD, CAGD is the abbreviation for the Computer Aided Geometric Design or in Malay Language, it is called "Rekabentuk Geometri Bantuan Komputer" or RGBKo Generating and controlling curves are important in computer aided designo The techniques for generating the curves and surfaces in CAGD were developed by Paul de Casteljau and Pierre Beziero This project will discuss about 2 subdivision algorithms used in the process of generating curves and surfaces, that are de Casteljau algorithm and Chaikin algorithm.o De Casteljau algorithm generates curves by interpolating the fIrst control point and last control point Chaikin algorithm generates curves by cutting every comer of original control polygono The Bezier curves and surfaces nowadays are established as the mathematical basis of many CAD systems and have fonned a major tool for the development of new methods for curves and surfaces description

Area-Construction Algorithms Using Tangent Circles

Computer aided geometric design employs mathematical and computational methods for describing geometric objects, such as curves, areas in two dimensions (2D) and surfaces, and solids in 3D. An area can be represented using its boundary curves, and a solid can be represented using its boundary surfaces with intersection curves among these boundary surfaces. In addition, other methods, such as the medial-axis transform, can also be used to represent an area. Although most researchers have presented algorithms that find the medial-axis transform from an area, a algorithm using the contrasting approach is proposed; i.e., it finds an area using a medial-axis transform. The medial-axis transform is constructed using discrete points on a curve and referred to as the skeleton of the area. Subsequently, using the aforementioned discrete points, medial-axis circles are generated and referred to as the muscles of the area. Finally, these medial-axis circles are blended and referred to as the blended boundary curves skin of the area; consequently, the boundary of the area generated is smooth

A resultant approach to detect intersecting curves in the projective space

Given two curves in the projective space, either implicitly or by a parameterization, we want to check if they intersect. For that purpose, we present and further develop generalized resultant techniques. Our aim is to provide a closed formula in the inputs which vanishes if and only if the two curves intersect. This could be useful in Computer Aided Design, for computing the intersection of algebraic surfaces