We present algorithms for computing the differential geometry properties of Frenet apparatus {t,n,b,κ,τ} and higher-order derivatives of intersection curves of implicit and parametric surfaces in R3 for transversal ...We present algorithms for computing the differential geometry properties of Frenet apparatus {t,n,b,κ,τ} and higher-order derivatives of intersection curves of implicit and parametric surfaces in R3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given and plotted.展开更多
To find starting points for all the intersection curves, one of the surfaces is subdivided into some small surface patches. Based on a correlative algorithm of computing the minimum distance of two surfaces, the inter...To find starting points for all the intersection curves, one of the surfaces is subdivided into some small surface patches. Based on a correlative algorithm of computing the minimum distance of two surfaces, the intersections of every patch with another surface are detected, and starting points are calculated by dichotomy. This algorithm shows superior efficiency in the computational complexity and number of iterations needed. It can be used to determine exact starting points on all possible solution curves between any kinds of parametric sculptured surfaces.展开更多
In this paper we present an algorithm with a new trace-terminating conditionfor tracing along surface-surface intersection curves on surface boundaries, while several tracingmethods and embedding methods that include ...In this paper we present an algorithm with a new trace-terminating conditionfor tracing along surface-surface intersection curves on surface boundaries, while several tracingmethods and embedding methods that include tracing scheme may cause false termination with atraditional trace-terminating condition: tracing stops when the surface-domain's boundary isreached. And we also suggest another iterative method to calculate intersection points on surfaceboundaries with parallel surface normal. Some numerical examples with these two ideas andcomparisons to 'DESIGNBASE', 'ACIS', and 'Parasolid' are included to demonstrate the effectivenessof our algorithm.展开更多
文摘We present algorithms for computing the differential geometry properties of Frenet apparatus {t,n,b,κ,τ} and higher-order derivatives of intersection curves of implicit and parametric surfaces in R3 for transversal and tangential intersection. This work is considered as a continuation to Ye and Maekawa [1]. We obtain a classification of the singularities on the intersection curve. Some examples are given and plotted.
文摘To find starting points for all the intersection curves, one of the surfaces is subdivided into some small surface patches. Based on a correlative algorithm of computing the minimum distance of two surfaces, the intersections of every patch with another surface are detected, and starting points are calculated by dichotomy. This algorithm shows superior efficiency in the computational complexity and number of iterations needed. It can be used to determine exact starting points on all possible solution curves between any kinds of parametric sculptured surfaces.
文摘In this paper we present an algorithm with a new trace-terminating conditionfor tracing along surface-surface intersection curves on surface boundaries, while several tracingmethods and embedding methods that include tracing scheme may cause false termination with atraditional trace-terminating condition: tracing stops when the surface-domain's boundary isreached. And we also suggest another iterative method to calculate intersection points on surfaceboundaries with parallel surface normal. Some numerical examples with these two ideas andcomparisons to 'DESIGNBASE', 'ACIS', and 'Parasolid' are included to demonstrate the effectivenessof our algorithm.
