Ray tracing parametric surface patches utilizing numerical techniques and ray coherence

1986 ◽  
Vol 20 (4) ◽  
pp. 279-285 ◽  
Author(s):  
Kenneth I. Joy ◽  
Murthy N. Bhetanabhotla
Keyword(s):  
Ray Tracing ◽  
Parametric Surface ◽  
Numerical Techniques ◽  
Surface Patches

Rational Polynomial Surface Intersections

1991 ◽  
Author(s):  
G. A. Kriezis ◽  
N. M. Patrikalakis
Keyword(s):  
Parameter Space ◽  
Numerical Techniques ◽  
B Spline ◽  
Partial Derivatives ◽  
Surface Patches ◽  
Spline Surface ◽  
Rational Polynomial ◽  
Convexity Properties ◽  
Surface Intersections ◽  
Polynomial Surface

Abstract This paper presents a new algorithm for the computation of the intersection of two rational B-spline surface patches. This algorithm is based on the computation of significant points of the intersection in the parameter space of one of the patches using direct numerical techniques; partitioning of the intersection domain at these points; tracing of the resulting intersection segments using subdivision and Newton or marching techniques; and verification of computation of all intersection branches using convexity properties of the two surfaces and their partial derivatives.

Intersection of Offset Surfaces of Parametric Patches

1992 ◽  
Author(s):  
Yu Wang
Keyword(s):  
Parametric Surface ◽  
Intersection Curve ◽  
B Spline ◽  
Numerical Examples ◽  
Surface Patches ◽  
Normal Projection ◽  
Offset Surfaces ◽  
Nurbs Surfaces ◽  
Effectiveness And Efficiency ◽  
Offset Surface

Abstract In this paper, we present a new method to calculate intersection curve of offset surfaces of two parametric surface patches. This method is based on the concept of normal projection and the intersection problem is formulated with a set of tensorial differential equations. The intersection is represented in the parametric spaces of the base surfaces and no offset surface approximation is needed. Numerical examples are presented for non-uniform rational b-spline (NURBS) surfaces to illustrate the effectiveness and efficiency of the proposed approach.

Ray tracing trimmed rational surface patches

1990 ◽  
Vol 24 (4) ◽  
pp. 337-345 ◽  
Author(s):  
Tomoyuki Nishita ◽  
Thomas W. Sederberg ◽  
Masanori Kakimoto
Keyword(s):  
Ray Tracing ◽  
Rational Surface ◽  
Surface Patches
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