Abstract
The problem of intersecting two parametric surfaces has been one of the main technical challenges in computer-aided design, computer graphics, solid modeling, and geometrics. This paper aims at reducing and minimizing time and space required for the computations process of parametric surface intersection. To do this, a new numerically accelerating method based on continuation technique was utilized first by calculating a starting point, and second by tracing sequential points along the intersection curve following Broyden's method. Two factors have been identified as influential in controlling component jumping: initial points and step size. Test examples of intersecting two parametric surfaces demonstrated that this method was highly efficient with high-speed parametric solution. The intersection results are often given as curve's points.
Highlights
The intersection between two parametric surfaces has been an incessantly fascinating yet challenging topic in algebraic geometry because it has significant applications in computer graphics, modeling and computeraided geometric design
This paper aims at reducing and minimizing time and space required for the computations process of parametric surface intersection
A new numerically accelerating method based on continuation technique was utilized first by calculating a starting point, and second by tracing sequential points along the intersection curve following Broyden’s method
Summary
The intersection between two parametric surfaces has been an incessantly fascinating yet challenging topic in algebraic geometry because it has significant applications in computer graphics, modeling and computeraided geometric design. A. M [15] presented two methods for computing the intersection points of two parametric surfaces and one technique for computing the start point based on extended Newton method. M [15] presented two methods for computing the intersection points of two parametric surfaces and one technique for computing the start point based on extended Newton method These methods gave an acceptable accurate result for computing the intersection curve between two surfaces. Continuation technique among these methods uses extended Newton method frequently. The paper aims to solve the dragging problem of intersection parametric surfaces including biquadratic B ezier form surface intersection by optimizing Alsaidi’s work [15] through minimizing the required memory and rendering the computations as simple as possible.
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