Loop detection in surface patch intersections
Computer Aided Geometric Design
Computer Aided Geometric Design
A marching method for parametric surface/surface intersection
Computer Aided Geometric Design
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
The NURBS book
An efficient surface intersection algorithm based on lower-dimensional formulation
ACM Transactions on Graphics (TOG)
A new approach to the surface intersection problem
Computer Aided Geometric Design
SIAM Review
Shape Interrogation for Computer Aided Design and Manufacturing
Shape Interrogation for Computer Aided Design and Manufacturing
Matlab-based problem-solving environment for geometric processing of surfaces
ICMS'06 Proceedings of the Second international conference on Mathematical Software
A new iterative mutually coupled hybrid GA-PSO approach for curve fitting in manufacturing
Applied Soft Computing
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In this paper, we focus on the parametric-implicit surface intersection problem. In our approach, this problem is formulated in terms of an initial value problem of first-order ordinary differential equations (ODEs). To this end, we take advantage of the orthogonality at any point on the intersection curve between the tangent vector to that curve and the normal vector to the implicit surface. This yields an initial value system of ODEs that is numerically integrated through an adaptive Runge-Kutta method. In order to determine the initial value for this system, a simple procedure based on the scalar and vector fields associated with the function defining the implicit surface and its gradient is described. Such a procedure yields a starting point on the nearest branch of the intersection curve. The performance of the presented method is analyzed by means of some illustrative examples.