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Special Surfaces refers to those having some special geometric properties of surfaces, such as spherical, ellipsoid, Bezier surface, torus, pipeline surfaces. Because they have some special properties, they are widely used in the computer field. Study the calculation of the distance between them and the positional relationship becomes very meaningful. The pipeline surface is a radius variation curve of movement of the ball along a space formed by the envelope. Pipe surfaces, an efficient and accurate method to calculate the distance between the surfaces of the two pipes with cone-sphere as a bounding box, by constant pruning to calculate the distance between the surfaces of the two pipes. The surfaces of the two pipes, the distance of the bounding box to approximate their distance, the accuracy of the approximation increases with curved constant breakdown. In this paper, we propose a fast and efficient method of pruning, collision detection, we only need the bounding box collision can be pruned, but doing so will produce incorrect results in the distance calculation, in order to to ensure the correctness of pruning, we use the distance interval instead of the distance between the bounding box, thereby ensuring the correctness of the results. This paper presents an efficient method to calculate the bounding box, by the nature of the use of Bernstein polynomials, to accelerate the bounding box of the calculation process to avoid solving high-order equation in the calculation process, greatly improve the efficiency of the algorithm. Finally, we also promote our algorithm to the distance between the calculated two dynamic deformation of the pipe surface. Pipeline for deformable surfaces, paper, based on the continuity of motion changes some acceleration measures to accelerate the speed of the algorithm. Finally, we also give some experimental results, the comparison of our methods and Lee's the method on GMP2010 method, the experimental results show that our new method is far superior to the above two methods, especially our approach is particularly efficient on complex objects. The torus is a donut shape of the surface of revolution, by a circle around an axis of rotation and the circle coplanar generated. The torus is another type of special surfaces, as one of the most simple and complex topological surfaces, widely used in geometric modeling, collision detection, the convex hull and arranged research, cluster analysis, as well as physics, chemistry, molecular mechanics simulation. In this article, we have conducted a preliminary exploration will have its positional relationship. Through contraction and inversion transform torus reduced order. The torus (four surfaces) by shrinking into round (quadratic curve), and then through the inverse transformation of the circle is converted into a straight line. In this paper, we reduced-order through above two torus positional relationship, and finally into two unary quartic equation root distribution. By analyzing the roots of the two unary four equation to enumerate all the positional relationship of the two torus, given the conditions of each position relationship between the equivalent. In this paper, we have given - some preliminary analysis of the results.
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