School of Computer & Communication Engineering, University of Science and Technology Beijing Beijing, China

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Abstract—The paper presents a solution to calculate intersection between a plane and bi-cubic Bezier curved surface. The paper first constructs bounding box based on the control grid by the characteristics of the Bezier surface, and then makes use of the plane half-space properties to convert the problem that calculates the intersection line between the plane and the parameter curved surface into calculating a series of intersection points by using the method that apply the bi-linear interpolation algorithm to the curved surface in representation of parameter area. The intersection line between the plane and the surface can be calculated by connecting the intersection points. This method can solve the surface intersection line well whether the line is discontinuous or form a closed cycle. The algorithm is relatively simple, and has good adaptability for calculating the intersection line between the plane and the curved surface.

Index Terms—Bounding box, Linear interpolation, Bezier surface.

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Cite: Hong Bao, Yanying Xu, "Intersection between Bi-cubic Bezier Curved Surface and Plane," Journal of Software vol. 8, no. 8, pp. 1976-1983, 2013.