Using Cubic Bezier Curve For Solving Geometric Constraint Problems Algorithm Research

Computer Aided Design technology is a kind of technology that use hardware and software of computer to do modeling, modify, analyze or optimize work. It widely applies to all kinds of field of scientific research and living life, the application level of CAD technology has already become one of the most important symbols to estimate the science and technology and the industry modernization of a country.The development of CAD technology has gone through four significant technology innovations, the last innovation is the appearance of variable technology. Geometric constraint solving is the core of parametric and variational Design, it means that once the dimension constraints and topological constraints are given, the system will produce the design graph automatically. Many problems in engineering can be treated as geometric constraint solving.At present, approaches to geometric constraint solving contain numerical approach, symbolic approach, rule-based approach and graph-based approach.The algorithms of geometric constraint solving mainly construct geometric graph, including points, lines and circles. But geometric graph often includes cubic curve or more complicated curve in practical engineering. The thesis expands the drawing scope of geometric constraint solving by increasing cubic Bezier curve as a new geometric primitive. This thesis gives the new geometric constraints and mathematics description between cubic Bezier curves based the reference [1], and gives the new algorithm about the construction of geometric constraint solving problems which contained cubic Bezier curves. This algorithm farther expands the drawing scope of geometric constraint solving. There is more practical significance for the research of geometric constraint solving, which is the core of parametric technology and variable technology.