Using Cubic Bezier Curve Geometric Constraint Solving

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 technology and variable technology,it means that once the demention constraints and topological constraints are given,the system will produce the design graph automatically.Many problems in engineering can be dealed as geometric constraint solving.At present,there are four basic approaches to geometric constraint solving: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.The innovation of thesis,one gives geometric constraints and mathematics description among points,lines,circles and cubic Bezier curves,the other gives construction of cubic Bezier curve by using these new geometric constraints,and put forward a new method of geometric constraint solving including points,lines,circles and cubic Bezier curves.There is more practical significance for the research of geometric constraint solving,which is the core of parametric technology and variable technology.