Research On Methods For DP Curves And Surfaces Modeling

In Computer Aided Geometric Design(CAGD),NURBS are developed mature in basic.But they are still insufficient,such as no encompassing transcendent curves and surfaces,spiral curve,cycloid,arc,cone,etc.In recent years,many scholars have studied the new type of curves not only in polynomial space,but also in non-polynomial space.Delgado and Pe?a presented a new type of curve.It is called DP curve.DP curve has stability in numerical calculation and linear complexity in computational time.And it is constructed by totally positive basis(NTP basis),which has shape preserving property.This thesis studies the curve and surface modeling method of DP curve.The main work is as follows:1.Pythagorean hodograph(PH)curves are an important subclass of polynomial parametric curves.Their most remarkable properties are that their arc-length function is piecewise polynomial,and that the fixed-distance offsets of PH curves are rational polynomial curves,which can be exactly represented in CAD systems.These properties are especially advantageous in applications such as computer numerical control(CNC),the design of highways and railways,and robotics trajectory planning,etc.Based on DP curve and the definition of PH curve,a necessary and sufficient geometric characterization in terms of the leg-lengths and angles of a control polygon is presented.By the stereographic projection,C~1Hermite PH interpolation curve for data on the spherical surface is constructed.2.Based on cubic DP curve with shape parameters,the tensor product method is used to construct DP surface with shape parameters.G~1-continuous condition between two adjacent DP patches based on the shape parameters is given.The curve can be adjusted more flexibly by adjusting shape parameters.It presents an effective method for the design of curves and surfaces.