Low-level With Shape Parameter Uniform B-spline

The uniform B spline bases have no shape parameter .Augmenting a shape parameter and Elevating the uniform B spline base once with support interval and continuity invariability, then the B spline base with shape parameter can be gained.When the control polygon is unchanged, the spline curve which is constructed by the uniform B spline bases with shape parameters can adjust the curve's shape and the approaching degree between the curve and its control polygon with changing the parameter value.In the first section, the development history of curve and surface constructing modelling is reviewed. For the shape adjusting,the purpose of this thesis is to construct uniform B spline curves with shape parameter .The uniform B spline bases with shape parameter are first constructed to adjust the curve's shape by the shape parameter.In the second section, the uniform B spline bases with shape parameter of five order are first constructed and their properties including the base's positivity, normalization, symmetry, continuity, linear independent are discussed; then uniform B spline curve with shape parameter of five order is constructed and its properties: convex hull,geometry invariability, local modification, continuity are discussed. When the control points are not changed, the curve's shape can be modified by the shape parameter.In the third section, the uniform B spline bases and curve with shape parameter of six order are contracted and their properties are discussed (the same as the second section).In the fourth section, firstly the main conclusions of this thesis are induced; then the work in the future is mentioned.