In the function space,a class of triangular B-spline curves and surfaces was constructed,featuring properties such as shape adjustability,high-order continuity,and variation diminishing.The triangular B-spline basis functions were defined,the role of the parameter in adjusting the shape of triangular B-spline curves was analyzed,and transcendental curves such as cycloids,spirals,and ellipses constructed from triangular B-splines were precisely depicted.Finally,triangular B-spline surfaces were constructed based on the tensor product form.Examples demonstrated the practicality and effectiveness of the triangular B-spline surfaces in CAGD geometric modeling.
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