Quintic B-spline Curve Generation and Modification based on specified Radius of Curvature
نویسنده
چکیده
A method to generate a quintic B-spline curve which passes through the given points is described. In this case, there are four more unknown control point positions than there are equations. To overcome this problem three methods are described. First, solve the underdetermined system as it stands. Secondly, decrease the number of unknown control point positions in an underdetermined system in order to convert it to a determined system. Third, a method to increase the number of equations is employed to change an underdetermined system to a determined system. In addition to this, another method to generate a quintic B-spline curve using given points with gradients in sequence is described. In this case, a linear system will be either overdetermined, determined or underdetermined. This depends on the number of given points with gradients in sequence. Additionally, a method to modify a quintic B-spline curve is described. The objective is to change an aesthetically unpleasing curve to an aesthetically pleasing curve. This is accomplished by minimizing the difference between the quintic B-spline curves radius of curvature and the specified radius of curvature using the least-squares method. Key-Words: B-spline curve generation, curvature vector, curve shape modification, given points, given points with gradients, underdetermined system, overdetermined system
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B-spline Curve Generation and Modification based on Specified Radius of Curvature
A method to generate a quintic B-spline curve which passes through given points is described. In this case, there are four more equations than there are control point positions. Two methods have been developed to compensate for the difference between the number of unknowns and that of the equations. These are assuming that the curvatures at both ends of the curve are zero, and assigning four gr...
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