Weight-Based Shape Modification of NURBS Curves

With the representation of homogeneous coordinates,we prove in the paper that when one weight changes,the points of NURBS curve move toward or away from the control point.The effect on the curve by modifying two weights is also discussed in the paper.When two weights change simultaneously,the motion of the points on the curve can be regarded as a composite of the two motions：each motion is toward or away from one control point.Furthermore,we also discuss a question that single position and tangent constraints could be realized by a modification of three weights simultaneously.Finally,examples are given to validate the new method.