The circle as a smoothly joined BR-curve on [0, 1] Original Research Article

The full circle as an image of [0, 1] is represented as a BR-curve with five massic vectors (i.e., weighted points or pure vectors). In order to obtain Ck smoothly joined circles, we determine different one-to-one rational changes of parameter. They lead to control polygons consisting in five (respectively seven, nine) massic vectors for k = 1 (respectively k = 3, k = 5). This study is completed by an algorithm and solutions with only positively weighted points.