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(with thanks to Mr. WizardMr. Wizard))

(with thanks to Mr. Wizard))

(with thanks to Mr. Wizard))

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Or usingOne can also use BSplineFuntion[]BSplineFunction[] andin ParametricPlot[] directly:

f = BSplineFunction[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}}, 
                    SplineDegree -> 2, 
                    SplineKnots -> {0, 0, 0, 1, 1, 1}, 
                    SplineWeights -> {1, -1/Sqrt[2], 1}]];
ParametricPlot[f[x], {x, 0, 1}]

Or using BSplineFuntion[] and ParametricPlot[] directly

f = BSplineFunction[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}}, 
                    SplineDegree -> 2, 
                    SplineKnots -> {0, 0, 0, 1, 1, 1}, 
                    SplineWeights -> {1, -1/Sqrt[2], 1}]
ParametricPlot[f[x], {x, 0, 1}]

One can also use BSplineFunction[] in ParametricPlot[]:

f = BSplineFunction[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}}, 
                    SplineDegree -> 2, SplineKnots -> {0, 0, 0, 1, 1, 1}, 
                    SplineWeights -> {1, -1/Sqrt[2], 1}];
ParametricPlot[f[x], {x, 0, 1}]
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Graphics[BSplineCurve[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}},
                      SplineDegree -> 2, SplineKnots -> {0, 0, 0, 1, 1, 1},
                      SplineWeights -> {1, -1/Sqrt[2], 1}],
         BaseStyle -> {BSplineCurveBoxOptions -> {Method -> {"SplinePoints" -> 30}}}, 
         PlotRange -> {{-1, 1}, {-1, 1}}]

(with thanks to Mr. Wizard))

Or using BSplineFuntion[] and ParametricPlot[] directly

f = BSplineFunction[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}}, 
                    SplineDegree -> 2, 
                    SplineKnots -> {0, 0, 0, 1, 1, 1}, 
                    SplineWeights -> {1, -1/Sqrt[2], 1}]
ParametricPlot[f[x], {x, 0, 1}]

enter image description here

Graphics[BSplineCurve[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}},
                      SplineDegree -> 2, SplineKnots -> {0, 0, 0, 1, 1, 1},
                      SplineWeights -> {1, -1/Sqrt[2], 1}],
         BaseStyle -> {BSplineCurveBoxOptions -> {Method -> {"SplinePoints" -> 30}}} 
         PlotRange -> {{-1, 1}, {-1, 1}}]

(with thanks to Mr. Wizard))

Graphics[BSplineCurve[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}},
                      SplineDegree -> 2, SplineKnots -> {0, 0, 0, 1, 1, 1},
                      SplineWeights -> {1, -1/Sqrt[2], 1}],
         BaseStyle -> {BSplineCurveBoxOptions -> {Method -> {"SplinePoints" -> 30}}}, 
         PlotRange -> {{-1, 1}, {-1, 1}}]

(with thanks to Mr. Wizard))

Or using BSplineFuntion[] and ParametricPlot[] directly

f = BSplineFunction[{{-1/Sqrt[2], 1/Sqrt[2]}, {0, Sqrt[2]}, {1/Sqrt[2], 1/Sqrt[2]}}, 
                    SplineDegree -> 2, 
                    SplineKnots -> {0, 0, 0, 1, 1, 1}, 
                    SplineWeights -> {1, -1/Sqrt[2], 1}]
ParametricPlot[f[x], {x, 0, 1}]

enter image description here

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