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In principle this should work:

pts = {{-1, 0}, {-1, 1}, {0, 0}, {1, 1}, {1, 0}};

g = Graphics[{FilledCurve@BSplineCurve[pts, SplineClosed -> True]}]

enter image description here

DiscretizeGraphics[g]

enter image description here

But as you can see, the result is wrong.

This may be the same bug as described here:

You may want to report it to Wolfram again in the hope that more reports equal a higher likelihood of fixing it ...

In principle this should work:

pts = {{-1, 0}, {-1, 1}, {0, 0}, {1, 1}, {1, 0}};

g = Graphics[{FilledCurve@BSplineCurve[pts, SplineClosed -> True]}]

enter image description here

DiscretizeGraphics[g]

enter image description here

But as you can see, the result is wrong.

This may be the same bug as described here:

You may want to report it to Wolfram again in the hope that more reports equal a higher likelihood of fixing it ...

In principle this should work:

pts = {{-1, 0}, {-1, 1}, {0, 0}, {1, 1}, {1, 0}};

g = Graphics[{FilledCurve@BSplineCurve[pts, SplineClosed -> True]}]

enter image description here

DiscretizeGraphics[g]

enter image description here

But as you can see, the result is wrong.

This may be the same bug as described here:

You may want to report it to Wolfram again in the hope that more reports equal a higher likelihood of fixing it ...

Source Link
Szabolcs
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In principle this should work:

pts = {{-1, 0}, {-1, 1}, {0, 0}, {1, 1}, {1, 0}};

g = Graphics[{FilledCurve@BSplineCurve[pts, SplineClosed -> True]}]

enter image description here

DiscretizeGraphics[g]

enter image description here

But as you can see, the result is wrong.

This may be the same bug as described here:

You may want to report it to Wolfram again in the hope that more reports equal a higher likelihood of fixing it ...