How many points are required to fix a given curve from a locus
$begingroup$
Say I have a locus on the $x,y$ plane defined by the parametric implicit function $$F(x, y, p_1, p_2, ..., p_n)=0$$ where $p_1, p_2, .., p_n$ are parameters.
I now want to constrain $F$ to pass through a given set of points of the plane.
Is there a general method to establish what is the minimum amount of points I have to use to fully define the $p_n$ parameters, i.e. to reduce the locus to a single curve?
locus implicit-function
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
$endgroup$
add a comment |
$begingroup$
Say I have a locus on the $x,y$ plane defined by the parametric implicit function $$F(x, y, p_1, p_2, ..., p_n)=0$$ where $p_1, p_2, .., p_n$ are parameters.
I now want to constrain $F$ to pass through a given set of points of the plane.
Is there a general method to establish what is the minimum amount of points I have to use to fully define the $p_n$ parameters, i.e. to reduce the locus to a single curve?
locus implicit-function
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
$endgroup$
add a comment |
$begingroup$
Say I have a locus on the $x,y$ plane defined by the parametric implicit function $$F(x, y, p_1, p_2, ..., p_n)=0$$ where $p_1, p_2, .., p_n$ are parameters.
I now want to constrain $F$ to pass through a given set of points of the plane.
Is there a general method to establish what is the minimum amount of points I have to use to fully define the $p_n$ parameters, i.e. to reduce the locus to a single curve?
locus implicit-function
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
$endgroup$
Say I have a locus on the $x,y$ plane defined by the parametric implicit function $$F(x, y, p_1, p_2, ..., p_n)=0$$ where $p_1, p_2, .., p_n$ are parameters.
I now want to constrain $F$ to pass through a given set of points of the plane.
Is there a general method to establish what is the minimum amount of points I have to use to fully define the $p_n$ parameters, i.e. to reduce the locus to a single curve?
locus implicit-function
locus implicit-function
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
asked Nov 27 '18 at 10:29
IncrediblyConvolutedIncrediblyConvoluted
11
11
add a comment |
add a comment |
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