Derivation of linear interpolation?
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Anyone know a good derivation of the linear interpolation:
$$frac{y-y_0}{x-x_0}=frac{y_1-y_0}{x_1-x_0}$$
Wikipedia gives one, which I don't understand.
interpolation
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
$endgroup$
add a comment |
$begingroup$
Anyone know a good derivation of the linear interpolation:
$$frac{y-y_0}{x-x_0}=frac{y_1-y_0}{x_1-x_0}$$
Wikipedia gives one, which I don't understand.
interpolation
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
$endgroup$
$begingroup$
Is this perhaps doable with similar triangles? peltiertech.com/images/2011-08/interpolationalgebra.png
$endgroup$
– mavavilj
Mar 25 '16 at 7:38
add a comment |
$begingroup$
Anyone know a good derivation of the linear interpolation:
$$frac{y-y_0}{x-x_0}=frac{y_1-y_0}{x_1-x_0}$$
Wikipedia gives one, which I don't understand.
interpolation
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
$endgroup$
Anyone know a good derivation of the linear interpolation:
$$frac{y-y_0}{x-x_0}=frac{y_1-y_0}{x_1-x_0}$$
Wikipedia gives one, which I don't understand.
interpolation
interpolation
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
asked Mar 25 '16 at 7:18
mavaviljmavavilj
2,72511035
2,72511035
$begingroup$
Is this perhaps doable with similar triangles? peltiertech.com/images/2011-08/interpolationalgebra.png
$endgroup$
– mavavilj
Mar 25 '16 at 7:38
add a comment |
$begingroup$
Is this perhaps doable with similar triangles? peltiertech.com/images/2011-08/interpolationalgebra.png
$endgroup$
– mavavilj
Mar 25 '16 at 7:38
$begingroup$
Is this perhaps doable with similar triangles? peltiertech.com/images/2011-08/interpolationalgebra.png
$endgroup$
– mavavilj
Mar 25 '16 at 7:38
$begingroup$
Is this perhaps doable with similar triangles? peltiertech.com/images/2011-08/interpolationalgebra.png
$endgroup$
– mavavilj
Mar 25 '16 at 7:38
add a comment |
1 Answer
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Since it is a linear interpolation, just consider a straight line $y=a+ bx$ which goes through two points $(x_0,y_0)$ and $(x_1,y_1)$. So $$y_0=a+b x_0$$ $$y_1=a+b x_1$$ Solve for $a,b$.
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
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add a comment |
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1 Answer
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1 Answer
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oldest
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active
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active
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votes
$begingroup$
Since it is a linear interpolation, just consider a straight line $y=a+ bx$ which goes through two points $(x_0,y_0)$ and $(x_1,y_1)$. So $$y_0=a+b x_0$$ $$y_1=a+b x_1$$ Solve for $a,b$.
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
$endgroup$
add a comment |
$begingroup$
Since it is a linear interpolation, just consider a straight line $y=a+ bx$ which goes through two points $(x_0,y_0)$ and $(x_1,y_1)$. So $$y_0=a+b x_0$$ $$y_1=a+b x_1$$ Solve for $a,b$.
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
$endgroup$
add a comment |
$begingroup$
Since it is a linear interpolation, just consider a straight line $y=a+ bx$ which goes through two points $(x_0,y_0)$ and $(x_1,y_1)$. So $$y_0=a+b x_0$$ $$y_1=a+b x_1$$ Solve for $a,b$.
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
$endgroup$
Since it is a linear interpolation, just consider a straight line $y=a+ bx$ which goes through two points $(x_0,y_0)$ and $(x_1,y_1)$. So $$y_0=a+b x_0$$ $$y_1=a+b x_1$$ Solve for $a,b$.
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
answered Mar 25 '16 at 8:07
Claude LeiboviciClaude Leibovici
120k1157132
120k1157132
add a comment |
add a comment |
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$begingroup$
Is this perhaps doable with similar triangles? peltiertech.com/images/2011-08/interpolationalgebra.png
$endgroup$
– mavavilj
Mar 25 '16 at 7:38