Approximate a ($y²-x²=1$) hyperbola with line segments and elliptic ($a(x-x_0)²+b(y-y_0)²=1$) arcs
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On some IT graphic systems, you have tools which draw line segments and circle or elipse arcs, but which do not draw parabolas or hyperbolas, and in many cases, those system keep track of graphical objets to redraw them for you, so, it wouldn't be efficient to draw the piwel by pixel.
So my question is, how could I find a good way to segment a simple hyperbola (like $y^2-x^2=1$) arc, with arcs of "horizontal" or "vertical" ellipses (like $a(x-x_0)^2+b(y-y_0)^2=1$), to make a good approximation with ellipses and lines ?
I calculated the radius of the tangent circle as a function for both hyperbola et ellipses, but then I feel blocked.
functions approximation conic-sections spline
asked Dec 3 '18 at 18:05
CamionCamion
165
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add a comment |
$begingroup$
On some IT graphic systems, you have tools which draw line segments and circle or elipse arcs, but which do not draw parabolas or hyperbolas, and in many cases, those system keep track of graphical objets to redraw them for you, so, it wouldn't be efficient to draw the piwel by pixel.
So my question is, how could I find a good way to segment a simple hyperbola (like $y^2-x^2=1$) arc, with arcs of "horizontal" or "vertical" ellipses (like $a(x-x_0)^2+b(y-y_0)^2=1$), to make a good approximation with ellipses and lines ?
I calculated the radius of the tangent circle as a function for both hyperbola et ellipses, but then I feel blocked.
functions approximation conic-sections spline
asked Dec 3 '18 at 18:05
CamionCamion
165
$endgroup$
$begingroup$
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
$endgroup$
– Camion
Dec 4 '18 at 21:28
add a comment |
$begingroup$
On some IT graphic systems, you have tools which draw line segments and circle or elipse arcs, but which do not draw parabolas or hyperbolas, and in many cases, those system keep track of graphical objets to redraw them for you, so, it wouldn't be efficient to draw the piwel by pixel.
So my question is, how could I find a good way to segment a simple hyperbola (like $y^2-x^2=1$) arc, with arcs of "horizontal" or "vertical" ellipses (like $a(x-x_0)^2+b(y-y_0)^2=1$), to make a good approximation with ellipses and lines ?
I calculated the radius of the tangent circle as a function for both hyperbola et ellipses, but then I feel blocked.
functions approximation conic-sections spline
asked Dec 3 '18 at 18:05
CamionCamion
165
$endgroup$
On some IT graphic systems, you have tools which draw line segments and circle or elipse arcs, but which do not draw parabolas or hyperbolas, and in many cases, those system keep track of graphical objets to redraw them for you, so, it wouldn't be efficient to draw the piwel by pixel.
So my question is, how could I find a good way to segment a simple hyperbola (like $y^2-x^2=1$) arc, with arcs of "horizontal" or "vertical" ellipses (like $a(x-x_0)^2+b(y-y_0)^2=1$), to make a good approximation with ellipses and lines ?
I calculated the radius of the tangent circle as a function for both hyperbola et ellipses, but then I feel blocked.
functions approximation conic-sections spline
functions approximation conic-sections spline
asked Dec 3 '18 at 18:05
CamionCamion
165
asked Dec 3 '18 at 18:05
CamionCamion
165
edited Dec 3 '18 at 18:42
Camion
asked Dec 3 '18 at 18:05
CamionCamion
165
asked Dec 3 '18 at 18:05
CamionCamion
165
asked Dec 3 '18 at 18:05
CamionCamion
165
165
$begingroup$
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
$endgroup$
– Camion
Dec 4 '18 at 21:28
add a comment |
$begingroup$
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
$endgroup$
– Camion
Dec 4 '18 at 21:28
$begingroup$
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
$endgroup$
– Camion
Dec 4 '18 at 21:28
$begingroup$
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
$endgroup$
– Camion
Dec 4 '18 at 21:28
add a comment |
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Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
$endgroup$
– Camion
Dec 4 '18 at 21:28