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 at 18:05
Camion
165
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up vote
1
down vote
favorite
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 at 18:05
Camion
165
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
– Camion
Dec 4 at 21:28
add a comment |
up vote
1
down vote
favorite
up vote
1
down vote
favorite
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 at 18:05
Camion
165
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 at 18:05
Camion
165
asked Dec 3 at 18:05
Camion
165
edited Dec 3 at 18:42
asked Dec 3 at 18:05
Camion
165
asked Dec 3 at 18:05
Camion
165
asked Dec 3 at 18:05
Camion
165
165
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
– Camion
Dec 4 at 21:28
add a comment |
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
– Camion
Dec 4 at 21:28
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
– Camion
Dec 4 at 21:28
Ok : problem solved : I made simulation on geogebra to see when it looked nice enough.
– Camion
Dec 4 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.
– Camion
Dec 4 at 21:28