Function for providing coordinates of next point along a pseudo Hilbert curve of a particular order?
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It's easy to write a recursive program to draw an n'th order pseudo Hilbert curve, but I am interested to know if there is an efficient linear-time solution (without an iterative or recursive program) to create a function that will directly return the sequence of coordinates of the points along a pseudo Hilbert curve of a given order.
e.g. Pi = H(n,i)
Where Pi is the (x,y) coordinate of the i'th point along the curve, and is given by the function H which takes the parameters i, and the order of the curve n.
I want to be able to "walk" along the curve, one point at a time, without having to calculate or store all the previous n-1 order pseudo curves in memory, just to calculate the next coordinate along the order n curve.
For my particular application 'n' can actually be fixed and "hard-coded", (typ. n=10)
I would also be happy with a function that just told me whether the next point in the sequence along the curve was a move up, down, left or right from the current point, as that would also allow me to "walk" along the curve.
algorithms curves
asked Nov 26 at 15:43
Lee Technology
113
add a comment |
up vote
0
down vote
favorite
It's easy to write a recursive program to draw an n'th order pseudo Hilbert curve, but I am interested to know if there is an efficient linear-time solution (without an iterative or recursive program) to create a function that will directly return the sequence of coordinates of the points along a pseudo Hilbert curve of a given order.
e.g. Pi = H(n,i)
Where Pi is the (x,y) coordinate of the i'th point along the curve, and is given by the function H which takes the parameters i, and the order of the curve n.
I want to be able to "walk" along the curve, one point at a time, without having to calculate or store all the previous n-1 order pseudo curves in memory, just to calculate the next coordinate along the order n curve.
For my particular application 'n' can actually be fixed and "hard-coded", (typ. n=10)
I would also be happy with a function that just told me whether the next point in the sequence along the curve was a move up, down, left or right from the current point, as that would also allow me to "walk" along the curve.
algorithms curves
asked Nov 26 at 15:43
Lee Technology
113
add a comment |
up vote
0
down vote
favorite
up vote
0
down vote
favorite
It's easy to write a recursive program to draw an n'th order pseudo Hilbert curve, but I am interested to know if there is an efficient linear-time solution (without an iterative or recursive program) to create a function that will directly return the sequence of coordinates of the points along a pseudo Hilbert curve of a given order.
e.g. Pi = H(n,i)
Where Pi is the (x,y) coordinate of the i'th point along the curve, and is given by the function H which takes the parameters i, and the order of the curve n.
I want to be able to "walk" along the curve, one point at a time, without having to calculate or store all the previous n-1 order pseudo curves in memory, just to calculate the next coordinate along the order n curve.
For my particular application 'n' can actually be fixed and "hard-coded", (typ. n=10)
I would also be happy with a function that just told me whether the next point in the sequence along the curve was a move up, down, left or right from the current point, as that would also allow me to "walk" along the curve.
algorithms curves
asked Nov 26 at 15:43
Lee Technology
113
It's easy to write a recursive program to draw an n'th order pseudo Hilbert curve, but I am interested to know if there is an efficient linear-time solution (without an iterative or recursive program) to create a function that will directly return the sequence of coordinates of the points along a pseudo Hilbert curve of a given order.
e.g. Pi = H(n,i)
Where Pi is the (x,y) coordinate of the i'th point along the curve, and is given by the function H which takes the parameters i, and the order of the curve n.
I want to be able to "walk" along the curve, one point at a time, without having to calculate or store all the previous n-1 order pseudo curves in memory, just to calculate the next coordinate along the order n curve.
For my particular application 'n' can actually be fixed and "hard-coded", (typ. n=10)
I would also be happy with a function that just told me whether the next point in the sequence along the curve was a move up, down, left or right from the current point, as that would also allow me to "walk" along the curve.
algorithms curves
algorithms curves
asked Nov 26 at 15:43
Lee Technology
113
asked Nov 26 at 15:43
Lee Technology
113
asked Nov 26 at 15:43
Lee Technology
113
asked Nov 26 at 15:43
Lee Technology
113
asked Nov 26 at 15:43
Lee Technology
113
113
add a comment |
add a comment |
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