How to compare B Spline Surfaces?
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We can define b spline surfaces over a set of points. However, is it possible to compare two set of b-spline surfaces fitted over different set of points ? The objective is to identify if the curves are similar.
geometry surfaces spline research
asked Aug 17 at 6:59
krammer
1013
add a comment |Â
up vote
0
down vote
favorite
We can define b spline surfaces over a set of points. However, is it possible to compare two set of b-spline surfaces fitted over different set of points ? The objective is to identify if the curves are similar.
geometry surfaces spline research
asked Aug 17 at 6:59
krammer
1013
add a comment |Â
up vote
0
down vote
favorite
up vote
0
down vote
favorite
We can define b spline surfaces over a set of points. However, is it possible to compare two set of b-spline surfaces fitted over different set of points ? The objective is to identify if the curves are similar.
geometry surfaces spline research
asked Aug 17 at 6:59
krammer
1013
We can define b spline surfaces over a set of points. However, is it possible to compare two set of b-spline surfaces fitted over different set of points ? The objective is to identify if the curves are similar.
geometry surfaces spline research
asked Aug 17 at 6:59
krammer
1013
asked Aug 17 at 6:59
krammer
1013
asked Aug 17 at 6:59
krammer
1013
asked Aug 17 at 6:59
krammer
1013
1013
add a comment |Â
add a comment |Â
1 Answer
1
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1
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A B-spline surface is defined by
1) degree in u and v direction,
2) knot sequence in u and v direction,
3) m x n (weighted) control points.
So, to compare two B-spline surfaces, you can check if these data are the same in the order they are listed above (i.e., degree, then knot sequence, then control points). If any of of them is different, then you can say the two B-spline surfaces are different.
Please note that two B-spline surfaces could be geometrically identical but have different data for degree, knot sequence and/or control points. For example, given any B-spline surface, we can always perform degree elevation to generate another B-spline surface that has higher degree and more control points. But these two surfaces are in fact geometrically identical. The "data-wise" comparison method mentioned above is certainly not suitable for such special cases.
answered Aug 17 at 22:47
fang
2,337156
Thanks. I read that comparing the relative distance between control points could be good measure. Can you direct me towards any approach which can compare surfaces in data independent manner (i.e. curvature etc.)
– krammer
Aug 18 at 5:23
You mean in "parametrization independent" manner?
– fang
Aug 18 at 20:13
I meant that a method which requires actual data points to be matched would not be robust to transformations, right ? So a method, which could help in determining the curve similarity would be of help.
– krammer
Aug 19 at 9:52
@OP: If you are talking about the data points the surface is fitted from, then yes it will not make sense to compare two set of data points to judge whether two B-spline surface are the same or not.
– fang
Aug 20 at 0:36
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
1
down vote
A B-spline surface is defined by
1) degree in u and v direction,
2) knot sequence in u and v direction,
3) m x n (weighted) control points.
So, to compare two B-spline surfaces, you can check if these data are the same in the order they are listed above (i.e., degree, then knot sequence, then control points). If any of of them is different, then you can say the two B-spline surfaces are different.
Please note that two B-spline surfaces could be geometrically identical but have different data for degree, knot sequence and/or control points. For example, given any B-spline surface, we can always perform degree elevation to generate another B-spline surface that has higher degree and more control points. But these two surfaces are in fact geometrically identical. The "data-wise" comparison method mentioned above is certainly not suitable for such special cases.
answered Aug 17 at 22:47
fang
2,337156
Thanks. I read that comparing the relative distance between control points could be good measure. Can you direct me towards any approach which can compare surfaces in data independent manner (i.e. curvature etc.)
– krammer
Aug 18 at 5:23
You mean in "parametrization independent" manner?
– fang
Aug 18 at 20:13
I meant that a method which requires actual data points to be matched would not be robust to transformations, right ? So a method, which could help in determining the curve similarity would be of help.
– krammer
Aug 19 at 9:52
@OP: If you are talking about the data points the surface is fitted from, then yes it will not make sense to compare two set of data points to judge whether two B-spline surface are the same or not.
– fang
Aug 20 at 0:36
add a comment |Â
up vote
1
down vote
A B-spline surface is defined by
1) degree in u and v direction,
2) knot sequence in u and v direction,
3) m x n (weighted) control points.
So, to compare two B-spline surfaces, you can check if these data are the same in the order they are listed above (i.e., degree, then knot sequence, then control points). If any of of them is different, then you can say the two B-spline surfaces are different.
Please note that two B-spline surfaces could be geometrically identical but have different data for degree, knot sequence and/or control points. For example, given any B-spline surface, we can always perform degree elevation to generate another B-spline surface that has higher degree and more control points. But these two surfaces are in fact geometrically identical. The "data-wise" comparison method mentioned above is certainly not suitable for such special cases.
answered Aug 17 at 22:47
fang
2,337156
Thanks. I read that comparing the relative distance between control points could be good measure. Can you direct me towards any approach which can compare surfaces in data independent manner (i.e. curvature etc.)
– krammer
Aug 18 at 5:23
You mean in "parametrization independent" manner?
– fang
Aug 18 at 20:13
I meant that a method which requires actual data points to be matched would not be robust to transformations, right ? So a method, which could help in determining the curve similarity would be of help.
– krammer
Aug 19 at 9:52
@OP: If you are talking about the data points the surface is fitted from, then yes it will not make sense to compare two set of data points to judge whether two B-spline surface are the same or not.
– fang
Aug 20 at 0:36
add a comment |Â
up vote
1
down vote
up vote
1
down vote
A B-spline surface is defined by
1) degree in u and v direction,
2) knot sequence in u and v direction,
3) m x n (weighted) control points.
So, to compare two B-spline surfaces, you can check if these data are the same in the order they are listed above (i.e., degree, then knot sequence, then control points). If any of of them is different, then you can say the two B-spline surfaces are different.
Please note that two B-spline surfaces could be geometrically identical but have different data for degree, knot sequence and/or control points. For example, given any B-spline surface, we can always perform degree elevation to generate another B-spline surface that has higher degree and more control points. But these two surfaces are in fact geometrically identical. The "data-wise" comparison method mentioned above is certainly not suitable for such special cases.
answered Aug 17 at 22:47
fang
2,337156
A B-spline surface is defined by
1) degree in u and v direction,
2) knot sequence in u and v direction,
3) m x n (weighted) control points.
So, to compare two B-spline surfaces, you can check if these data are the same in the order they are listed above (i.e., degree, then knot sequence, then control points). If any of of them is different, then you can say the two B-spline surfaces are different.
Please note that two B-spline surfaces could be geometrically identical but have different data for degree, knot sequence and/or control points. For example, given any B-spline surface, we can always perform degree elevation to generate another B-spline surface that has higher degree and more control points. But these two surfaces are in fact geometrically identical. The "data-wise" comparison method mentioned above is certainly not suitable for such special cases.
answered Aug 17 at 22:47
fang
2,337156
answered Aug 17 at 22:47
fang
2,337156
answered Aug 17 at 22:47
fang
2,337156
answered Aug 17 at 22:47
fang
2,337156
2,337156
Thanks. I read that comparing the relative distance between control points could be good measure. Can you direct me towards any approach which can compare surfaces in data independent manner (i.e. curvature etc.)
– krammer
Aug 18 at 5:23
You mean in "parametrization independent" manner?
– fang
Aug 18 at 20:13
I meant that a method which requires actual data points to be matched would not be robust to transformations, right ? So a method, which could help in determining the curve similarity would be of help.
– krammer
Aug 19 at 9:52
@OP: If you are talking about the data points the surface is fitted from, then yes it will not make sense to compare two set of data points to judge whether two B-spline surface are the same or not.
– fang
Aug 20 at 0:36
add a comment |Â
Thanks. I read that comparing the relative distance between control points could be good measure. Can you direct me towards any approach which can compare surfaces in data independent manner (i.e. curvature etc.)
– krammer
Aug 18 at 5:23
You mean in "parametrization independent" manner?
– fang
Aug 18 at 20:13
I meant that a method which requires actual data points to be matched would not be robust to transformations, right ? So a method, which could help in determining the curve similarity would be of help.
– krammer
Aug 19 at 9:52
@OP: If you are talking about the data points the surface is fitted from, then yes it will not make sense to compare two set of data points to judge whether two B-spline surface are the same or not.
– fang
Aug 20 at 0:36
Thanks. I read that comparing the relative distance between control points could be good measure. Can you direct me towards any approach which can compare surfaces in data independent manner (i.e. curvature etc.)
– krammer
Aug 18 at 5:23
Thanks. I read that comparing the relative distance between control points could be good measure. Can you direct me towards any approach which can compare surfaces in data independent manner (i.e. curvature etc.)
– krammer
Aug 18 at 5:23
You mean in "parametrization independent" manner?
– fang
Aug 18 at 20:13
You mean in "parametrization independent" manner?
– fang
Aug 18 at 20:13
I meant that a method which requires actual data points to be matched would not be robust to transformations, right ? So a method, which could help in determining the curve similarity would be of help.
– krammer
Aug 19 at 9:52
I meant that a method which requires actual data points to be matched would not be robust to transformations, right ? So a method, which could help in determining the curve similarity would be of help.
– krammer
Aug 19 at 9:52
@OP: If you are talking about the data points the surface is fitted from, then yes it will not make sense to compare two set of data points to judge whether two B-spline surface are the same or not.
– fang
Aug 20 at 0:36
@OP: If you are talking about the data points the surface is fitted from, then yes it will not make sense to compare two set of data points to judge whether two B-spline surface are the same or not.
– fang
Aug 20 at 0:36
add a comment |Â
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