Re: [Numpy-discussion] Creating parallel curves
You can get polygon buffer from http://angusj.com/delphi/clipper.php and make cython interface to it. HTH Niki ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
On Mon, Feb 13, 2012 at 1:01 AM, Niki Spahiev niki.spah...@gmail.com wrote: You can get polygon buffer from http://angusj.com/delphi/clipper.php and make cython interface to it. This should be built into GEOS as well, and the shapely package provides a python wrapper already. -Chris HTH Niki ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion -- Christopher Barker, Ph.D. Oceanographer Emergency Response Division NOAA/NOS/ORR (206) 526-6959 voice 7600 Sand Point Way NE (206) 526-6329 fax Seattle, WA 98115 (206) 526-6317 main reception chris.bar...@noaa.gov ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
HI Chris and All, On 10 February 2012 17:53, Chris Barker wrote: Andrea, Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: http://pyx.sourceforge.net/examples/drawing2/parallel.html THis is called buffering in GIS parlance -- there are functions available to do it in GIS an computational geometry libraries: you might look in the shapely package: https://github.com/sgillies/shapely Thanks, I hoped this one would prove itself useful, but unfortunately to me it looks like one of the most impenetrable Python code I have ever seen. Or maybe my Python is just too weak. The end result is the same. I have surfed quite a lot and found many reference to Bezier curves, with a lot of mathematical acrobatics but little of practical value (i.e., code :-) ). In the end I stumbled upon a nice function in the matplotlib library (obviously) which can give me the normal line to every point in the curve, and I almost got there. I still have 2 problems (attached sample), picture at http://img689.imageshack.us/img689/7246/exampleplot.png 1) If you run the attached sample, you'll see a plot of a cubic polynomial with two almost parallel lines to it on the first subplot. I say almost because at the inflection points of the cubic something funny happens (see suplot number 2); 2) You can see in subplot 3 that the 3 lines are nicely shown as almost parallel (except the problem at point 1), as the X and Y axes have the same scale. Unfortunately I can't keep the same scales in my real plot and I can't use axis=square in matplotlib either. How do I normalize the get_normal_points method to get the same visual appearance of parallelism on X and Y having different X and Y scales (i.e., the same X and Y scales as in subplot 1)? But by plotting these thing out with matplotlib it seems to me they don't really look very parallel nor very constant-distance. as we say on the wxPython list -- post a fully functional example, so we can check it out. Attached as promised. Thank you in advance for any suggestion. Andrea. Imagination Is The Only Weapon In The War Against Reality. http://xoomer.alice.it/infinity77/ sample_buffer.py Description: Binary data ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
Andrea, Here is how to do it with splines. I would be more standard to return an array of normals, rather than two arrays of x and y components, but it actually requires less housekeeping this way. As an aside, I would prefer to work with rotations via matrices, but it looks like there's no support for that built in to Numpy or Scipy? def normal_vectors(x, y, scalar=1.0): tck = scipy.interpolate.splrep(x, y) y_deriv = scipy.interpolate.splev(x, tck, der=1) normals_rad = np.arctan(y_deriv)+np.pi/2. return np.cos(normals_rad)*scalar, np.sin(normals_rad)*scalar # Jonathan On Sun, Feb 12, 2012 at 4:47 AM, Andrea Gavana andrea.gav...@gmail.com wrote: HI Chris and All, On 10 February 2012 17:53, Chris Barker wrote: Andrea, Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: http://pyx.sourceforge.net/examples/drawing2/parallel.html THis is called buffering in GIS parlance -- there are functions available to do it in GIS an computational geometry libraries: you might look in the shapely package: https://github.com/sgillies/shapely Thanks, I hoped this one would prove itself useful, but unfortunately to me it looks like one of the most impenetrable Python code I have ever seen. Or maybe my Python is just too weak. The end result is the same. I have surfed quite a lot and found many reference to Bezier curves, with a lot of mathematical acrobatics but little of practical value (i.e., code :-) ). In the end I stumbled upon a nice function in the matplotlib library (obviously) which can give me the normal line to every point in the curve, and I almost got there. I still have 2 problems (attached sample), picture at http://img689.imageshack.us/img689/7246/exampleplot.png 1) If you run the attached sample, you'll see a plot of a cubic polynomial with two almost parallel lines to it on the first subplot. I say almost because at the inflection points of the cubic something funny happens (see suplot number 2); 2) You can see in subplot 3 that the 3 lines are nicely shown as almost parallel (except the problem at point 1), as the X and Y axes have the same scale. Unfortunately I can't keep the same scales in my real plot and I can't use axis=square in matplotlib either. How do I normalize the get_normal_points method to get the same visual appearance of parallelism on X and Y having different X and Y scales (i.e., the same X and Y scales as in subplot 1)? But by plotting these thing out with matplotlib it seems to me they don't really look very parallel nor very constant-distance. as we say on the wxPython list -- post a fully functional example, so we can check it out. Attached as promised. Thank you in advance for any suggestion. Andrea. Imagination Is The Only Weapon In The War Against Reality. http://xoomer.alice.it/infinity77/ ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
On Fri, Feb 10, 2012 at 9:38 AM, Andrea Gavana andrea.gav...@gmail.comwrote: Hi All, my apologies for my deep ignorance about math stuff; I guess I should be able to find this out but I keep getting impossible results. Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: Note that curves produced in this way aren't actually 'parallel' and can even cross themselves. snip Chuck ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
Jonathan, On 12 February 2012 20:53, Jonathan Hilmer wrote: Andrea, Here is how to do it with splines. I would be more standard to return an array of normals, rather than two arrays of x and y components, but it actually requires less housekeeping this way. As an aside, I would prefer to work with rotations via matrices, but it looks like there's no support for that built in to Numpy or Scipy? def normal_vectors(x, y, scalar=1.0): tck = scipy.interpolate.splrep(x, y) y_deriv = scipy.interpolate.splev(x, tck, der=1) normals_rad = np.arctan(y_deriv)+np.pi/2. return np.cos(normals_rad)*scalar, np.sin(normals_rad)*scalar Thank you for this, I'll give it a go in a few minutes (hopefully I will also be able to correctly understand what you did). One thing though, at first glance, it appears to me that your approach is very similar to mine (meaning it will give parallel curves that cross themselves as in the example I posted). But maybe I am wrong, my apologies if I missed something. Thank you so much for your answer. Andrea. ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
Charles, On 12 February 2012 21:00, Charles R Harris wrote: On Fri, Feb 10, 2012 at 9:38 AM, Andrea Gavana andrea.gav...@gmail.com wrote: Hi All, my apologies for my deep ignorance about math stuff; I guess I should be able to find this out but I keep getting impossible results. Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: Note that curves produced in this way aren't actually 'parallel' and can even cross themselves. I know, my definition of parallel was probably not orthodox enough. What I am looking for is to generate 2 curves that look graphically parallel enough to the original one, and not parallel in the true mathematical sense. Andrea. Imagination Is The Only Weapon In The War Against Reality. http://xoomer.alice.it/infinity77/ ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
On Sun, Feb 12, 2012 at 1:21 PM, Andrea Gavana andrea.gav...@gmail.comwrote: Jonathan, On 12 February 2012 20:53, Jonathan Hilmer wrote: Andrea, Here is how to do it with splines. I would be more standard to return an array of normals, rather than two arrays of x and y components, but it actually requires less housekeeping this way. As an aside, I would prefer to work with rotations via matrices, but it looks like there's no support for that built in to Numpy or Scipy? def normal_vectors(x, y, scalar=1.0): tck = scipy.interpolate.splrep(x, y) y_deriv = scipy.interpolate.splev(x, tck, der=1) normals_rad = np.arctan(y_deriv)+np.pi/2. return np.cos(normals_rad)*scalar, np.sin(normals_rad)*scalar Thank you for this, I'll give it a go in a few minutes (hopefully I will also be able to correctly understand what you did). One thing though, at first glance, it appears to me that your approach is very similar to mine (meaning it will give parallel curves that cross themselves as in the example I posted). But maybe I am wrong, my apologies if I missed something. Thank you so much for your answer. Crossing curves is the correct behavior for this method, think propagating wavefronts and the appearance of light on the bottom of a swimming pool when there are ripples on the surface. I think you need to define what you really want from 'parallel'. Chuck ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
On Sun, Feb 12, 2012 at 1:26 PM, Andrea Gavana andrea.gav...@gmail.comwrote: Charles, On 12 February 2012 21:00, Charles R Harris wrote: On Fri, Feb 10, 2012 at 9:38 AM, Andrea Gavana andrea.gav...@gmail.com wrote: Hi All, my apologies for my deep ignorance about math stuff; I guess I should be able to find this out but I keep getting impossible results. Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: Note that curves produced in this way aren't actually 'parallel' and can even cross themselves. I know, my definition of parallel was probably not orthodox enough. What I am looking for is to generate 2 curves that look graphically parallel enough to the original one, and not parallel in the true mathematical sense. You could try setting a point and 'contracting' the curve towards the point. A point a infinity would give the usual parallel curves. There are probably a lot of perspective like transformations that would do something similar. Chuck ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
Andrea, I realized that my answer wouldn't be complete, but as people have pointed out that's a substantially more difficult question, so I wanted to give you a complete answer to just a subset of your problem. I'm currently writing a variant that avoids the overlapping normal vectors by interatively 1.) expanding along normals then 2.) condensing points, for every iteration. However, I'm doing it mostly for my own interest since I'm pretty sure it will not be functional when complete: your problem is that calculation of derivatives/normals is going to become unstable in acute convex regions, and the overlap issue there will become more severe. I would strongly recommend adapting some existing library for this problem. Jonathan On Sun, Feb 12, 2012 at 1:37 PM, Charles R Harris charlesr.har...@gmail.com wrote: On Sun, Feb 12, 2012 at 1:26 PM, Andrea Gavana andrea.gav...@gmail.com wrote: Charles, On 12 February 2012 21:00, Charles R Harris wrote: On Fri, Feb 10, 2012 at 9:38 AM, Andrea Gavana andrea.gav...@gmail.com wrote: Hi All, my apologies for my deep ignorance about math stuff; I guess I should be able to find this out but I keep getting impossible results. Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: Note that curves produced in this way aren't actually 'parallel' and can even cross themselves. I know, my definition of parallel was probably not orthodox enough. What I am looking for is to generate 2 curves that look graphically parallel enough to the original one, and not parallel in the true mathematical sense. You could try setting a point and 'contracting' the curve towards the point. A point a infinity would give the usual parallel curves. There are probably a lot of perspective like transformations that would do something similar. Chuck ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
Jonathan, On 12 February 2012 21:59, Jonathan Hilmer wrote: Andrea, I realized that my answer wouldn't be complete, but as people have pointed out that's a substantially more difficult question, so I wanted to give you a complete answer to just a subset of your problem. I'm currently writing a variant that avoids the overlapping normal vectors by interatively 1.) expanding along normals then 2.) condensing points, for every iteration. However, I'm doing it mostly for my own interest since I'm pretty sure it will not be functional when complete: your problem is that calculation of derivatives/normals is going to become unstable in acute convex regions, and the overlap issue there will become more severe. I would strongly recommend adapting some existing library for this problem. Thank you for your clear explanation. I feared something like that, but then again I was almost expecting it... I do wonder, however, if the problem I am having could be somehow simplified/modified by looking at another situation, in 3D this time: streamtubes and 3D representation of tubes/pipes are relatively common (i.e., VTKTubeFilter from the VTK library, streamtubes in Mayavi). They all build some kind of cylindrical shape around the main path (curve in 3D) to give the visual effect of some tube surrounding the main path. What I am trying to do is basically the same thing but in 2D: now, I have no idea if this can be done, and not even how it could be done. My math is relatively weak, I can't fathom how to build a 3D tube let alone splatter it back on a 2D map to give that effect. I am not sure my original problem and this one are related or not, but again every suggestion is most welcome. Thank you. Andrea. Jonathan On Sun, Feb 12, 2012 at 1:37 PM, Charles R Harris charlesr.har...@gmail.com wrote: On Sun, Feb 12, 2012 at 1:26 PM, Andrea Gavana andrea.gav...@gmail.com wrote: Charles, On 12 February 2012 21:00, Charles R Harris wrote: On Fri, Feb 10, 2012 at 9:38 AM, Andrea Gavana andrea.gav...@gmail.com wrote: Hi All, my apologies for my deep ignorance about math stuff; I guess I should be able to find this out but I keep getting impossible results. Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: Note that curves produced in this way aren't actually 'parallel' and can even cross themselves. I know, my definition of parallel was probably not orthodox enough. What I am looking for is to generate 2 curves that look graphically parallel enough to the original one, and not parallel in the true mathematical sense. You could try setting a point and 'contracting' the curve towards the point. A point a infinity would give the usual parallel curves. There are probably a lot of perspective like transformations that would do something similar. Chuck ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion -- Andrea. Imagination Is The Only Weapon In The War Against Reality. http://xoomer.alice.it/infinity77/ import PyQt4.QtGui Traceback (most recent call last): File interactive input, line 1, in module ImportError: No module named PyQt4.QtGui import pygtk Traceback (most recent call last): File interactive input, line 1, in module ImportError: No module named pygtk import wx ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
On Sun, Feb 12, 2012 at 20:26, Andrea Gavana andrea.gav...@gmail.com wrote: I know, my definition of parallel was probably not orthodox enough. What I am looking for is to generate 2 curves that look graphically parallel enough to the original one, and not parallel in the true mathematical sense. There is a rigorous way to define the curve that you are looking for, and fortunately it gives some hints for implementation. For each point (x,y) in space, associate with it the nearest distance D from that point to the reference curve. The parallel curves are just two sides of the level set where D(x,y) is equal to the specified distance (possibly removing the circular caps that surround the ends of the reference curve). If performance is not a constraint, then you could just evaluate that D(x,y) function on a fine-enough grid and do marching squares to find the level set. matplotlib's contour plotting routines can help here. There is a hint in the PyX page that you linked to that you should consider. Angles in the reference curve become circular arcs in the parallel curves. So if your reference curve is just a bunch of line segments, then what you can do is take each line segment, and make parallel copies the same length to either side. Now you just need to connect up these parallel segments with each other. You do this by using circular arcs centered on the vertices of the reference curve. Do this on both sides. On the outer side, the arcs will go forward while on the inner side, the arcs will go backwards just like the cusps that you saw in your attempt. Now let's take care of that. You will have two self-intersecting curves consisting of alternating line segments and circular arcs. Parts of these curves will be too close to the reference curve. You will have to go through these curves to find the locations of self-intersection and remove the parts of the segments and arcs that are too close to the reference curve. This is tricky to do, but the formulae for segment-segment, segment-arc, and arc-arc intersection can be found online. -- Robert Kern I have come to believe that the whole world is an enigma, a harmless enigma that is made terrible by our own mad attempt to interpret it as though it had an underlying truth. -- Umberto Eco ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
Re: [Numpy-discussion] Creating parallel curves
Andrea, Basically I have a set of x, y data (around 1,000 elements each) and I want to create 2 parallel curves (offset curves) to the original one; parallel means curves which are displaced from the base curve by a constant offset, either positive or negative, in the direction of the curve's normal. Something like this: http://pyx.sourceforge.net/examples/drawing2/parallel.html THis is called buffering in GIS parlance -- there are functions available to do it in GIS an computational geometry libraries: you might look in the shapely package: https://github.com/sgillies/shapely or CGAL http://www.cgal.org/ If the overhead of these packages is too much, and you still want to write your own code, try googling: buffering a line GIS algorithm or something like that, and you'll find pointers. But by plotting these thing out with matplotlib it seems to me they don't really look very parallel nor very constant-distance. as we say on the wxPython list -- post a fully functional example, so we can check it out. -Chris -- Christopher Barker, Ph.D. Oceanographer Emergency Response Division NOAA/NOS/ORR (206) 526-6959 voice 7600 Sand Point Way NE (206) 526-6329 fax Seattle, WA 98115 (206) 526-6317 main reception chris.bar...@noaa.gov ___ NumPy-Discussion mailing list NumPy-Discussion@scipy.org http://mail.scipy.org/mailman/listinfo/numpy-discussion
