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## Re: [PyX-user] merging graphs and paths

 Re: [PyX-user] merging graphs and paths From: Ken Starks - 2008-08-25 18:27:06 Attachments: Message as HTML ```Reply sent privately (in error) on 24 August Mico Filós wrote: > Hi, > > I am sorry if this is a trivial question but I cannot figure out how > to do this. > > Imagine I have a nonlinear function f(x) and its linearization at some > point (x0,f(x0)), > given by y(x) = f'(x0) (x - x0) + y0, where y0 = f(x0). Imagine also that > I don't use the same scale for the x and y axes. How can I obtain a > straight line that > *looks* perpendicular to the tangent y(x)? > > Since the x and y scales are not the same, a line with slope equal to > -1/f'(x0) > does not look perpendicular to y(x). I want to plot a straight line > that passes through > an arbitrary point of the tangent (not necessarily (x0,y0)) and that > looks perpendicular to > it. My idea is actually to plot the projection of an arbitrary point > of the nonlinear function, > (x1,f(x1)) to the subspace spanned by the tangent at x0. For me the > most straightforward thing to do would be: > > * Compute the angle theta (on the actual canvas, i.e., as it looks > on the screen) of the path > defined by the tangent function y(x) > > * Plot a line path L with an angle theta + pi/2 that passes through > some particular point > of the tangent Q=(x0', y0'), which I specify. > > * Find the intersection R of the line L with the path defined by > the nonlinear function. > > * Ideally, I would stroke only the portion of L that connects the > point > (x0',y0') with the intersection point R. > > Describing this in words is painful. I hope you see what I mean. > > Thanks a lot in for your patience. > > Mico > > ------------------------------------------------------------------------- > This SF.Net email is sponsored by the Moblin Your Move Developer's > challenge > Build the coolest Linux based applications with Moblin SDK & win great > prizes > Grand prize is a trip for two to an Open Source event anywhere in the > world > http://moblin-contest.org/redirect.php?banner_id=100&url=/ > _______________________________________________ > PyX-user mailing list > PyX-user@... > https://lists.sourceforge.net/lists/listinfo/pyx-user > > > ------------------------------------------------------------------------ from pyx import * g = graph.graphxy(width=8, x=graph.axis.linear(min=-5, max=5)) g.plot(graph.data.function("y(x)=x*x")) # Let us plot the tangent at (x0,y0) = (2,4) slope 4 g.plot(graph.data.function("y(x)=4*(x-1)")) """ Let us take two more points on the tangent """ slope=4 deltaX=2 x1=-3 # example, you can change this x2 = x1 + deltaX y1 = slope * (x1 -1) y2 = slope * (x2 - 1) """ Now you need to get the two points (x1,y1), (x2,y2) into canvas-coordinates rather than scaled coordinates. This is the crucial stage that will provide for your peculiar request that the line *looks* perpendicular to the tangent line. I shall call these U-V coordinates, and their origin is bottom left of the canvas (g), their units the usual user-units (e.g cm) """ u1,v1= g.pos(x1,y1) u2,v2= g.pos(x2,y2) deltaU=u2-u1 deltaV=v2-v1 # lastly a point (u3,v3) that can define your 'normal' from (u1,v1) u3=u1-deltaV v3=v1+deltaU # as these are in canvas coordinates, not graph ones, we use # stroke .. path .. etc to plot a segment from u1,v1 to u3,v3 g.stroke(path.path(path.moveto(u1,v1),path.lineto(u3,v3))) g.writePDFfile("graph3") ```

 Re: [PyX-user] merging graphs and paths From: Ken Starks - 2008-08-25 18:27:06 Attachments: Message as HTML ```Reply sent privately (in error) on 24 August Mico Filós wrote: > Hi, > > I am sorry if this is a trivial question but I cannot figure out how > to do this. > > Imagine I have a nonlinear function f(x) and its linearization at some > point (x0,f(x0)), > given by y(x) = f'(x0) (x - x0) + y0, where y0 = f(x0). Imagine also that > I don't use the same scale for the x and y axes. How can I obtain a > straight line that > *looks* perpendicular to the tangent y(x)? > > Since the x and y scales are not the same, a line with slope equal to > -1/f'(x0) > does not look perpendicular to y(x). I want to plot a straight line > that passes through > an arbitrary point of the tangent (not necessarily (x0,y0)) and that > looks perpendicular to > it. My idea is actually to plot the projection of an arbitrary point > of the nonlinear function, > (x1,f(x1)) to the subspace spanned by the tangent at x0. For me the > most straightforward thing to do would be: > > * Compute the angle theta (on the actual canvas, i.e., as it looks > on the screen) of the path > defined by the tangent function y(x) > > * Plot a line path L with an angle theta + pi/2 that passes through > some particular point > of the tangent Q=(x0', y0'), which I specify. > > * Find the intersection R of the line L with the path defined by > the nonlinear function. > > * Ideally, I would stroke only the portion of L that connects the > point > (x0',y0') with the intersection point R. > > Describing this in words is painful. I hope you see what I mean. > > Thanks a lot in for your patience. > > Mico > > ------------------------------------------------------------------------- > This SF.Net email is sponsored by the Moblin Your Move Developer's > challenge > Build the coolest Linux based applications with Moblin SDK & win great > prizes > Grand prize is a trip for two to an Open Source event anywhere in the > world > http://moblin-contest.org/redirect.php?banner_id=100&url=/ > _______________________________________________ > PyX-user mailing list > PyX-user@... > https://lists.sourceforge.net/lists/listinfo/pyx-user > > > ------------------------------------------------------------------------ from pyx import * g = graph.graphxy(width=8, x=graph.axis.linear(min=-5, max=5)) g.plot(graph.data.function("y(x)=x*x")) # Let us plot the tangent at (x0,y0) = (2,4) slope 4 g.plot(graph.data.function("y(x)=4*(x-1)")) """ Let us take two more points on the tangent """ slope=4 deltaX=2 x1=-3 # example, you can change this x2 = x1 + deltaX y1 = slope * (x1 -1) y2 = slope * (x2 - 1) """ Now you need to get the two points (x1,y1), (x2,y2) into canvas-coordinates rather than scaled coordinates. This is the crucial stage that will provide for your peculiar request that the line *looks* perpendicular to the tangent line. I shall call these U-V coordinates, and their origin is bottom left of the canvas (g), their units the usual user-units (e.g cm) """ u1,v1= g.pos(x1,y1) u2,v2= g.pos(x2,y2) deltaU=u2-u1 deltaV=v2-v1 # lastly a point (u3,v3) that can define your 'normal' from (u1,v1) u3=u1-deltaV v3=v1+deltaU # as these are in canvas coordinates, not graph ones, we use # stroke .. path .. etc to plot a segment from u1,v1 to u3,v3 g.stroke(path.path(path.moveto(u1,v1),path.lineto(u3,v3))) g.writePDFfile("graph3") ```