Even with integers, you still get complex expressions with square roots as
the solutions.
Aaron Meurer
On Feb 6, 2013, at 12:54 AM, Ahmed Kachkach <ahmed.kachk...@gmail.com>
wrote:
I'd need to derive a formula that takes into account all the shapes that
are on my map and returns the closest distance (if any). Not sure I can do
this.
Actually, floating points coordinates are not a requirement in my program,
I guess I could just use integers.
I just tried converting all the coordinates to integers and it seems like
It's still as slow as before. (collision points are rational) ; Maybe
because of internal conversions to rationals ?
*
------
**Ahmed Kachkach**
**Web & graphic designer - Kachkach.com
Élève ingénieur à l'INSA de Lyon - 3ème année - Département informatique
*
*Engineering student at INSA de Lyon - 3rd year - Computer science
department*
2013/2/6 Aaron Meurer <asmeu...@gmail.com>
> I also didn't try very hard, but it may be difficult to do this. To
> make geometry return a symbolic result, it has to be completely
> convinced that a Point is contained in another geometry object. I
> tried intersecting an arbitrary ellipse with and arbitrary ray, and I
> got:
>
> Undecidable: Cannot determine if Point(x + (x - z)*(sqrt(-((e**2*(x -
> z)**2 + hr**2*(t - y)**2)*(-e**2*hr**2 + e**2*(x - x1)**2 + hr**2*(y -
> y1)**2) - (e**2*(x - x1)*(x - z) - hr**2*(t - y)*(y -
> y1))**2)/(e**4*hr**4)) - (x - x1)*(x - z)/hr**2 + (t - y)*(y -
> y1)/e**2)/((x - z)**2/hr**2 + (t - y)**2/e**2), y - (t -
> y)*(sqrt(-((e**2*(x - z)**2 + hr**2*(t - y)**2)*(-e**2*hr**2 + e**2*(x
> - x1)**2 + hr**2*(y - y1)**2) - (e**2*(x - x1)*(x - z) - hr**2*(t -
> y)*(y - y1))**2)/(e**4*hr**4)) - (x - x1)*(x - z)/hr**2 + (t - y)*(y -
> y1)/e**2)/((x - z)**2/hr**2 + (t - y)**2/e**2)) is in Ray(Point(x, y),
> Point(z, t))
>
> which is not too surprising, since as you note, not all rays intersect
> all ellipses. But it might be hard to convince the geometry module
> using the assumptions that they do. Or it may work. It depends on what
> conditions you know ahead of time.
>
> It would be nice if instead of raising Undecidable, it created some
> kind of symbolic Intersection object, which then becomes evaluated if
> symbols are replaced with numbers, and also knows how to numerically
> compute itself efficiently given floating point values (so that it
> would be useable with something like lambdify).
>
> Aaron Meurer
>
> On Tue, Feb 5, 2013 at 6:02 PM, Ronan Lamy <ronan.l...@gmail.com> wrote:
> > Le 05/02/2013 19:54, Ahmed Kachkach a écrit :
> >
> >> Hi !
> >>
> >> For a robotics simulation, I need to calculate the distance that an
> >> ultrasound sensor would measure (=> distance to the closest obstacle).
> >>
> >> Here's the code I'm using to do so (knowing that what's in "self.shapes"
> >> has been parsed from an SVG file and is mainly ellipses):
> >>
> >> def RayDistance(self, x, y, headingAngle):
> >>
> >> ray = Ray(Point(x,y), angle=headingAngle)
> >>
> >> minDist = None
> >>
> >> for shape in self.shapes:
> >>
> >> intersections = ray.intersection(shape)
> >>
> >> for intersection in intersections:
> >>
> >> distance = intersection.distance(ray.source)
> >>
> >> print "Shape {} ; Intersection {} ; Distance {}".format(shape,
> >> intersection, distance)
> >>
> >> if minDist == None:
> >>
> >> minDist = distance
> >>
> >> elif distance < minDist:
> >>
> >> minDist = distance
> >>
> >> return minDist
> >>
> >>
> >> Doing this is extremely slow, even with just 3 shapes. If I go up to 200
> >> shapes, I only get about 1 frame per second. And I only detectect a
> >> collision from time to time (especially if I slightly change my heading
> >> angle while facing a same obstacle).
> >>
> >> For instance, I'm using Qt for the visualisation and my "headingAngle"
> >> is in radians and ccw (0 being horizantal, headed to the positive x), my
> >> coordinates are floats and using the graphical reference system (=>
> >> positive Xs to the "right" and positive Ys to the bottom)
> >>
> >> It's my first experience with Sympy, so I may just be using the wrong
> >> tools for what I'm trying to do.
> >
> >
> > Well, whenever you try to call sympy functions with floating point
> arguments
> > repeatedly, you are doing it wrong. In this case, you should not call
> sympy
> > functions at runtime. Instead, you should use symbolic computations to
> > derive the relevant formulas, convert them to numpy functions, and use
> only
> > numpy at runtime. Schematically, it would look like:
> >
> > import sympy as sy
> > import numpy as np
> >
> > x, y, angle, a, b, c = sy.symbols("x, y, theta, a, b, c", real=True)
> >
> > def make_ellipse(param_a, param_b, param_c):
> > """Convert ellipse params to Ellipse object"""
> > ...
> >
> > # Derive the formula
> > ray = sy.Ray(sy.Point(x, y), angle=angle)
> > ellipse = make_ellipse(a, b, c)
> > intersection = ray.intersection(ellipse)
> > closest_point = intersection[0] # a bit of wishful thinking here...
> > distance = closest_point.distance(ray.source)
> >
> > # Make a numerical function
> > n_distance = sy.lambdify([x, y, angle, a, b, c], distance, "numpy")
> >
> > # assuming self.params is a n-by-3 numpy array of ellipse parameters
> > def ray_distance(self, x, y, angle):
> > return np.min(n_distance(x, y, angle, self.params[:, 0],
> > self.params[:, 1], self.params[:, 2]))
> >
> > Now, I haven't tested this, and I have completely ignored the fact that
> not
> > all ellipses intersect the ray, but I hope that you get the idea. If you
> can
> > put your calculations in this form, it should be orders magnitudes faster
> > than your first attempt.
> >
> > Ronan
> >
> >
> >
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> >
>
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