#!/usr/bin/env python """ Plotting Examples Suggested Usage: python -i plotting.py """ from sympy import symbols from sympy.plotting.pygletplot import PygletPlot from sympy import sin, cos, pi, sqrt, exp from time import sleep, clock def main(): x, y, z = symbols('x,y,z') # toggle axes visibility with F5, colors with F6 axes_options = 'visible=false; colored=true; label_ticks=true; label_axes=true; overlay=true; stride=0.5' #axes_options = 'colored=false; overlay=false; stride=(1.0, 0.5, 0.5)' p = PygletPlot(width=600, height=500, ortho=False, invert_mouse_zoom=False, axes=axes_options, antialiasing=True) examples = [] def example_wrapper(f): examples.append(f) return f @example_wrapper def mirrored_saddles(): p[5] = x**2 - y**2, [20], [20] p[6] = y**2 - x**2, [20], [20] @example_wrapper def mirrored_saddles_saveimage(): p[5] = x**2 - y**2, [20], [20] p[6] = y**2 - x**2, [20], [20] p.wait_for_calculations() # although the calculation is complete, # we still need to wait for it to be # rendered, so we'll sleep to be sure. sleep(1) p.saveimage("plot_example.png") @example_wrapper def mirrored_ellipsoids(): p[2] = x**2 + y**2, [40], [40], 'color=zfade' p[3] = -x**2 - y**2, [40], [40], 'color=zfade' @example_wrapper def saddle_colored_by_derivative(): f = x**2 - y**2 p[1] = f, 'style=solid' p[1].color = abs(f.diff(x)), abs(f.diff(x) + f.diff(y)), abs(f.diff(y)) @example_wrapper def ding_dong_surface(): f = sqrt(1.0 - y)*y p[1] = f, [x, 0, 2*pi, 40], [y, -1, 4, 100], 'mode=cylindrical; style=solid; color=zfade4' @example_wrapper def polar_circle(): p[7] = 1, 'mode=polar' @example_wrapper def polar_flower(): p[8] = 1.5*sin(4*x), [160], 'mode=polar' p[8].color = z, x, y, (0.5, 0.5, 0.5), (0.8, 0.8, 0.8), (x, y, None, z) # z is used for t @example_wrapper def simple_cylinder(): p[9] = 1, 'mode=cylindrical' @example_wrapper def cylindrical_hyperbola(): ## (note that polar is an alias for cylindrical) p[10] = 1/y, 'mode=polar', [x], [y, -2, 2, 20] @example_wrapper def extruded_hyperbolas(): p[11] = 1/x, [x, -10, 10, 100], [1], 'style=solid' p[12] = -1/x, [x, -10, 10, 100], [1], 'style=solid' @example_wrapper def torus(): a, b = 1, 0.5 # radius, thickness p[13] = (a + b*cos(x))*cos(y), (a + b*cos(x))*sin(y), b*sin(x), [x, 0, pi*2, 40], [y, 0, pi*2, 40] @example_wrapper def warped_torus(): a, b = 2, 1 # radius, thickness p[13] = (a + b*cos(x))*cos(y), (a + b*cos(x))*sin(y), b*sin(x) + 0.5*sin(4*y), [x, 0, pi*2, 40], [y, 0, pi*2, 40] @example_wrapper def parametric_spiral(): p[14] = cos(y), sin(y), y/10.0, [y, -4*pi, 4*pi, 100] p[14].color = x, (0.1, 0.9), y, (0.1, 0.9), z, (0.1, 0.9) @example_wrapper def multistep_gradient(): p[1] = 1, 'mode=spherical', 'style=both' #p[1] = exp(-x**2-y**2+(x*y)/4), [-1.7,1.7,100], [-1.7,1.7,100], 'style=solid' #p[1] = 5*x*y*exp(-x**2-y**2), [-2,2,100], [-2,2,100] gradient = [ 0.0, (0.3, 0.3, 1.0), 0.30, (0.3, 1.0, 0.3), 0.55, (0.95, 1.0, 0.2), 0.65, (1.0, 0.95, 0.2), 0.85, (1.0, 0.7, 0.2), 1.0, (1.0, 0.3, 0.2) ] p[1].color = z, [None, None, z], gradient #p[1].color = 'zfade' #p[1].color = 'zfade3' @example_wrapper def lambda_vs_sympy_evaluation(): start = clock() p[4] = x**2 + y**2, [100], [100], 'style=solid' p.wait_for_calculations() print("lambda-based calculation took %s seconds." % (clock() - start)) start = clock() p[4] = x**2 + y**2, [100], [100], 'style=solid; use_sympy_eval' p.wait_for_calculations() print("sympy substitution-based calculation took %s seconds." % (clock() - start)) @example_wrapper def gradient_vectors(): def gradient_vectors_inner(f, i): from sympy import lambdify from sympy.plotting.plot_interval import PlotInterval from pyglet.gl import glBegin, glColor3f from pyglet.gl import glVertex3f, glEnd, GL_LINES def draw_gradient_vectors(f, iu, iv): """ Create a function which draws vectors representing the gradient of f. """ dx, dy, dz = f.diff(x), f.diff(y), 0 FF = lambdify( [x, y], [x, y, f] ) FG = lambdify( [x, y], [dx, dy, dz] ) iu.v_steps /= 5 iv.v_steps /= 5 Gvl = list(list([FF(u, v), FG(u, v)] for v in iv.frange()) for u in iu.frange()) def draw_arrow(p1, p2): """ Draw a single vector. """ glColor3f(0.4, 0.4, 0.9) glVertex3f(*p1) glColor3f(0.9, 0.4, 0.4) glVertex3f(*p2) def draw(): """ Iterate through the calculated vectors and draw them. """ glBegin(GL_LINES) for u in Gvl: for v in u: point = [ [v[0][0], v[0][1], v[0][2]], [v[0][0] + v[1][0], v[0][1] + v[1][1], v[0][2] + v[1][2]] ] draw_arrow(point[0], point[1]) glEnd() return draw p[i] = f, [-0.5, 0.5, 25], [-0.5, 0.5, 25], 'style=solid' iu = PlotInterval(p[i].intervals[0]) iv = PlotInterval(p[i].intervals[1]) p[i].postdraw.append(draw_gradient_vectors(f, iu, iv)) gradient_vectors_inner( x**2 + y**2, 1) gradient_vectors_inner(-x**2 - y**2, 2) def help_str(): s = ("\nPlot p has been created. Useful commands: \n" " help(p), p[1] = x**2, print p, p.clear() \n\n" "Available examples (see source in plotting.py):\n\n") for i in xrange(len(examples)): s += "(%i) %s\n" % (i, examples[i].__name__) s += "\n" s += "e.g. >>> example(2)\n" s += " >>> ding_dong_surface()\n" return s def example(i): if callable(i): p.clear() i() elif i >= 0 and i < len(examples): p.clear() examples[i]() else: print("Not a valid example.\n") print(p) example(0) # 0 - 15 are defined above print(help_str()) if __name__ == "__main__": main()