gen_cube3d.py 4.69 KB
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#!/usr/bin/env python3
from sympy import *
from gcode2contour import Position, contour
from sympy.plotting import plot3d
from mpl_toolkits.mplot3d import Axes3D
import matplotlib.colors as mcolors

import matplotlib.pyplot as plt
import numpy as np


def set_aspect_equal_3d(ax):
    """Fix equal aspect bug for 3D plots."""

    xlim = ax.get_xlim3d()
    ylim = ax.get_ylim3d()
    zlim = ax.get_zlim3d()

    from numpy import mean
    xmean = mean(xlim)
    ymean = mean(ylim)
    zmean = mean(zlim)

    plot_radius = max([abs(lim - mean_)
                       for lims, mean_ in ((xlim, xmean),
                                           (ylim, ymean),
                                           (zlim, zmean))
                       for lim in lims])

    ax.set_xlim3d([xmean - plot_radius, xmean + plot_radius])
    ax.set_ylim3d([ymean - plot_radius, ymean + plot_radius])
    ax.set_zlim3d([zmean - plot_radius, zmean + plot_radius])


def plot_contours(*args):
    """
    Plots a list of contours

    Each input arguement is a list of contours
      All contours within each list will be the same color
      Contours in different lists will be different colors
    """
    fig = plt.figure()
    ax = Axes3D(fig)
#    colors = [k for k in mcolors.cnames]
    colors = ['blue', 'red', 'green']

    for i, contours in enumerate(args):
        for c in contours:
            xs = [pos[0] for pos in c.pos]
            ys = [pos[1] for pos in c.pos]
            zs = [pos[2] for pos in c.pos]
            ax.plot(xs, ys, zs, color=colors[i])

    set_aspect_equal_3d(ax)
    plt.show()
    return


class solver:
    """
    Handles symbolic variables to solve for layer 
    positions in various planes
    """

    def __init__(self, cl, cx, cy, dz):

        self.x, self.y, self.z, self.cz = symbols('x y z cz')
        self.layer = cl * sin(cx*self.x)*sin(cy*self.y) + self.cz

        self.dz = dz

        self.def_prism()


    def get_z(self, x, y, layer=0):
        return float(self.layer.subs([(self.x, x), (self.y, y), (self.cz, layer*self.dz)]))


    def def_prism(self, x_min = -0.05, x_max = 0.05,
                 y_min = -0.05, y_max = 0.05,
                 z_min = 0., z_max = 0.1):
        """
        save the prism size
        """

        self.range = {
            self.x: (x_min, x_max),
            self.y: (y_min, y_max),
            self.z: (z_min, z_max),
        }


    def plane_intersection(self, sym, val, layer = 0):
        """
        Takes a plane (not any plane, only x,y or z=val)
        and interesects it with the nth layer

        Returns symbolic expression for the intersection.
        Need to sample
        """
        return self.layer.subs([(sym, val), (self.cz, layer*self.dz)])


    def sample(self, expression, sym_in, res = 0.001):
        """
        sample across one variable, get values of second variable in an expression
        """

        v1 = np.arange(self.range[sym_in][0], self.range[sym_in][1]+ res, res)
        zs = []
        for v in v1:
            zs.append(float(expression.subs(sym_in, v)))

        return v1, zs


    def contour_n(self, n):
        """
        Get 4 contours for the nth layer
        4 sides of the prism unlinked
        """

        contours = []

        expr1 = self.plane_intersection(self.x, self.range[self.x][0], layer = n)
        ys, zs = self.sample(expr1, self.y)
        contours.append(contour([Position(self.range[self.x][0],ys[i],zs[i]) for i in range(len(ys))], 0))

        expr2 = self.plane_intersection(self.x, self.range[self.x][1], layer = n)
        ys, zs = self.sample(expr2, self.y)
        contours.append(contour([Position(self.range[self.x][1],ys[i],zs[i]) for i in range(len(ys))], 0))

        expr3 = self.plane_intersection(self.y, self.range[self.y][0], layer = n)
        xs, zs = self.sample(expr3, self.x)
        contours.append(contour([Position(xs[i],self.range[self.y][0],zs[i]) for i in range(len(ys))], 0))

        expr4 = self.plane_intersection(self.y, self.range[self.y][1], layer = n)
        xs, zs = self.sample(expr4, self.x)
        contours.append(contour([Position(xs[i],self.range[self.y][1],zs[i]) for i in range(len(ys))], 0))

        # TODO Join the 4 contours into one
        # TODO break up contours at z limits
        return contours


    def show(self):
        """
        Show the surface of the layer
        in the range of the cube at layer 0
        """
        plot3d(self.layer.subs(self.cz, 0),
               (self.x, self.range[self.x][0], self.range[self.x][1]),
               (self.y, self.range[self.y][0], self.range[self.y][1]))


if __name__ == '__main__':
    s =  solver(0.02, 100, 100, 0.01)

    contours = []
    for i in range(10):
        contours += s.contour_n(i)

    plot_contours(contours)