gen_cube3d.py 5.96 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
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from copy import deepcopy, copy
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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


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    def trim_contour(self, c, zlims):
        """
        take a contour and split it at z limits

        returns a list of contours.
        This list will be the original contour if it doesnt reach out of the limits
        If it doesn, regions outside the limits will be cut off, and regions inside 
        will be split
        """

        c_out = []
        j = 0 # index of last intersection with limit
        state = zlims[0] < c.pos[0][2] < zlims[1]
        for i, pos in enumerate(c):
            if (zlims[0] < pos[2] < zlims[1]) is not state:
                # State change has happened
                if state:
                    # Leaving zlim, save contour so far
                    c_out.append(contour(c.pos[j:i],0))
                else:
                    # Entering zlim, set start point
                    j = i

                state = not state #save new state

        if state:
            # the last stretch was in range
            c_out.append(contour(c.pos[j:i],0))
        return c_out

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    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)
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        contours += self.trim_contour(
            contour([Position(self.range[self.x][0],ys[i],zs[i]) for i in range(len(ys))], 0),
            self.range[self.z]
        )
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        expr2 = self.plane_intersection(self.x, self.range[self.x][1], layer = n)
        ys, zs = self.sample(expr2, self.y)
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        contours += self.trim_contour(
            contour([Position(self.range[self.x][1],ys[i],zs[i]) for i in range(len(ys))], 0),
            self.range[self.z]
        )
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        expr3 = self.plane_intersection(self.y, self.range[self.y][0], layer = n)
        xs, zs = self.sample(expr3, self.x)
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        contours += self.trim_contour(
            contour([Position(xs[i],self.range[self.y][0],zs[i]) for i in range(len(ys))], 0),
            self.range[self.z]
        )
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        expr4 = self.plane_intersection(self.y, self.range[self.y][1], layer = n)
        xs, zs = self.sample(expr4, self.x)
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        contours += self.trim_contour(
            contour([Position(xs[i],self.range[self.y][1],zs[i]) for i in range(len(ys))], 0),
            self.range[self.z]
        )
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        # TODO Join adjacent contours into one
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        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__':
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    s =  solver(0.02, 100, 100, 0.003)
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    contours = []
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    for i in np.arange(-15,55):
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        contours += s.contour_n(i)

    plot_contours(contours)