discretize_circle_dense.py

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import os
import numpy as np
import csv
import sys
 
def print_point(point, area, prefix = ""):
    str = prefix + " area = " + "%4.6e" %(area) + ", point = ["
    N = 2
    for i in xrange(N):
        str += "%4.6e" % (point[i])
        if i < N - 1:
            str += ", "
        else:
            str += "]\n"
 
    print(str)
 
def mult(matrix, vector):
    return [matrix[0][0] * vector[0] + matrix[0][1] * vector[1], matrix[1][0] * vector[0] + matrix[1][1] * vector[1]]
 
def discretize_circle(radius, num_r_points):
    """Generates discretization of circle so that area of all nodes are same"""
 
    # particle data
    sim_particle_r = radius
 
    # store location of nodes 
    sim_particles = []
 
    # store area of nodes
    sim_particles_area = []
 
    # width of annuli
    sim_num_r_points = num_r_points
    sim_annlui_width = 1. / sim_num_r_points
 
    # loop over annulus
    for i in xrange(sim_num_r_points):
 
        radius_inner = (i + 1.) * sim_annlui_width
        radius_outer = (i) * sim_annlui_width
 
        # num divisions in angle
        dn = 6 * (i + 1) - 3
        dtheta = 2. * np.pi / float(dn)
 
        # loop over theta
        for theta in xrange(dn):
 
            # get point
            radius_quad = (i - 1. / 2.) * sim_annlui_width
            x = [radius_quad * np.cos(theta * dtheta), radius_quad * np.sin(theta * dtheta)]
 
            area = sim_annlui_width * sim_annlui_width * np.pi / 3.
 
            sim_particles.append(x)
            sim_particles_area.append(area)
            print_point(x, area)
 
        # End loop over theta
 
    # End loop over annulus
 
    # 
    # loop over points again and scale them to circle of given radius
    #
    sim_particles_new = []
    sim_particles_area_new = []
    for i in xrange(len(sim_particles)):
 
        x = [radius * sim_particles[i][0], radius * sim_particles[i][1]]
        area = radius * radius * sim_particles_area[i]
        sim_particles_new.append(x)
        sim_particles_area_new.append(area)
 
    # End loop over particles
 
    # print points to csv file
    # generate csv file
    inpf = open('mesh_cir.csv','w')
 
    # header
    inpf.write("id, x, y, volume\n")
 
    for i in xrange(len(sim_particles_new)):
        inpf.write("%d, %4.6e, %4.6e, %4.6e\n" % (i, sim_particles_new[i][0], sim_particles_new[i][1], sim_particles_area_new[i]))
 
    inpf.close()
 
discretize_circle(0.001, 10)