demo.py

#!/usr/bin/python

import math


class Vector(object):

    def __init__(self, x, y, z):
        self.x = x
        self.y = y
        self.z = z

    def __abs__(self):
        return math.sqrt(self.x * self.x +
                         self.y * self.y +
                         self.z * self.z)

    def __add__(self, other):
        return Vector(self.x + other.x,
                      self.y + other.y,
                      self.z + other.z)

    def __sub__(self, other):
        return Vector(self.x - other.x,
                      self.y - other.y,
                      self.z - other.z)

    def __mul__(self, factor):
        return Vector(self.x * factor,
                      self.y * factor,
                      self.z * factor)

    def gcode(self):
        return 'X%.3f Y%.3f Z%.3f' % (self.x, self.y, self.z)


SIN_60 = math.sin(math.pi / 3)
COS_60 = 0.5

RADIUS = 175 - 33 - 18
ZERO_OFFSET = -7
TOWER_1 = Vector(-SIN_60 * RADIUS, -COS_60*RADIUS, 0)
TOWER_2 = Vector(SIN_60 * RADIUS, -COS_60*RADIUS, 0)
TOWER_3 = Vector(0, RADIUS, 0)


def delta(v):
    t1 = TOWER_1 - v
    t2 = TOWER_2 - v
    t3 = TOWER_3 - v
    return Vector(
        v.z + math.sqrt(250*250 - t1.x*t1.x - t1.y*t1.y) + ZERO_OFFSET,
        v.z + math.sqrt(250*250 - t2.x*t2.x - t2.y*t2.y) + ZERO_OFFSET,
        v.z + math.sqrt(250*250 - t3.x*t3.x - t3.y*t3.y) + ZERO_OFFSET)


def linear(start, stop, speed):
    cartesian_mm = abs(stop - start)
    steps = max(1, int(cartesian_mm * 50 / min(speed, 200)))
    cartesian_mm /= steps
    previous = delta(start)
    for step in range(steps):
        d = delta(start + (stop - start) * (float(step + 1) / steps))
        print 'G1', d.gcode(),
        delta_mm = abs(d - previous)
        factor = delta_mm / cartesian_mm
        print 'F%.3f' % (60 * speed * factor)
        previous = d


print 'G21 ; set units to millimeters'
print 'G90 ; use absolute positioning'
print 'G28 ; home all axes'

SIZE = 60
SIZE2 = SIZE * math.sqrt(2)  # diagonal

previous = Vector(0, 0, 0)
print 'G1 F3000'

speeds = [100, 200, 300, 400]
for speed in speeds:
    print 'G1 F%d' % (speed * 60)
    z = 0  # (speed - 100) / 5
    for a in xrange(0, 1441, min(speed/100, 3)):
        v = Vector(math.sin(a * math.pi / 180) * SIZE,
                   math.cos(a * math.pi / 180) * SIZE,
                   z)
        d = delta(v)
        print 'G1', d.gcode()
        previous = v
    for y in xrange(-int(SIZE2), int(SIZE2), 10):
        x = SIZE2 - abs(y)
        vector = Vector(-x, y, z)
        linear(previous, vector, speed)
        previous = vector
        vector = Vector(x, y, z)
        linear(previous, vector, speed)
        previous = vector

# linear(previous, Vector(0, 0, 0), 300)
print 'G1 X400 Y400 Z400'
print 'M84 ; all motors off'