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# Copyright 2008 by Peter Moxhay and Wade Brainerd.
# This file is part of Math.
#
# Math is free software: you can redistribute it and/or modify
# it under the terms of the GNU General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# Math is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU General Public License for more details.
#
# You should have received a copy of the GNU General Public License
# along with Math. If not, see <http://www.gnu.org/licenses/>.
from objectarea import Object
from vector import Vector
from movableobject import MovableObject
from faucetobject import FaucetObject
import gtk, math
class VolumeObject(MovableObject):
"""Quasi three-dimensional container object."""
FILL_RATE = 50000
def __init__(self, symbol, pos, height = 400, lower_radius = 50, upper_radius = 100):
MovableObject.__init__(self)
self.symbol = symbol
self.area = 0
self.centroid = Vector(0, 0)
self.bounds_min = Vector(0, 0)
self.bounds_max = Vector(0, 0)
self.height = height
self.lower_radius = lower_radius
self.upper_radius = upper_radius
#if upper_radius > lower_radius:
self.points = [ Vector(-self.upper_radius, -self.height/2.), Vector(self.upper_radius-self.lower_radius, self.height/2.), \
Vector(self.lower_radius, self.height/2.), Vector(-self.lower_radius, self.height/2.) ]
#else:
# self.points = [ Vector(-self.upper_radius, -self.height/2.), Vector(self.upper_radius-self.lower_radius, self.height/2.), \
# Vector(self.lower_radius, self.height/2.), Vector(self.upper_radius, self.height/2.) ]
self.water_height = 0
self.water_lower_radius = lower_radius
self.pos = pos
self.volume = self.calculate_volume()
self.water_volume = 0
self.animated_water_volume = 0
self.animated_water_height = 0
self.filling_from_faucet = False
self.selectable = True
self.symbol_visible = True
self.rotatable = False
self.contains_water = False
self.full = False
# Get the current bounding rectangle.
self.calculate_bounds()
def calculate_volume(self):
return (math.pi * self.height / 3.0) * \
(self.lower_radius * self.lower_radius + self.lower_radius * self.upper_radius + self.upper_radius * self.upper_radius)
def calculate_water_height(self, volume):
a = (self.upper_radius - self.lower_radius)**2
b = 3.0 * self.lower_radius * (self.upper_radius - self.lower_radius)
c = 3.0 * self.lower_radius ** 2
d = -3.0 * volume/(math.pi * self.height)
solution = self.cubic(a, b, c, d)
#if volume <= 0.0:
if volume <= 0.0001:
return 0.0
else:
return solution[0] * self.height
def fill_to_given_volume(self, volume):
self.water_height = self.calculate_water_height(volume)
self.water_volume = volume
self.start_animating()
# Solve the cubic equation.
def cubic(self, a, b, c, d=None):
from math import cos
if a == 0:
return self.quadratic(b, c, d)[0], self.quadratic(b, c, d)[1], 0
if d:
# (ax^3 + bx^2 + cx + d = 0)
a, b, c = b / float(a), c / float(a), d / float(a)
t = a / 3.0
p, q = b - 3 * t**2, c - b * t + 2 * t**3
u, v = self.quadratic(q, -(p/3.0)**3)
if type(u) == type(0j):
# Complex cube root.
r, w = polar(u.real, u.imag)
y1 = 2 * self.cbrt(r) * cos(w / 3.0)
else:
# Real root.
y1 = self.cbrt(u) + self.cbrt(v)
y2, y3 = self.quadratic(y1, p + y1**2)
return y1 - t, y2 - t, y3 - t
# Solve the squadratic equation.
def quadratic(self, a, b, c=None):
import math, cmath
if a == 0:
return -c/float(b), 0
if c: # (ax^2 + bx + c = 0)
a, b = b / float(a), c / float(a)
t = a / 2.0
r = t**2 - b
if r >= 0:
# Real roots.
y1 = math.sqrt(r)
else:
# Complex roots.
y1 = cmath.sqrt(r)
y2 = -y1
return y1 - t, y2 - t
# Calculate a cube root.
def cbrt(self, x):
from math import pow
if x >= 0:
return pow(x, 1.0/3.0)
else:
return -pow(abs(x), 1.0/3.0)
def draw_ellipse(self, cr, x, y, width, height):
cr.new_sub_path()
cr.save()
cr.translate (x + width / 2., y)
cr.scale(width / 2., height / 2.)
cr.arc(0., 0., 1., 0., 2 * math.pi)
cr.restore()
def animate(self):
if self.animated_water_volume < self.water_volume:
self.animated_water_volume = min(self.animated_water_volume + VolumeObject.FILL_RATE, self.water_volume)
self.animated_water_height = self.calculate_water_height(self.animated_water_volume)
self.calculate_bounds()
self.queue_draw()
elif self.animated_water_volume > self.water_volume:
self.animated_water_volume = max(self.animated_water_volume - VolumeObject.FILL_RATE, self.water_volume)
self.animated_water_height = self.calculate_water_height(self.animated_water_volume)
self.calculate_bounds()
self.queue_draw()
else:
self.calculate_bounds()
self.queue_draw()
self.stop_animating()
self.filling_from_faucet = False
def draw(self, cr):
cr.translate(self.pos.x, self.pos.y)
cr.rotate(self.angle)
cr.scale(self.scale, self.scale)
ul = Vector(-self.upper_radius, -self.height/2)
ur = Vector(self.upper_radius, -self.height/2)
lr = Vector(self.lower_radius, self.height/2)
ll = Vector(-self.lower_radius, self.height/2)
if self.animated_water_height > 1:
t = self.animated_water_height / float(self.height)
water_radius = self.upper_radius*t + self.lower_radius*(1-t)
wl = Vector(-water_radius, self.height/2 - self.animated_water_height)
wr = Vector(water_radius, self.height/2 - self.animated_water_height)
cr.set_source_rgb(0.37, 0.74, 1.0)
cr.line_to(wl.x, wl.y)
cr.line_to(wr.x, wr.y)
cr.line_to(lr.x, lr.y)
cr.line_to(ll.x, ll.y)
cr.close_path()
self.draw_ellipse(cr, wl.x, wl.y, 2.0 * water_radius, water_radius/2.0)
self.draw_ellipse(cr, ll.x, ll.y, 2.0 * self.lower_radius, self.lower_radius/2.0)
cr.fill()
cr.set_source_rgb(0.0, 0.0, 1.0)
cr.set_line_width(4.0)
self.draw_ellipse(cr, wl.x, wl.y, 2.0 * water_radius, water_radius/2.0)
cr.stroke()
# Draw the faucet filling.
if self.filling_from_faucet:
assert self.scale == 1.0
stream_x = self.container.problem.faucet_object.pos.x + FaucetObject.STREAM_X - self.pos.x
stream_y = self.container.problem.faucet_object.pos.y + FaucetObject.STREAM_Y - self.pos.y
cr.rectangle(stream_x, stream_y, FaucetObject.STREAM_WIDTH, self.height/2 - self.animated_water_height - stream_y)
cr.set_source_rgb(0.37, 0.74, 1.0)
cr.fill()
# Now draw the shape of the container.
if self.selected:
cr.set_dash((10, 10), 0)
cr.set_source_rgb(0.0, 0.0, 0.0)
cr.set_line_width(4.0)
cr.move_to(ul.x, ul.y)
cr.line_to(ll.x, ll.y)
cr.move_to(ur.x, ur.y)
cr.line_to(lr.x, lr.y)
self.draw_ellipse(cr, ll.x, ll.y, 2.0 * self.lower_radius, self.lower_radius/2.0)
self.draw_ellipse(cr, ul.x, ul.y, 2.0 * self.upper_radius, self.upper_radius/2.0)
cr.stroke()
# Draw the symbol (capital letter representing the shape's area).
if self.symbol_visible:
cr.set_source_rgb(0, 0, 0)
cr.set_font_size(50)
x_bearing, y_bearing, width, height = cr.text_extents(self.symbol)[:4]
cr.move_to(-x_bearing - width/2, -y_bearing - height/2)
cr.show_text(self.symbol)
def calculate_bounds(self):
r = max(self.upper_radius, self.lower_radius)
# 50 is a hack to account for a slight rotation
halfsize = Vector(r + 2 + 50, self.height/2 + r/2 + 2) * self.scale
self.bounds_min = self.pos - halfsize
self.bounds_max = self.pos + halfsize
# Include the stream when animating.
if self.filling_from_faucet:
stream_y = self.container.problem.faucet_object.pos.y + FaucetObject.STREAM_Y
self.bounds_min.y = stream_y
def get_bounds(self):
return self.bounds_min, self.bounds_max
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