# -*- coding: utf-8 -*-
"""math.sin.2D.v2.3.ipynb

Automatically generated by Colaboratory.

Original file is located at
    https://colab.research.google.com/drive/12tdDRtHdW_zRudl6hjX2uIAunriDdGjw

# Ploting Functional Curves

## Display a pattern using character grids
"""

#
# A display device normally consists of a matrix of grid points
#   or lines of grid points.
# A figure or picture is displayed by turning some points ON and other points OFF.
#
# Example:
#   A 8x8 dot matrix that represent the 'A' character,
#   'a': ON, '.' (or blank): OFF
#
dotMatrix = """
...aa...
..a..a..
.a....a.
a......a
aaaaaaaa
a......a
a......a
........
"""

print(dotMatrix)
print(dotMatrix.replace('.',' '))
print(dotMatrix.replace('.',' ').replace('a','*'))

"""## Representing a display device using strings"""

# To display a 2D pattern or curve, that is, a list of (x,y) coordinate pairs,
# we need to be able to turn points at these (x,y)'s ON, given an initial blank screen.

# Each grid line can be represented by a string variable, which is initially blank.
# We then replace some blank points with special marks to turn them ON.

"""## Turning a grid point ON"""

#
# Mark a special position (y) with a special symbol
#

#
# How to replace a character at a particular position in a string with a special symbol??
#

# Eample:
#   How to replace the first 'o' in the HelloWorld string with 'O'
s = 'Hello World'
print s

#
# How to replace the character s[4] (small 'o') with 'O' (big O)??
#
# s[4] = 'O'      # ERROR: TypeError: 'str' object does not support item assignment
# Unlike change of list elements, we CANNOT directly assign a new value to it.
#
# Instead, we can compose a string consisting of:
#   1. the substring BEFORE the character to be replaced
#   2. the new replacement character or symbol
#   3. the substring AFTER the character to be replaced
# We can concatenate these 3 pieces and save it to the original string variable.
#
# s = s[:4] + 'x' + s[5:]	# replace the 3rd char with 'x'

print(s[:4],s[4],s[5:])     # s[:4]: substring before s[4], s[5:]: substring after s[4]
print(s[:4],'O',s[5:])      # replace s[4] with 'O'
print(s[:4]+'O'+s[5:])      # concate them

s = s[:4]+'*'+s[5:]         # replace the 4-th character with '*'
print(s)

#
# How to replace a character at any position 'y'
#
print("." * 10)
s = '           '
# s = s[:4]+'*'+s[5:]     # replace s[4]

y = 8
s = s[:y]+'*'+s[y+1:]     # replace s[y]
print(s)

# So, if s represent a vertical grid line (for some particular x)
# we can use the above statement to 'turn the point (x,y) ON' ...

"""## Example: ploting a functional curve"""

#
# Basics: Plot (x,y) pairs using a string variable
#

import random

def myfunc(x):                    # y = f(x), y calculated from x
  # y = int(random.random()*10)     # f-1: random numbers
  y = x + 1                       # f-2: linear
  # y = x ** 2                    # f-3: quadratic
  # y = x ** 2 - 20                   # f-4: quadratic (with negative values)
  return y

#
# logical to device coordinates conversion parameters
#
yScale = 1                        # magnification in y-direction
# yScale = 0.1                      # f3/f4: magnification in y-direction
y0 = 0                            # translation/shift in y-direction
# y0 = 2                            # f4

print("(%2s, %2s) %s" % ('x', 'y', "-" * 40))
random.seed(10)

for x in range(20):               # iterate through some x's
  s = "." * 40                    # a scan line with no data mark (OFF)
  y = myfunc(x)                   # y calculated from x (use random number here)

  # logical coordinates to device coordinates conversion
  y *= yScale                     # magnify to fit device width/height
  y += y0                         # shift y=0 line (to change negative y to fit into positive device index ranges)
  y = int(y)                      # round to integer index

  # We may also need to reverse y's polarity (y = -y)
  # before scaling
  # if the device coordinates have opposite y-direction
  # as logical coordinates.

  # place a marker at position y for the scanline for x
  s = s[:y]+'*'+s[y+1:]           # mark data point (x,y) at the y-th position of the scan line
  print("(%2d, %2d) %s" % (x, y, s))

"""# Ploting Sine/Cosine Waves

## Plotting Parameters
"""

#
# Polt Sine/Cosine Waves...
#

#
# Author: Jing-Shin Chang
# Emails: jshin@csie.ncnu.edu.tw, shin@nlp.csie.ncnu.edu.tw, shin.jsc@gmail.com
# Revision: 2.3
# Last Update: 2019/12/25
# Language: Python 2
#

#
# Hint:
#
# Replace a character in-place...
#
# s = 'foobar'
# s = s[:3] + 'x' + s[4:]	# replace the 3rd char with 'x'
# print s

import math as m

y_0 = 20          # number of grid points above/below the central axis line
y_scale = 10      # magnification in the y-direction

x_resolution = 10 # increment pi/10 per step
deltaAngle = m.pi/x_resolution

x_ticks = 41      # run 41 steps (== 4 * pi)
x_step = 1

"""## Sine (with one string as vertical scan line)"""

#
# Plot (1) - Sine
#
hbar = '-' * y_0 + '+' + '-' * y_0
print hbar

n_rows = len(hbar)

for x in range(0,x_ticks,x_step):
    bar = "'" * n_rows
    # bar = ' ' * n_rows

    # mark '|' at origin (y=0)
    bar = bar[:y_0+0]+'|'+bar[y_0+1:]
    
    # mark 's' at y=sin(x) [with magnification & translation to fit device coordinates]
    sin = m.sin(deltaAngle * x)
    y = int(sin * y_scale)	# scale up in y-direction
    y += y_0                # translate/shift up in y-direction (to make positive character index)
    bar = bar[:y]+'s'+bar[y+1:]

    # mark 'c' at y=cos(x) [with magnification & translation to fit device coordinates]
    # cos = m.cos(deltaAngle * x)
    # y = int(cos * y_scale)	# scale up in y-direction
    # y += y_0                # translate/shift up in y-direction (to make positive character index)
    # bar = bar[:y]+'c'+bar[y+1:]

    print bar

"""### Cosine"""

#
# Plot (2) - Cosine
#
hbar = '-' * y_0 + '+' + '-' * y_0
print hbar

n_rows = len(hbar)

for x in range(0,x_ticks,x_step):
    # bar = "'" * n_rows
    bar = ' ' * n_rows

    # mark '|' at origin (y=0)
    bar = bar[:y_0+0]+'|'+bar[y_0+1:]
    
    # mark 's' at y=sin(x) [with magnification & translation to fit device coordinates]
    # sin = m.sin(deltaAngle * x)
    # y = int(sin * y_scale)	# scale up in y-direction
    # y += y_0                # translate/shift up in y-direction (to make positive character index)
    # bar = bar[:y]+'s'+bar[y+1:]

    # mark 'c' at y=cos(x) [with magnification & translation to fit device coordinates]
    cos = m.cos(deltaAngle * x)
    y = int(cos * y_scale)	# scale up in y-direction
    y += y_0                # translate/shift up in y-direction (to make positive character index)
    bar = bar[:y]+'c'+bar[y+1:]

    print bar

"""### Sine + Cosine"""

#
# Plot (3) - Sin + Cos
#
hbar = '-' * y_0 + '+' + '-' * y_0
print hbar

n_rows = len(hbar)

for x in range(0,x_ticks,x_step):
    # bar = "'" * n_rows
    bar = ' ' * n_rows

    # mark '|' at origin (y=0)
    bar = bar[:y_0+0]+'|'+bar[y_0+1:]
    
    # mark 's' at y=sin(x) [with magnification & translation to fit device coordinates]
    sin = m.sin(deltaAngle * x)
    y = int(sin * y_scale)	# scale up in y-direction
    y += y_0                # translate/shift up in y-direction (to make positive character index)
    bar = bar[:y]+'s'+bar[y+1:]

    # mark 'c' at y=cos(x) [with magnification & translation to fit device coordinates]
    cos = m.cos(deltaAngle * x)
    y = int(cos * y_scale)	# scale up in y-direction
    y += y_0                # translate/shift up in y-direction (to make positive character index)
    bar = bar[:y]+'c'+bar[y+1:]

    print bar

"""## Sine (without using auxilirary strings)"""

#
# Plot (4) - Sine
#
print '-' * y_0, '+', '-' * y_0
for x in range(0,x_ticks,x_step):
    sin = m.sin(deltaAngle * x)
    y = int(sin * y_scale)	# # y = sin * y_scale

    #+ print ' ' * y_0, '*' * (y+y_0)
    #+ print ' ' * (y+y_0), '$'
    #+ print "sin(",x,"/",x_resolution," pi) =", sin, y

    if ( y > 0 ):
	print ' ' * y_0, '|', ' ' * (y-1), '@'
    elif y == 0:
	print ' ' * y_0, '@'
    else:
	print ' ' * (y_0+y-2), '@', ' ' * (-y-1), '|'

print

#
# Plot (5) - Sine
#
print '-' * y_0, '+', '-' * y_0
for x in range(0,x_ticks,x_step):
    sin = m.sin(deltaAngle * x)
    y = int(sin * y_scale)	# # y = sin * y_scale
    if ( y > 0 ):
	print ' ' * y_0, '|', '@' * y
    else:
	print ' ' * (y_0+y-1), '@' * (-y), '|'

# y_axis = "                         "
    # y_axis[y] = '*'	# CANNOT change string member
    # print y_axis

"""# Using Rows of Horizontal Scan Lines

We can also use a list of strings to represent different (horizontal) scan lines, use the list index as y-coordinate (row address) and character position as x-cordinate (column address) to place special markers to point (x,y).

## Hint
"""

#'''
# Hints:
rows = [    # initial OFF state scan lines
      '.' * 10,
      '=' * 10,
      '-' * 10
]
# place markers at different (device) coordinates
rows[0]=rows[0][:3]+'a'+rows[0][4:]   # x=3, y=0
rows[1]=rows[1][:4]+'b'+rows[1][5:]   # x=4, y=1
rows[2]=rows[2][:5]+'c'+rows[2][6:]   # x=5, y=2
print ('y=2: %s\ny=1: %s\ny=0: %s\n' % (rows[2], rows[1], rows[0]))
#'''

"""## Sine (Using 2D Scan Lines)"""

#
# Using 2D scan lines -- Example
#


#
# Plot (6) - Sine + Cosine
#
rows = []
n_rows = y_0*2+1
n_cols = 80
#
# create blank screen (y_0*2+1 rows & n_cols columns)
#
for y in range(n_rows):
    rows.append(' ' * n_cols)
    row_id = len(rows)-1
    #+ print ('%2d: %s' % (row_id, rows[row_id]))

#
# create centeral line
#
rows[y_0]= '-' * n_cols

#
# create function curves
#
for x in range(0, x_ticks*2-1, x_step):     # double #ticks for higher resolution

    sin = m.sin(deltaAngle * x * 0.5)     # half deltaAngle for higher resolution
    y = int(sin * y_scale *1.5)           # # y = sin * y_scale
    y += y_0			                        # shift up

    rows[y]=rows[y][:x]+'s'+rows[y][x+1:]   # add mark at y-th row & x-th col

    cos = m.cos(deltaAngle * x * 0.5)
    y = int(cos * y_scale *1.5)           # # y = sin * y_scale
    y += y_0

    rows[y]=rows[y][:x]+'c'+rows[y][x+1:]   # add mark at y-th row & x-th col

#
# print the curves
#

#+ n_rows = len(rows)
print 'n_rows =', n_rows
for y in range(n_rows-1,-1,-1):
    # print ('%3d: %s' % (y, rows[y]))    # without offset
    print ('%3d: %s' % (y-y_0, rows[y]))

#
# print the curves upside-down (smaller y first (at top))
#
print 'n_rows =', n_rows, '(reversed)'
for y in range(n_rows):
    # print ('%3d: %s' % (y, rows[y]))    # without offset
    print ('%3d: %s' % (y-y_0, rows[y]))

"""## Challenge

Implement a string function to place a specified marker character at designated position, like:
  - placeMarker(string, marker, potision)
  - re-write the above drawing functions using placeMarker()

## TODO
"""

#
# Using Array module (TODO)
#

x = '''
import array as arr
a = arr.array('d', [1.1, 3.5, 4.5])
print(a)
print(a[0])
print(a[1])
print(a[2])
'''