+
+
+
+
+
+ Graphing Functions
+Problem written by Moussa Doumbouya
++
+ In this exercice, you are going to write a program that creates the graphical representation of a function of your choice. Like the followings: +
+ ++
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+
+
+ y = math.cos(x)
+ 
+
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+
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+ y = 1/x
+ 
+
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+ y = x ** 3
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+ + This is done by findng the pixels that correspond to (x, y) points of the plotted function, and setting the color of those pixels to green. + The axes are also drawn in a similar fashion. +
+ + + +Coordinate Systems
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+ In order to plot functions, you will need to write functions that convert x and y positions from
+ the plot coordinate system to the pixel coordinate system (illustrated in the adjacent figure).
+ The starter code suggests the
+
+ x_to_pixel_x() and y_to_pixel_y() functions for this purpose. The starter code also contains
+ "doctests" to help you check your implementation. You may run the test cases as follow: +
python -m doctests your_file.py+
+ 
+
+
+ Starter Code
++ A starter code is provided below. This contains useful constants and a suggested high level decomposition of the problem. +
+ ++from simpleimage import SimpleImage +import math + +# Domain of the plot +X_MIN = -10 +X_MAX = 10 + +# Range of the plot +Y_MIN = -10 +Y_MAX = 10 + +# Size of the plot in pixels +PLOT_WIDTH = 400 +PLOT_HEIGHT = 400 + +# Color of the axes +AXIS_COLOR_R = 200 +AXIS_COLOR_G = 0 +AXIS_COLOR_B = 0 + +# Color of the plot +PLOT_COLOR_R = 0 +PLOT_COLOR_G = 200 +PLOT_COLOR_B = 0 + +# x and y step sizes +DELTA_X = 0.01 +DELTA_Y = 0.01 + + +def main(): + """ + Make a blank plot, draw the x and y axis, plot the + function defined by plotted_function and show the plot. + """ + plot = make_blank_plot() + plot = draw_axes(plot) + plot = plot_function(plot) + plot.show() + + +def ploted_function(x): + """ + Compute the y value of the ploted function for the given :param:x value. + Implement a function of your choice + """ + return math.cos(x) + + +def x_to_pixel_x(x): + """ + Compute the horizontal pixel position for horizontal + position :param:x in the plotted coordinate system. + + Test Cases: + + x = 0 should correspond to middle of the plot + >>> x_to_pixel_x(0) + 200 + + x = -10 should correspond to far left of the plot + >>> x_to_pixel_x(-10) + 0 + + x = 10 should correspond to far right of the plot + Note: x=10 is outside of the plotting area + >>> x_to_pixel_x(10) + 400 + """ + + # TODO: Your code here + # calculate the pixel x position and store it in px + + return int(px) + + +def y_to_pixel_y(y): + """ + Compute the horizontal pixel position for vertical + position :param:y in the plotted coordinate system + + Test Cases: + + y = 0 should correspond to the middle of the plot + >>> y_to_pixel_y(0) + 200 + + y=10 should correspond to the top of the plot. + >>> y_to_pixel_y(10) + 0 + + y=-10 should correspond to the bottom of the plot + Note y=-10 is actually outside of the plotting area + >>> y_to_pixel_y(-10) + 400 + """ + + # TODO: your code here + # Calculate the pixel y position and store it in py + + return int(py) + +if __name__ == '__main__': + main() ++ + + + +
Solution
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+
+ from simpleimage import SimpleImage +import math + +# Domain of the plot +X_MIN = -10 +X_MAX = 10 + +# Range of the plot +Y_MIN = -10 +Y_MAX = 10 + +# Size of the plot in pixels +PLOT_WIDTH = 400 +PLOT_HEIGHT = 400 + +# Color of the axes +AXIS_COLOR_R = 200 +AXIS_COLOR_G = 0 +AXIS_COLOR_B = 0 + +# Color of the plot +PLOT_COLOR_R = 0 +PLOT_COLOR_G = 200 +PLOT_COLOR_B = 0 + +# x and y step sizes +DELTA_X = 0.01 +DELTA_Y = 0.01 + + +def main(): + """ + Make a blank plot, draw the x and y axis, plot the + function defined by plotted_function and show the plot. + """ + plot = make_blank_plot() + plot = draw_axes(plot) + plot = plot_function(plot) + plot.show() + + +def ploted_function(x): + """ + Compute the ploted function at point :param:x + """ + # return math.cos(x) + # return math.tanh(x) + # return x**3 + return x ** 2 + + +def make_blank_plot(): + """ + Create an image with all pixel colors set to black + """ + plot = SimpleImage.blank(PLOT_WIDTH, PLOT_HEIGHT) + for px in plot: + px.red = 0 + px.green = 0 + px.blue = 0 + return plot + + +def x_to_pixel_x(x): + """ + Compute the horizontal pixel position for horizontal + position :param:x in the plotted coordinate system. + + Test Cases: + + x = 0 should correspond to middle of the plot + >>> x_to_pixel_x(0) + 200 + + x = -10 should correspond to far left of the plot + >>> x_to_pixel_x(-10) + 0 + + x = 10 should correspond to far right of the plot + Note: x=10 is outside of the plotting area + >>> x_to_pixel_x(10) + 400 + """ + h_pixel_per_point = PLOT_WIDTH / (X_MAX - X_MIN) + px = x * h_pixel_per_point + PLOT_WIDTH/2 + return int(px) + + +def y_to_pixel_y(y): + """ + Compute the horizontal pixel position for vertical + position :param:y in the plotted coordinate system + + Test Cases: + + y = 0 should correspond to the middle of the plot + >>> y_to_pixel_y(0) + 200 + + y=10 should correspond to the top of the plot. + >>> y_to_pixel_y(10) + 0 + + y=-10 should correspond to the bottom of the plot + Note y=-10 is actually outside of the plotting area + >>> y_to_pixel_y(-10) + 400 + """ + v_pixel_per_point = PLOT_HEIGHT / (Y_MAX - Y_MIN) + py = PLOT_HEIGHT/2 - y * v_pixel_per_point + return int(py) + + +def draw_axes(plot): + """ + Draw the horizontal and vertical axes + """ + draw_x_axis(plot) + draw_y_axis(plot) + return plot + + +def draw_x_axis(plot): + """ + Draw the horizontal axis + Set of points for which (x, 0) where x in [X_MIN, XMAX[ (x-max not included) + """ + x = X_MIN + while x<X_MAX: + px = x_to_pixel_x(x) + py = y_to_pixel_y(0) + pixel = plot.get_pixel(px, py) + pixel.red = AXIS_COLOR_R + pixel.green = AXIS_COLOR_G + pixel.blue = AXIS_COLOR_B + x+=DELTA_X + return plot + + +def draw_y_axis(plot): + """ + Draw the vertical axis + Set of points for which (0, y) where x in ]Y_MIN, Y_MAX] (Y_MIN not included) + """ + y = Y_MIN + DELTA_Y + while y<Y_MAX: + px = x_to_pixel_x(0) + py = y_to_pixel_y(y) + pixel = plot.get_pixel(px, py) + pixel.red = AXIS_COLOR_R + pixel.green = AXIS_COLOR_G + pixel.blue = AXIS_COLOR_B + y += DELTA_Y + return plot + + +def plot_function(plot): + """ + Draw the points of the function defined by plotted_function() + that are in range + """ + x = X_MIN + while x < X_MAX: + y = ploted_function(x) + if y > Y_MIN and y <= Y_MAX: + px = x_to_pixel_x(x) + py = y_to_pixel_y(y) + pixel = plot.get_pixel(px, py) + pixel.red = PLOT_COLOR_R + pixel.green = PLOT_COLOR_G + pixel.blue = PLOT_COLOR_B + + x += DELTA_X + return plot + + +if __name__ == '__main__': + main()+
+