# Code for Midterm Exam 2, Summer 2009, CS8, P. Conrad, UCSB CS Dept.
import cTurtle
import math
#
#
#
#
Here are two functions that will compute the x value (or y value)
of the point number i of n points distributed evenly around a
circle of radius r, centered at 0,0, with the first point being
at 0 degrees on the standard "unit circle"
#
#
#
#
#
#
#
#
function ithOfNPointsOnCircleX (or ithOfNPointsOnCircleY)
contract: (int,int,float) => float
consumes:
i: the point number (between 0 and n-1)
n: the number of points
r: the radius of the circle (assumed to be centered at 0,0)
produces:
the x value (or y value) of that point in the cartesian plane
def ithOfNPointsOnCircleX(i,n,r):
return r * math.cos((i/n)*(2*math.pi))
def ithOfNPointsOnCircleY(i,n,r):
return r * math.sin((i/n)*(2*math.pi))
#
#
#
#
#
#
#
#
#
#
#
#
drawPolygon (turtle, float, int) => void
consumes:
t: a turtle we'll use to draw the polygon
r: the radius of the polygon
n: the number of sides the polygon has
produces: nothing
side-effect:
the turtle draws a polygon of n sides, centered at 0,0
the size of the polygon is determined by r---it is the right size
that it could be inscribed in a circle of radius r
the turtle is left at position 0,0, facing right
the old position and direction of the turtle is lost.
def drawPolygon(t,r,n):
# pick up the pen, move to the starting point, and put down the pen
t.up(); t.goto(r,0); t.down()
# connect the dots for all the points
for i in range(1,n):
# gives points 1 thorugh n-1
t.goto( ithOfNPointsOnCircleX(i,n,r),
ithOfNPointsOnCircleY(i,n,r) )
# That drew almost all the way around---for example, it drew
# three sides if we are drawing a square. To finish, we need to
# return to the starting point
t.goto(r,0); t.up()
#
#
#
#
#
#
#
#
#
#
#
#
#
#
drawStar (turtle, float, int) => void
consumes:
t: a turtle (that was already constructed) we'll use to draw the polygon
r: the radius of the polygon
n: the number of points the star has (must be >= 5)
produces: nothing
side-effect:
if n < 5, the function returns without doing anything
else:
the turtle draws a star of n points, centered at 0,0
the size of the star is determined by r---it is the right size
that it could be inscribed in a circle of radius r
The star is drawn by connecting each point to a point that is
two points away (i.e. we skip one point)
def drawStar(t,r,n):
# if n < 5, we can't really draw a star, so just return
if n<5:
return
# Doesn't return anything.
It just ends the function call
# pick up the pen
t.up();
# connect the dots for all the points
for i in range(n):
# gives points 0 through n-1
# pen is up---we move to this point
t.goto( ithOfNPointsOnCircleX(i,n,r),
ithOfNPointsOnCircleY(i,n,r) )
# put the pen down
t.down()
# now draw a line to the point two points away from this one
t.goto( ithOfNPointsOnCircleX(i+2,n,r),
ithOfNPointsOnCircleY(i+2,n,r) )
# lift the pen back up
t.up()