函数计算的角度不一致

Question

我有一个函数旨在将多边形向左或向右旋转 5 度并返回它们的新点。该函数如下，连同它需要的函数player_center。

# finds center of player shape
# finds slope and midpoint of each vertice-midpoint line on the longer sides, 
# then the intercept of them all
def player_center(player):
  left_mid = line_midpoint(player[0], player[1])
  right_mid = line_midpoint(player[0], player[2])
 

  left_mid_slope = line_slope(left_mid, player[2])
  right_mid_slope = line_slope(right_mid, player[1])
  
  

  left_mid_line = find_equation(player[2], left_mid_slope, True)
  right_mid_line = find_equation(player[1], right_mid_slope, True)
 

 

  standard_left_mid_line = slope_intercept_to_standard(left_mid_line[0], left_mid_line[1], left_mid_line[2])
  standard_right_mid_line = slope_intercept_to_standard(right_mid_line[0], right_mid_line[1], right_mid_line[2])


  lines = sym.Matrix([standard_left_mid_line, standard_right_mid_line])

  return (float(lines.rref()[0].row(0).col(2)[0]), float(lines.rref()[0].row(1).col(2)[0]))

  




# rotates the player using SOHCAHTOA
# divides x coordinate by radius to find angle, then adds or subtracts increment of 5 to it depending on direction
# calculates the position of point at incremented angle, then appends to new set of points
# finally, new set is returned


# direction; 1 is left, 0 is right
def rotate_player(player, direction):
  increment = math.pi/36 # radian equivalent of 5 degrees
  full_circle = 2 * math.pi # radian equivalent of 360 degrees

  center = player_center(player)
  
  new_player = []

  for point in player:
    radius = line_distance(point, center)
    point_sin = (center[1] - point[1])/radius
    while (point_sin > 1):
      point_sin -= 1
    point_angle = math.asin(point_sin)

    if (direction == 1):
      if ((point_angle+increment) > math.pi * 2):
        new_angle = (point_angle+increment) - math.pi * 2
      else:
        new_angle = point_angle + increment
    else:
      if ((point_angle-increment) < 0):
        new_angle = 2 * math.pi + (point_angle-increment)
      else:
        new_angle = point_angle-increment
    print("The angle was {}".format(math.degrees(point_angle)))
    print("The angle is now {}".format(math.degrees(new_angle))) # print lines are for debug purposes
    new_point = ((radius * math.cos(new_angle)) + center[0], -(radius * math.sin(new_angle)) + center[1])
    new_player.append(new_point)
    
  print(new_player)
  return new_player

它所依赖的几何函数都在这个文件中定义在这里：

import math
import sympy as sym

# shape is in form of list of tuples e.g [(1,1), (2,1), (1,0), (2,0)]
# angle is in degrees
# def rotate_shape(shape, angle): 


def line_distance(first_point, second_point):
  return math.sqrt( (second_point[0] - first_point[0]) ** 2 + (second_point[1] - first_point[1]) ** 2) 

# undefined is represented by None in this program
def line_slope(first_point, second_point):
  if (second_point[0] - first_point[0] == 0):
    return None
  elif (second_point[1] - first_point[1] == 0):
    return 0
  else:
    return (second_point[1] - first_point[1])/(second_point[0] - first_point[0])


def line_midpoint(first_point, second_point):
  return ( (first_point[0] + second_point[0])/2, (first_point[1] + second_point[1])/2 )


def find_equation(coord_pair, slope, array_form):
  # Array form useful for conversion into standard form
  if (array_form == True):
    if (slope == 0):
      intercept = coord_pair[1]
      return [0, 1, intercept]
    elif (slope == None):
      intercept = coord_pair[0]
      return [1, 0, intercept]
    else:
      intercept = coord_pair[1] - (coord_pair[0] * slope)
      return [slope, 1, intercept]
  else:
    
    
    if (slope == 0):
      intercept = coord_pair[1]
      print("y = {0}".format(intercept))
      return
    elif (slope == None):
      intercept = coord_pair[0]
      print("x = {0}".format(intercept))
      return
    else:
       intercept = coord_pair[1] - (coord_pair[0] * slope)

    if (intercept >= 0):
      print("y = {0}x + {1}".format(slope, intercept))
      return
    else:
      print("y = {0}x - {1}".format(slope, intercept))


def find_perpendicular(slope):
  if (slope == 0):
    return None
  elif (slope == None):
    return 0 
  else:
    return -(1/slope)

def find_perp_bisector(first_point, second_point):
  # This function finds the perpendicular bisector between two points, using funcs made previously
  midpoint = line_midpoint(first_point, second_point)
  slope = line_slope(first_point, second_point)
  return find_equation(midpoint, -(1/slope)) 

def find_perp_equation(x, y, m, array_form):
  # returns the perpendicular equation of a given line
  if (array_form == True):
    return [find_perpendicular(x), y, m] 

  else:
    if (m >= 0):
      print("{0}y = {1}x + {2}".format(y, find_perpendicular(x), m))
    else:
      print("{0}y = {1}x - {2}".format(y, find_perpendicular(x), m))


def find_hyp(a, b):
 return math.sqrt((a**2) + (b**2)) 

def find_tri_area(a, b, c): 
  # finds area of triangle using Heron's formula
  semi = (a+b+c)/2 
  return math.sqrt(semi * (semi - a) * (semi - b) * (semi - c) )


def r_tri_check(a, b, c):
  if (a**2) + (b**2) != (c**2):
    print("This thing fake, bro.")


def find_point_section(first_point, second_point, ratio):
  # I coded this half a year ago and can't remember what for, but kept it here anyway.
  # separtions aren't necessary, but good for code readability
  first_numerator = (ratio[0] * second_point[0]) + (ratio[1] * first_point[0])  
  second_numerator = (ratio[0] * second_point[1]) + (ratio[1] * first_point[1]) 
  return ( first_numerator/(ratio[0]+ratio[1]), second_numerator/(ratio[0] + ratio[1]))


def slope_intercept_to_standard(x, y, b):
  # x and y are the coeffients of the said variables, for example 5y = 3x + 8 would be inputted as (3, 5, 8) 
  if (x == 0):
    return [0, 1, b]
  elif (y == 0):
    return [x, 0, b]
  else:
    return [x, -y, -b]

它在数学上看起来很合理，但是当我尝试应用它时，一切都变得松散了。 例如，当尝试将其应用到集合 polygon_points 等于 [(400, 300), (385, 340), (415, 340)] 时，所有地狱都崩溃了。

polygon_points 上重复调用函数的输出示例（为清楚起见，手动间隔输出）：

The angle was 90.0
The angle is now 95.0
The angle was -41.633539336570394

The angle is now -36.633539336570394
The angle was -41.63353933657017
The angle is now -36.63353933657017

The angle was 64.4439547804165
The angle is now 69.4439547804165
The angle was -64.44395478041695

The angle is now -59.44395478041695
The angle was -64.44395478041623
The angle is now -59.44395478041624

The angle was 80.94458887142648
The angle is now 85.94458887142648
The angle was -80.9445888714264

The angle is now -75.9445888714264
The angle was -80.94458887142665
The angle is now -75.94458887142665 

谁能解释一下？

Answer 1

太多不相关的代码，很多像 while (point_sin > 1): point_sin -= 1 这样的魔法 - 很难重现。

要围绕某个中心旋转点，您只需要这个（在您的情况下，cos(fi), sin(fi) 是预先计算的值）：

new_x = center_x + (old_x - center_x) * cos(fi) - (old_y - center_y) * sin(fi)
new_y = center_y + (old_x - center_x) * sin(fi) + (old_y - center_y) * cos(fi)

Answer 2

这是 SymPy 中 RegularPolygon 的内置功能：

>>> from sympy import RegularPolygon, rad
>>> p = RegularPolygon((0,0), 1, 5)
>>> p.vertices[0]
Point2D(1, 0)
>>> p.rotate(rad(30))  # or rad(-30)
>>> p.vertices[0]
Point2D(sqrt(3)/2, 1/2)