所以我創建了這個拋物線類，它可以用 3 個引數（a、b 和 c）或屬于拋物線的 3 個點來實體化。該函式回傳由和punti()定義的范圍內屬于拋物線的所有點。這是代碼（大部分是意大利語，抱歉）：nm
class Parabola:
def __init__(self, tipo=0, *params):
'''
Il tipo è 0 per costruire la parabola con a, b, c; 1 per costruire la parabola con
tre punti per la quale passa
'''
if tipo == 0:
self.__a = params[0]
self.__b = params[1]
self.__c = params[2]
self.__delta = self.__b ** 2 - (4 * self.__a * self.__c)
elif tipo == 1:
matrix_a = np.array([
[params[0][0]**2, params[0][0], 1],
[params[1][0]**2, params[1][0], 1],
[params[2][0]**2, params[2][0], 1]
])
matrix_b = np.array([params[0][1], params[1][1], params[2][1]])
matrix_c = np.linalg.solve(matrix_a, matrix_b)
self.__a = round(matrix_c[0], 2)
self.__b = round(matrix_c[1], 2)
self.__c = round(matrix_c[2], 2)
self.__delta = self.__b ** 2 - (4 * self.__a * self.__c)
def trovaY(self, x):
y = self.__a * x ** 2 self.__b * x self.__c
return y
def punti(self, n, m, step=1):
output = []
for x in range(int(min(n, m)), int(max(n, m)) 1, step):
output.append((x, self.trovaY(x)))
return output
現在我的小游戲是關于用弓射擊目標，我必須使用拋物線作為軌跡，它經過 3 個點：
- 球員中心
- 帶有游標 x 和玩家 y 的點
- 中間的一個點，游標的 y
軌跡由一條黑線表示，但它顯然不起作用，我不明白為什么。這是游戲的代碼（不要介意弓的旋轉，我仍然必須使其正常運行）：
import os
import sys
import pygame
from random import randint
sys.path.insert(
1, __file__.replace("pygame-prototype\\" os.path.basename(__file__), "coniche\\")
)
import parabola
# Initialization
pygame.init()
WIDTH, HEIGHT = 1024, 576
screen = pygame.display.set_mode((WIDTH, HEIGHT))
# Function to rotate without losing quality
def rot_from_zero(surface, angle):
rotated_surface = pygame.transform.rotozoom(surface, angle, 1)
rotated_rect = rotated_surface.get_rect()
return rotated_surface, rotated_rect
# Function to map a range of values to another
def map_range(value, leftMin, leftMax, rightMin, rightMax):
# Figure out how 'wide' each range is
leftSpan = leftMax - leftMin
rightSpan = rightMax - rightMin
# Convert the left range into a 0-1 range (float)
valueScaled = float(value - leftMin) / float(leftSpan)
# Convert the 0-1 range into a value in the right range.
return rightMin (valueScaled * rightSpan)
# Player class
class Player:
def __init__(self, x, y, width=64, height=64):
self.rect = pygame.Rect(x, y, width, height)
self.dirx = 0
self.diry = 0
def draw(self):
rectangle = pygame.draw.rect(screen, (255, 0, 0), self.rect)
# Target class
class Target:
def __init__(self, x, y, acceleration=0.25):
self.x, self.y = x, y
self.image = pygame.image.load(
__file__.replace(os.path.basename(__file__), "target.png")
)
self.speed = 0
self.acceleration = acceleration
def draw(self):
screen.blit(self.image, (self.x, self.y))
def update(self):
self.speed -= self.acceleration
self.x = int(self.speed)
if self.speed < -1:
self.speed = 0
player = Player(64, HEIGHT - 128)
# Targets init
targets = []
targets_spawn_time = 3000
previous_ticks = pygame.time.get_ticks()
# Ground animation init
ground_frames = []
for i in os.listdir(__file__.replace(os.path.basename(__file__), "ground_frames")):
ground_frames.append(
pygame.image.load(
__file__.replace(os.path.basename(__file__), "ground_frames\\" i)
)
) # Load all ground frames
ground_frame_counter = 0 # Keep track of the current ground frame
frame_counter = 0
# Bow
bow = pygame.image.load(__file__.replace(os.path.basename(__file__), "bow.png"))
angle = 0
while 1:
for event in pygame.event.get():
if event.type == pygame.QUIT:
sys.exit()
# Spawning the targets
current_ticks = pygame.time.get_ticks()
if current_ticks - previous_ticks >= targets_spawn_time:
targets.append(Target(WIDTH, randint(0, HEIGHT - 110)))
previous_ticks = current_ticks
screen.fill((101, 203, 214))
player.draw()
for i, e in list(enumerate(targets))[::-1]:
e.draw()
e.update()
if e.x <= -e.image.get_rect().width:
del targets[i]
# Calculating the angle of the bow
mouse_pos = pygame.Vector2(pygame.mouse.get_pos())
angle = map_range(mouse_pos.x, 0, WIDTH, 90, 0)
# Rotate the bow
rotated_bow, rotated_bow_rect = rot_from_zero(bow, angle)
rotated_bow_rect.center = player.rect.center
screen.blit(rotated_bow, rotated_bow_rect)
# Animate the ground
if frame_counter % 24 == 0:
ground_frame_counter = 1
if ground_frame_counter >= len(ground_frames):
ground_frame_counter = 0
for i in range(round(WIDTH / ground_frames[ground_frame_counter].get_rect().width)):
screen.blit(
ground_frames[ground_frame_counter],
(
ground_frames[ground_frame_counter].get_rect().width * i,
HEIGHT - ground_frames[ground_frame_counter].get_rect().height,
),
)
# Calculating the trajectory
mouse_pos.x = (
mouse_pos.x if mouse_pos.x != rotated_bow_rect.centerx else mouse_pos.x 1
)
# print(mouse_pos, rotated_bow_rect.center)
v_x = rotated_bow_rect.centerx ((mouse_pos.x - rotated_bow_rect.centerx) / 2)
trajectory_parabola = parabola.Parabola(
1,
rotated_bow_rect.center,
(mouse_pos.x, rotated_bow_rect.centery),
(v_x, mouse_pos.y),
)
trajectory = [(i[0], int(i[1])) for i in trajectory_parabola.punti(0, WIDTH)]
pygame.draw.lines(screen, (0, 0, 0), False, trajectory)
pygame.draw.ellipse(
screen, (128, 128, 128), pygame.Rect(v_x - 15, mouse_pos.y - 15, 30, 30)
)
pygame.draw.ellipse(
screen,
(128, 128, 128),
pygame.Rect(mouse_pos.x - 15, rotated_bow_rect.centery - 15, 30, 30),
)
pygame.display.update()
if frame_counter == 120:
for i in trajectory:
print(i)
frame_counter = 1
您可以運行所有這些并了解它有什么問題，幫助？
uj5u.com熱心網友回復：
您將 a、b 和 c 的值四舍五入到小數點后 2 位。這對于此應用程式來說太不準確了：
self.__a = round(matrix_c[0], 2)
self.__b = round(matrix_c[1], 2)
self.__c = round(matrix_c[2], 2)
self.__a = matrix_c[0]
self.__b = matrix_c[1]
self.__c = matrix_c[2]
uj5u.com熱心網友回復：
類似于上面的答案......四舍五入是這里的問題。當坐標的比例變大時，這一點會被放大。
但是，不同意其他解決方案：將坐標傳遞到拋物線構造中的順序無關緊要。任何訂單都可以正常作業。點就是點。
這是由于舍入誤差而導致的原始拋物線函式“下垂”的圖片：
p1 = (0, 10) # left
p2 = (100, 10) # right
p3 = (50, 100) # apex
p = Parabola(1, p3, p2, p1)
traj = p.punti(0, 100)
xs, ys = zip(*traj)
plt.scatter(xs, ys)
plt.plot([0, 100], [10, 10], color='r')
plt.show()
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