使用 pygame 生成并绘制正弦波

我正在尝试生成并绘制正弦波。我正在使用我在网上找到的这个公式y = Amp * sin(2 * PI * frequency * time + shift)

import pygame
import math
import time

window = pygame.display.set_mode((600, 600))

class Point:
    def __init__(self):
        self.x = 0
        self.y = 0

class Line:
    def __init__(self):
        self.points = []

def generateLine(startX, nPoints, length, y):
    line = Line()
    for i in range(nPoints):
        p = Point()
        p.x = startX + ((i / nPoints) * length)
        p.y = y
        line.points.append(p)
    return line;

nPoints = 100
line = generateLine(10, nPoints, 590, 300)
start = time.time()
accNPoints = 0
frequency = 100
amplitude = 30
overallY = 300

while True:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            pygame.quit()

    window.fill((255, 255, 255))

    keys = pygame.key.get_pressed()
    
    if (keys[pygame.K_a]): frequency -= 0.002
    if (keys[pygame.K_d]): frequency += 0.002

    if (keys[pygame.K_s]): amplitude -= 0.05
    if (keys[pygame.K_w]): amplitude += 0.05

    if (keys[pygame.K_q]): overallY += 0.5
    if (keys[pygame.K_e]): overallY -= 0.5

    if (keys[pygame.K_p]): accNPoints += 0.5
    if (keys[pygame.K_o]): accNPoints -= 0.5

    if accNPoints > 50:
        line = generateLine(10, nPoints, 590, 300)
        accNPoints = 0
        nPoints += 1
    elif accNPoints < -50:
        line = generateLine(10, nPoints, 590, 300)
        accNPoints = 0
        nPoints -= 1

    for i in range(1, len(line.points)):
        #calculate y based on x
        #y = A * sin(2 * PI * f * t + shift)
        #yStart = (amplitude * math.sin(2 * math.pi * frequency * ((time.time() - start) * 0.01) + line.points[i].x))     + overallY
        #yEnd =   (amplitude * math.sin(2 * math.pi * frequency * ((time.time() - start) * 0.01) + line.points[i - 1].x)) + overallY
        yStart = (amplitude * math.sin(2 * math.pi * frequency + line.points[i].x))     + overallY
        yEnd =   (amplitude * math.sin(2 * math.pi * frequency + line.points[i - 1].x)) + overallY

        
        pygame.draw.circle(window, (255, 0, 0), (line.points[i].x, yStart), 1)
        pygame.draw.circle(window, (255, 0, 0), (line.points[i - 1].x, yEnd), 1)
            
        pygame.draw.aaline(
            window,
            (0, 0, 0),
            (line.points[i].x, yStart),
            (line.points[i - 1].x, yEnd)
            )

    
    pygame.display.flip()

似乎有两个问题。改变frequency值似乎并没有真正改变波的频率。频率似乎取决于nPoints变量位于生成行的函数中，即def generateLine(startX, nPoints, length, y):.

公式是错误的。 x 坐标取决于循环的控制变量（i）。 y 坐标需要依赖于 x 坐标：

例如：频率 5（5 波）

frequency = 5
amplitude = 50
overallY = 300

while True:
    # [...]

    no_pts = window.get_width()
    for i in range(no_pts):
        x = i/no_pts * 2 * math.pi
        y = (amplitude * math.cos(x * frequency)) + overallY
        if i > 0:
            pygame.draw.aaline(window, (0, 0, 0),  prev_pt, (i, y))
        prev_pt = (i, y)

    # [...]