尝试对 Recaman 序列进行编码，但我为绘制弧线传递的参数出现问题

Question

这个问题有两个部分：

1. 逻辑 - 构造 Recaman 序列的半圆的酷模式，我的逻辑/代码是否有效？

2. Pygame 特定问题。 运行代码时出现以下错误：

   pg.draw.arc(screen, black, [xi,yi,dx,dy], 180,0,1) ValueError: 宽度大于椭圆半径

我不知道宽度最终是如何 > 椭圆的半径......我已经研究了大约两个小时，我真的需要一些外部帮助。谢谢！

我的代码：

def recaman():

    sequence = [0]
    limit = 10
    def genNums(n):
        index = 0
        for i in range(1,n):
            if index-i>0 and index-i not in sequence:
                index-=i
                sequence.append(index)
            else:
                index+=i
                sequence.append(index)

    screen = pg.display.set_mode((display_width,display_height),pg.FULLSCREEN)
    tick = 0
    genNums(limit)
    while tick < 1000000:

        zx = display_width//limit
        zy = (display_height/2)//limit
        xi = 0
        yi = 0
        xf = 0
        yf = 0
        curX = 0
        curY = 540
        dx = xf - xi
        dy = yf - yi

        for event in pg.event.get():
            if event.type == pg.QUIT:
                tick = 1000
        screen.fill(white)

        direction = 'down'
        for n in range(0,len(sequence)-1):
            yi = 540
            if n % 2 == 0:
                direction = 'down'
            else:
                direction = 'up'

            if sequence[n+1] > sequence[n]:
                curX += n * zx
                xf = curX
                xi = curX - (n * zx)
            else:
                curX -= n * zx
                xf = curX
                xi = curX + (n*zx)

            if direction == 'up':
                yf = curY - (n*zy)

            if direction == 'down':
                yf = curY + (n*zy)

            p1 = (xi,yi)
            p2 = (xf,yf)
            pg.draw.arc(screen, black, [xi,yi,dx,dy], 180,0,1)

        pg.display.update()
        tick += 1

recaman()

Answer 1

pygame.draw.arc() 的角度必须设置为弧度。此外，矩形区域的宽度和高度必须大于 0。

Recaman 序列的部分是半圆。计算一个零件的直径，并计算该零件对应直径的圆周围正方形的左下角原点。绘制上半圆（从0 到math.pi）或下半圆（从math.pi 到2*math.pi）。

import math

line_width = 5
diameter   = abs(dx) + line_width
px         = xi if dx > 0 else xi + dx
py         = display_height/2 - diameter/2.0

if diameter > line_width*2: 
    start_ang = 0 if dy < 0 else math.pi
    end_ang   = start_ang + math.pi + 0.01
    pg.draw.arc(screen, black, [px, py, diameter, diameter], start_ang, end_ang, line_width)

例如曲线与limit = 40:

完整代码：

import pygame as pg
import math

pg.init()

white = (255,255,255)
black = (  0,  0,  0)
display_width, display_height = (800,600)

def recaman():

    sequence = [0]
    limit = 40
    def genNums(n):
        index = 0
        for i in range(1,n):
            if index-i>0 and index-i not in sequence:
                index-=i
                sequence.append(index)
            else:
                index+=i
                sequence.append(index)

    #screen = pg.display.set_mode((display_width,display_height),pg.FULLSCREEN)
    screen = pg.display.set_mode((display_width,display_height))
    tick = 0
    genNums(limit)

    done = False
    while tick < 1000000 and not done:

        for event in pg.event.get():
            if event.type == pg.QUIT:
                done = True

        zx = display_width/limit
        zy = (display_height/2)/limit
        xi = 0
        yi = 0
        xf = 0
        yf = 0
        curX = 0
        curY = 500

        screen.fill(white)

        direction = 'down'
        for n in range(0,len(sequence)-1):
            yi = 500
            if n % 2 == 0:
                direction = 'down'
            else:
                direction = 'up'

            if sequence[n+1] > sequence[n]:
                curX += n * zx
                xf = curX
                xi = curX - (n * zx)
            else:
                curX -= n * zx
                xf = curX
                xi = curX + (n*zx)

            if direction == 'up':
                yf = curY - (n*zy)

            if direction == 'down':
                yf = curY + (n*zy)

            p1 = (xi,yi)
            p2 = (xf,yf)

            dx = xf - xi
            dy = yf - yi

            line_width = 5
            diameter   = abs(dx) + line_width
            px         = xi if dx > 0 else xi + dx
            py         = display_height/2 - diameter/2.0

            if diameter > line_width*2: 
                start_ang = 0 if dy < 0 else math.pi
                end_ang   = start_ang + math.pi + 0.01
                pg.draw.arc(screen, black, [px, py, diameter, diameter], start_ang, end_ang, line_width)

        pg.display.update()
        tick += 1

recaman()