识别光线投射器中的光线沿水平轴与墙壁相交的位置的问题

Answer 1

计算射线向量：

rx = math.cos(player_angle)
ry = math.sin(player_angle)

计算地图中玩家位置的行列：

map_x = player_x // tile_size
map_y = player_y // tile_size

计算相对于瓦片和方向的初始位置：

t_max_x = player_x/tile_size - map_x
if rx > 0:
    t_max_x = 1 - t_max_x
t_max_y = player_y/tile_size - map_y
if ry > 0:
    t_max_y = 1 - t_max_y

向前走，直到您离开地图或在循环中撞到一个块。这是性能关键部分，即实际的光线投射循环：

while True:
    if ry == 0 or t_max_x < t_max_y * abs(rx / ry):
        side = 'x'
        map_x += 1 if rx > 0 else -1
        t_max_x += 1
        if map_x < 0 or map_x >= map_size:
            break
    else:
        side = 'y'
        map_y += 1 if ry > 0 else -1
        t_max_y += 1
        if map_x < 0 or map_y >= map_size:
            break
    if MAP[int(map_x * map_size + map_y)] == "#":
        break

计算命中块边缘的位置：

if side == 'x':
    x = (map_x + (1 if rx < 0 else 0)) * tile_size
    y = player_y + (x - player_x) * ry / rx
else:
    y = (map_y + (1 if ry < 0 else 0)) * tile_size
    x = player_x + (y - player_y) * rx / ry

绘制射线：

pygame.draw.line(win, (0,255, 0), (player_x, player_y), (x, y))

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完整示例：

import pygame
import sys
import math

pygame.init()

screen_height = 480
screen_width = screen_height * 2
map_size = 8
tile_size = screen_height / 8
player_x = screen_width / 4
player_y = screen_width / 4
FOV = math.pi / 3
HALF_FOV = FOV / 2
player_angle = math.pi + math.pi / 2
casted_rays = 120
step_angle = FOV / casted_rays
scale = screen_height / casted_rays

MAP = (
    '########'
    '#   #  #'
    '#   #  #'
    '#  ##  #'
    '#      #'
    '###    #'
    '###    #'
    '########'
    )
def draw_map():
    for row in range(8):
        for col in range(8):
            # square index
            square = row * map_size + col
            pygame.draw.rect(win, (200,200,200) if MAP[square] == '#' else (100,100,100),(row * tile_size, col * tile_size, tile_size - 2, tile_size - 2))
    pygame.draw.circle(win, (255,0,0), (player_x, player_y), 8)
    #pygame.draw.line(win, (0,255,0), (player_x, player_y), (player_x + math.cos(player_angle) * 50,  player_y + math.sin(player_angle) * 50) ,3)
    #pygame.draw.line(win, (0,255,0), (player_x, player_y), (player_x + math.cos(player_angle - HALF_FOV) * 50,  player_y + math.sin(player_angle - HALF_FOV) * 50) ,3)
    #pygame.draw.line(win, (0,255,0), (player_x, player_y), (player_x + math.cos(player_angle + HALF_FOV) * 50,  player_y + math.sin(player_angle + HALF_FOV) * 50) ,3)

def cast_rays():
    rx = math.cos(player_angle)
    ry = math.sin(player_angle)
    map_x = player_x // tile_size
    map_y = player_y // tile_size

    t_max_x = player_x/tile_size - map_x
    if rx > 0:
        t_max_x = 1 - t_max_x
    t_max_y = player_y/tile_size - map_y
    if ry > 0:
        t_max_y = 1 - t_max_y

    while True:
        if ry == 0 or t_max_x < t_max_y * abs(rx / ry):
            side = 'x'
            map_x += 1 if rx > 0 else -1
            t_max_x += 1
            if map_x < 0 or map_x >= map_size:
                break
        else:
            side = 'y'
            map_y += 1 if ry > 0 else -1
            t_max_y += 1
            if map_x < 0 or map_y >= map_size:
                break
        if MAP[int(map_x * map_size + map_y)] == "#":
            break

    if side == 'x':
        x = (map_x + (1 if rx < 0 else 0)) * tile_size
        y = player_y + (x - player_x) * ry / rx
    else:
        y = (map_y + (1 if ry < 0 else 0)) * tile_size
        x = player_x + (y - player_y) * rx / ry

    pygame.draw.line(win, (0,255, 0), (player_x, player_y), (x, y))
        

win = pygame.display.set_mode((screen_width, screen_height))

clock = pygame.time.Clock()

while True:
    for event in pygame.event.get():
        if event.type == pygame.QUIT:
            pygame.quit()
            sys.exit()
    pygame.draw.rect(win, (0,0,0), (0, 0, screen_width, screen_height))
    draw_map()
    cast_rays()
    keys = pygame.key.get_pressed()
    if keys[pygame.K_LEFT]:
        player_angle -= 0.1
    if keys[pygame.K_RIGHT]:
        player_angle += 0.1
    if keys[pygame.K_UP]:
        player_x, player_y = player_x + math.cos(player_angle) * 3, player_y + math.sin(player_angle) * 3
    if keys[pygame.K_DOWN]:
        player_x, player_y = player_x - math.cos(player_angle) * 3, player_y - math.sin(player_angle) * 3
    pygame.display.flip()
    clock.tick(30)

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我实际上在一个简单的体素光线追踪器中使用了相同的算法（只是 3D 版本）：
Voxel Ray Tracing