如何修复光线投射器中的扭曲透视？

问题描述

我正在使用 SDL 的 C API 编写光线投射器。我花了数周时间试图修复臭名昭著的鱼眼效应，但无济于事。根据 this 来源，我可以将计算出的距离乘以一半 FOV 的余弦值来修复它。这对我不起作用。尽管如此，我的代码中仍然有余弦校正。

这里有两张图片展示了失真：

我认为我的代码的一个核心问题可能是我的角度增量是恒定的，而增量应该更小，因为我更接近屏幕边界。不幸的是，我不知道如何开始实施。

如果可能的话，有人可以看看我的代码并给我一个关于如何去除鱼眼的提示吗？要向任何方向移动，请使用箭头键。使用“a”和“s”键分别向左和向右转。

这就是我的编译方式：clang `pkg-config --cflags --libs sdl2` raycaster.c

#include <SDL2/SDL.h>
#include <math.h>

typedef struct {
    float x,y,prev_x,prev_y,angle,fov;
} Player;

enum {
    map_width = 12,map_height = 15,screen_width = 800,screen_height = 500
};

const float
    move_speed_decr = 0.08,angle_turn = 2.0,ray_theta_step = 0.4,ray_dist_step = 0.8,darkening = 1.8,width_ratio = (float) screen_width / map_width,height_ratio = (float) screen_height / map_height;

const unsigned char map[map_height][map_width] = {
    {1,1,1},{1,4,3,2,1}
};

SDL_Window* window;
SDL_Renderer* renderer;

float to_radians(float degrees) {
    return degrees * M_PI / 180;
}

float distance(float x0,float y0,float x1,float y1) {
    return sqrt(((x1 - x0) * (x1 - x0)) + ((y1 - y0) * (y1 - y0)));
}

void shade(int* color,int darkener) {
    int darkened = *color - darkener;
    *color = darkened < 0 ? 0 : darkened;
}

void draw_rectangle(SDL_Rect rectangle,int r,int g,int b) {
    SDL_SetRenderDrawColor(renderer,r,g,b,SDL_ALPHA_OPAQUE);
    SDL_RenderFillRect(renderer,&rectangle);
    SDL_RenderDrawRect(renderer,&rectangle);
}

void raycast(Player player) {
    float relative_x = player.x * width_ratio;
    float relative_y = player.y * height_ratio;
    float half_fov = player.fov / 2;
    float width_fov_ratio = (screen_width / player.fov) / 2;
    float distort_adjust = cos(to_radians(half_fov));

    // the core of my problem may be in the constant increment of my angle
    for (float theta = player.angle - half_fov,screen_x = 0;
        theta < player.angle + half_fov;
        theta += ray_theta_step,screen_x += width_fov_ratio) {

        float radian_theta = to_radians(theta);
        float cos_theta = cos(radian_theta),sin_theta = sin(radian_theta);

        float d = 0,new_x,new_y;
        while (d += ray_dist_step) {
            new_x = cos_theta * d + relative_x;
            new_y = sin_theta * d + relative_y;

            int map_x = new_x / width_ratio,map_y = new_y / height_ratio;
            int map_point = map[map_y][map_x];

            if (map_point) {
                int dist_wall = distance(relative_x,relative_y,new_y) * distort_adjust;
                int twice_dist_wall = 2 * dist_wall;
                if (twice_dist_wall >= screen_height) break;
                else if (map_point) { // succeeds when a wall is present
                    int r,b;
                    switch (map_point) {
                        case 1: r = 255,g = 255,b = 0; break;
                        case 2: r = 0,g = 128,b = 128; break;
                        case 3: r = 255,g = 165,b = 0; break;
                        case 4: r = 255,g = 0,b = 0; break;
                    }

                    int color_decr = dist_wall / darkening;
                    shade(&r,color_decr);
                    shade(&g,color_decr);
                    shade(&b,color_decr);

                    SDL_Rect vertical_line = {
                        screen_x,dist_wall,width_fov_ratio + 1,screen_height - twice_dist_wall
                    };

                    draw_rectangle(vertical_line,b);
                    break;
                }
            }
        }
    }
}

void handle_input(const Uint8* keys,Player* player) {
    SDL_Event event;

    while (SDL_PollEvent(&event)) {
        if (event.type == SDL_QUIT) {
            SDL_DestroyWindow(window);
            SDL_DestroyRenderer(renderer);
            exit(0);
        }

        else if (event.type == SDL_KEYDOWN) {
            float radian_theta = to_radians(player -> angle);
            float move_x = cos(radian_theta) * move_speed_decr,move_y = sin(radian_theta) * move_speed_decr;

            // handle arrow keys
            if (keys[SDL_SCANCODE_UP]) player -> x += move_x,player -> y += move_y;
            if (keys[SDL_SCANCODE_DOWN]) player -> x -= move_x,player -> y -= move_y;
            if (keys[SDL_SCANCODE_LEFT]) player -> x += move_y,player -> y -= move_x;
            if (keys[SDL_SCANCODE_RIGHT]) player -> x -= move_y,player -> y += move_x;

            // handle 'a' and 's' for angle changes
            if (keys[SDL_SCANCODE_A]) player -> angle -= angle_turn;
            if (keys[SDL_SCANCODE_S]) player -> angle += angle_turn;

            // safeguards for invalid positions and angles
            if (player -> x < 0) player -> x = 0;
            else if (player -> x > screen_width) player -> x = screen_width;

            if (player -> y < 0) player -> y = 0;
            else if (player -> y > screen_height) player -> y = screen_height;

            // move the player to their prevIoUs coordinate if they're in a wall
            if (map[(int) player -> y][(int) player -> x])
                player -> y = player -> prev_y,player -> x = player -> prev_x;

            if (player -> angle > 360) player -> angle = 0;
            else if (player -> angle < 0) player -> angle = 360;

            player -> prev_y = player -> y,player -> prev_x = player -> x;
        }
    }
}

int main() {
    SDL_CreateWindowAndRenderer(screen_width,screen_height,&window,&renderer);
    SDL_SetwindowTitle(window,"Raycaster");    

    Player player = {5,5,60};
    SDL_Rect the_ceiling = {0,screen_width,screen_height / 2};
    SDL_Rect the_floor = {0,screen_height / 2,screen_height};
    const Uint8* keys = SDL_GetKeyboardState(NULL);

    while (1) {
        handle_input(keys,&player);

        draw_rectangle(the_ceiling,96,96);
        draw_rectangle(the_floor,210,180,140);

        raycast(player);

        SDL_RenderPresent(renderer);
        SDL_UpdateWindowSurface(window);
    }
}