如何修复光线投射器中的扭曲透视? [英] How do I fix the warped perspective in my raycaster?
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
好吧，我找到了一个
因此，为了消除视觉失真，从图 17 中的等式获得的所得距离必须乘以 cos(BETA)；其中 BETA 是投射的光线相对于视角的角度.在上图中，视角 (ALPHA) 为 90 度，因为玩家面朝上.因为我们有 60 度的视野，所以最左边的光线的 BETA 是 30 度，最右边的光线是 -30 度.
I am writing a raycaster using SDL's C API. I have spent weeks trying to fix the notorious fisheye effect to no avail. According to this source, I can multiply my calculated distance by the cosine of half of the FOV to fix it. That has not worked for me. I still have the cosine correction in my code nonetheless.
Here are two images demonstrating the distortion:
I think a core problem of my code may be that my angle increment is constant, while the increment should be smaller as I'm closer to the screen borders. Unfortunately, I don't know how to start implementing this.
If possible, could anyone please take a look at my code and give me a tip on how to remove the fisheye? To move in any direction, use the arrow keys. Use the 'a' and 's' keys to turn left and right respectively.
This is how I'm compiling: 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, 1, 1, 1, 1, 1, 1, 1, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1},
{1, 0, 4, 3, 2, 0, 0, 0, 2, 0, 0, 1},
{1, 0, 0, 0, 1, 0, 0, 0, 3, 0, 0, 1},
{1, 0, 0, 0, 4, 3, 2, 1, 4, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1},
{1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 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_x, 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, g, 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, r, g, 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, 0, &window, &renderer);
SDL_SetWindowTitle(window, "Raycaster");
Player player = {5, 5, 0, 0, 0, 60};
SDL_Rect the_ceiling = {0, 0, screen_width, screen_height / 2};
SDL_Rect the_floor = {0, screen_height / 2, screen_width, screen_height};
const Uint8* keys = SDL_GetKeyboardState(NULL);
while (1) {
handle_input(keys, &player);
draw_rectangle(the_ceiling, 96, 96, 96);
draw_rectangle(the_floor, 210, 180, 140);
raycast(player);
SDL_RenderPresent(renderer);
SDL_UpdateWindowSurface(window);
}
}
After help from RandomDavis, the distortion is lessened. Here is the new result. Nonetheless, some warping remains:
NOTE: To anyone who is still struggling with this problem, I solved it here: How do I fix warped walls in my raycaster?
Okay I found a guide which talks about this exact issue.
Before drawing the wall, there is one problem that must be taken care of. This problem is known as the "fishbowl effect." Fishbowl effect happens because ray-casting implementation mixes polar coordinate and Cartesian coordinate together. Therefore, using the above formula on wall slices that are not directly in front of the viewer will gives a longer distance. This is not what we want because it will cause a viewing distortion such as illustrated below.
Thus to remove the viewing distortion, the resulting distance obtained from equations in Figure 17 must be multiplied by cos(BETA); where BETA is the angle of the ray that is being cast relative to the viewing angle. On the figure above, the viewing angle (ALPHA) is 90 degrees because the player is facing straight upward. Because we have 60 degrees field of view, BETA is 30 degrees for the leftmost ray and it is -30 degrees for the rightmost ray.
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