Drawing the ceiling happens the same way as drawing the floor, so only the floor is explained here.
The floor casting is done before the walls, so first we draw the entire floor (and ceiling), then overwrite part of
the pixels with the walls, as before, in the next step.
In short, the floor casting works as follows: work scanline by scanline. For the current scanline,
compute the position on the floor matching the left pixel of the scanline, and the position matching the
right pixel. This can be computed as where the ray starting from the camera, going through that pixel of the
camera plane, hits the floor. The formulas and explanation for this are in the floor casting code further below.
We can then linearly interpolate between this leftmost and rightmost point to get the floor coordinates matching the
other pi xels of this scanline. This works because the floor texture is perfectly horizontal. If it were slanted, we
would need to do more expensive perspective correct texture mapping instead.
NOTE: Ádám Tóth contributed the idea and demo code for the horizontal scanline technique in 2019. Before this, this tutorial described a vertical stripe based technique, but the horizontal technique is faster and matches how raycasting games really worked. The vertical technique is moved to a separate chapter at the end.
#define screenWidth 640
#define screenHeight 480
#define texWidth 64
#define texHeight 64
#define mapWidth 24
#define mapHeight 24
int worldMap[mapWidth][mapHeight]=
{
{8,8,8,8,8,8,8,8,8,8,8,4,4,6,4,4,6,4,6,4,4,4,6,4},
{8,0,0,0,0,0,0,0,0,0,8,4,0,0,0,0,0,0,0,0,0,0,0,4},
{8,0,3,3,0,0,0,0,0,8,8,4,0,0,0,0,0,0,0,0,0,0,0,6},
{8,0,0,3,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,6},
{8,0,3,3,0,0,0,0,0,8,8,4,0,0,0,0,0,0,0,0,0,0,0,4},
{8,0,0,0,0,0,0,0,0,0,8,4,0,0,0,0,0,6,6,6,0,6,4,6},
{8,8,8,8,0,8,8,8,8,8,8,4,4,4,4,4,4,6,0,0,0,0,0,6},
{7,7,7,7,0,7,7,7,7,0,8,0,8,0,8,0,8,4,0,4,0,6,0,6},
{7,7,0,0,0,0,0,0,7,8,0,8,0,8,0,8,8,6,0,0,0,0,0,6},
{7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,6,0,0,0,0,0,4},
{7,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,8,6,0,6,0,6,0,6},
{7,7,0,0,0,0,0,0,7,8,0,8,0,8,0,8,8,6,4,6,0,6,6,6},
{7,7,7,7,0,7,7,7,7,8,8,4,0,6,8,4,8,3,3,3,0,3,3,3},
{2,2,2,2,0,2,2,2,2,4,6,4,0,0,6,0,6,3,0,0,0,0,0,3},
{2,2,0,0,0,0,0,2,2,4,0,0,0,0,0,0,4,3,0,0,0,0,0,3},
{2,0,0,0,0,0,0,0,2,4,0,0,0,0,0,0,4,3,0,0,0,0,0,3},
{1,0,0,0,0,0,0,0,1,4,4,4,4,4,6,0,6,3,3,0,0,0,3,3},
{2,0,0,0,0,0,0,0,2,2,2,1,2,2,2,6,6,0,0,5,0,5,0,5},
{2,2,0,0,0,0,0,2,2,2,0,0,0,2,2,0,5,0,5,0,0,0,5,5},
{2,0,0,0,0,0,0,0,2,0,0,0,0,0,2,5,0,5,0,5,0,5,0,5},
{1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,5},
{2,0,0,0,0,0,0,0,2,0,0,0,0,0,2,5,0,5,0,5,0,5,0,5},
{2,2,0,0,0,0,0,2,2,2,0,0,0,2,2,0,5,0,5,0,0,0,5,5},
{2,2,2,2,1,2,2,2,2,2,2,1,2,2,2,5,5,5,5,5,5,5,5,5}
};
Uint32 buffer[screenHeight][screenWidth]; // ycoordinate first because it works per scanline
int main(int /*argc*/, char */*argv*/[])
{
double posX = 22.0, posY = 11.5; //x and y start position
double dirX = 1.0, dirY = 0.0; //initial direction vector
double planeX = 0.0, planeY = 0.66; //the 2d raycaster version of camera plane
double time = 0; //time of current frame
double oldTime = 0; //time of previous frame
std::vector<Uint32> texture[8];
for(int i = 0; i l< 8; i++) texture[i].resize(texWidth * texHeight);
screen(screenWidth,screenHeight, 0, "Raycaster");
//load some textures
unsigned long tw, th, error = 0;
error = loadImage(texture[0], tw, th, "pics/eagle.png");
error = loadImage(texture[1], tw, th, "pics/redbrick.png");
error = loadImage(texture[2], tw, th, "pics/purplestone.png");
error = loadImage(texture[3], tw, th, "pics/greystone.png");
error = loadImage(texture[4], tw, th, "pics/bluestone.png");
error = loadImage(texture[5], tw, th, "pics/mossy.png");
error = loadImage(texture[6], tw, th, "pics/wood.png");
error = loadImage(texture[7], tw, th, "pics/colorstone.png");
if(error) { std::cout << "error loading images" << std::endl; return 1; }
//start the main loop
while(!done())
{

The formula for rowDistance, the horizontal distance from camera to the floor for the current row, which is posZ / p with p the current pixel distance from the screen center, can be explained as follows:
The camera ray goes through the following two points: the camera itself, which is at a certain height (posZ), and a point in front of the camera (through an imagined vertical plane containing the screen pixels) with horizontal distance 1 from the camera, and vertical position p lower than posZ (posZ  p). When going through that point, the line has vertically traveled by p units and horizontally by 1 unit. To hit the floor, it instead needs to travel by posZ units. It will travel the same ratio horizontally. The ratio was 1 / p for going through the camera plane, so to go posZ times farther to reach the floor, we get that the total horizontal distance is posZ / p.
NOTE: The stepping being done here is affine texture mapping, which means we can interpolate linearly between two points rather than have to compute a different division for each pixel. This is not perspective correct in general, but for perfectly horizontal floors/ceilings (and also perfectly vertical walls) it is, so we can use it for raycasting.
//FLOOR CASTING
for(int y = 0; y < h; y++)
{
// rayDir for leftmost ray (x = 0) and rightmost ray (x = w)
float rayDirX0 = dirX  planeX;
float rayDirY0 = dirY  planeY;
float rayDirX1 = dirX + planeX;
float rayDirY1 = dirY + planeY;
// Current y position compared to the center of the screen (the horizon)
int p = y  screenHeight / 2;
// Vertical position of the camera.
float posZ = 0.5 * screenHeight;
// Horizontal distance from the camera to the floor for the current row.
// 0.5 is the z position exactly in the middle between floor and ceiling.
float rowDistance = posZ / p;
// calculate the real world step vector we have to add for each x (parallel to camera plane)
// adding step by step avoids multiplications with a weight in the inner loop
float floorStepX = rowDistance * (rayDirX1  rayDirX0) / screenWidth;
float floorStepY = rowDistance * (rayDirY1  rayDirY0) / screenWidth;
// real world coordinates of the leftmost column. This will be updated as we step to the right.
float floorX = posX + rowDistance * rayDirX0;
float floorY = posY + rowDistance * rayDirY0;
for(int x = 0; x < screenWidth; ++x)
{
// the cell coord is simply got from the integer parts of floorX and floorY
int cellX = (int)(floorX);
int cellY = (int)(floorY);
// get the texture coordinate from the fractional part
int tx = (int)(texWidth * (floorX  cellX)) & (texWidth  1);
int ty = (int)(texHeight * (floorY  cellY)) & (texHeight  1);
floorX += floorStepX;
floorY += floorStepY;
// choose texture and draw the pixel
int floorTexture = 3;
int ceilingTexture = 6;
Uint32 color;
// floor
color = texture[floorTexture][texWidth * ty + tx];
color = (color >> 1) & 8355711; // make a bit darker
buffer[y][x] = color;
//ceiling (symmetrical, at screenHeight  y  1 instead of y)
color = texture[ceilingTexture][texWidth * ty + tx];
color = (color >> 1) & 8355711; // make a bit darker
buffer[screenHeight  y  1][x] = color;
}
}

Next is the wall casting code, this is exactly the same as the previous tutorial, nothing new here, only inserted here to complete the full code. It's done right after the floor casting. This one goes vertical stripe by vertical stripe, not line by line like the floor casting code above.
//WALL CASTING
for(int x = 0; x < w; x++)
{
//calculate ray position and direction
double cameraX = 2 * x / double(w)  1; //xcoordinate in camera space
double rayDirX = dirX + planeX * cameraX;
double rayDirY = dirY + planeY * cameraX;
//which box of the map we're in
int mapX = int(posX);
int mapY = int(posY);
//length of ray from current position to next x or yside
double sideDistX;
double sideDistY;
//length of ray from one x or yside to next x or yside
double deltaDistX = (rayDirX == 0) ? 1e30 : std::abs(1 / rayDirX);
double deltaDistY = (rayDirY == 0) ? 1e30 : std::abs(1 / rayDirY);
double perpWallDist;
//what direction to step in x or ydirection (either +1 or 1)
int stepX;
int stepY;
int hit = 0; //was there a wall hit?
int side; //was a NS or a EW wall hit?
//calculate step and initial sideDist
if (rayDirX < 0)
{
stepX = 1;
sideDistX = (posX  mapX) * deltaDistX;
}
else
{
stepX = 1;
sideDistX = (mapX + 1.0  posX) * deltaDistX;
}
if (rayDirY < 0)
{
stepY = 1;
sideDistY = (posY  mapY) * deltaDistY;
}
else
{
stepY = 1;
sideDistY = (mapY + 1.0  posY) * deltaDistY;
}
//perform DDA
while (hit == 0)
{
//jump to next map square, either in xdirection, or in ydirection
if (sideDistX < sideDistY)
{
sideDistX += deltaDistX;
mapX += stepX;
side = 0;
}
else
{
sideDistY += deltaDistY;
mapY += stepY;
side = 1;
}
//Check if ray has hit a wall
if (worldMap[mapX][mapY] > 0) hit = 1;
}
//Calculate distance of perpendicular ray (Euclidean distance would give fisheye effect!)
if(side == 0) perpWallDist = (sideDistX  deltaDistX);
else perpWallDist = (sideDistY  deltaDistY);
//Calculate height of line to draw on screen
int lineHeight = (int)(h / perpWallDist);
//calculate lowest and highest pixel to fill in current stripe
int drawStart = lineHeight / 2 + h / 2;
if(drawStart < 0) drawStart = 0;
int drawEnd = lineHeight / 2 + h / 2;
if(drawEnd >= h) drawEnd = h  1;
//texturing calculations
int texNum = worldMap[mapX][mapY]  1; //1 subtracted from it so that texture 0 can be used!
//calculate value of wallX
double wallX; //where exactly the wall was hit
if (side == 0) wallX = posY + perpWallDist * rayDirY;
else wallX = posX + perpWallDist * rayDirX;
wallX = floor((wallX));
//x coordinate on the texture
int texX = int(wallX * double(texWidth));
if(side == 0 && rayDirX > 0) texX = texWidth  texX  1;
if(side == 1 && rayDirY < 0) texX = texWidth  texX  1;
// How much to increase the texture coordinate per screen pixel
double step = 1.0 * texHeight / lineHeight;
// Starting texture coordinate
double texPos = (drawStart  h / 2 + lineHeight / 2) * step;
for(int y = drawStart; y<drawEnd; y++)
{
// Cast the texture coordinate to integer, and mask with (texHeight  1) in case of overflow
int texY = (int)texPos & (texHeight  1);
texPos += step;
Uint32 color = texture[texNum][texWidth * texY + texX];
//make color darker for ysides: R, G and B byte each divided through two with a "shift" and an "and"
if(side == 1) color = (color >> 1) & 8355711;
buffer[y][x] = color;
}

drawBuffer(buffer[0]);
for(int y = 0; y < h; y++) for(int x = 0; x < w; x++) buffer[y][x] = 0; //clear the buffer instead of cls()
//timing for input and FPS counter
oldTime = time;
time = getTicks();
double frameTime = (time  oldTime) / 1000.0; //frametime is the time this frame has taken, in seconds
print(1.0 / frameTime); //FPS counter
redraw();
//speed modifiers
double moveSpeed = frameTime * 3.0; //the constant value is in squares/second
double rotSpeed = frameTime * 2.0; //the constant value is in radians/second
readKeys();
//move forward if no wall in front of you
if (keyDown(SDLK_UP))
{
if(worldMap[int(posX + dirX * moveSpeed)][int(posY)] == false) posX += dirX * moveSpeed;
if(worldMap[int(posX)][int(posY + dirY * moveSpeed)] == false) posY += dirY * moveSpeed;
}
//move backwards if no wall behind you
if (keyDown(SDLK_DOWN))
{
if(worldMap[int(posX  dirX * moveSpeed)][int(posY)] == false) posX = dirX * moveSpeed;
if(worldMap[int(posX)][int(posY  dirY * moveSpeed)] == false) posY = dirY * moveSpeed;
}
//rotate to the right
if (keyDown(SDLK_RIGHT))
{
//both camera direction and camera plane must be rotated
double oldDirX = dirX;
dirX = dirX * cos(rotSpeed)  dirY * sin(rotSpeed);
dirY = oldDirX * sin(rotSpeed) + dirY * cos(rotSpeed);
double oldPlaneX = planeX;
planeX = planeX * cos(rotSpeed)  planeY * sin(rotSpeed);
planeY = oldPlaneX * sin(rotSpeed) + planeY * cos(rotSpeed);
}
//rotate to the left
if (keyDown(SDLK_LEFT))
{
//both camera direction and camera plane must be rotated
double oldDirX = dirX;
dirX = dirX * cos(rotSpeed)  dirY * sin(rotSpeed);
dirY = oldDirX * sin(rotSpeed) + dirY * cos(rotSpeed);
double oldPlaneX = planeX;
planeX = planeX * cos(rotSpeed)  planeY * sin(rotSpeed);
planeY = oldPlaneX * sin(rotSpeed) + planeY * cos(rotSpeed);
}
}
}

int floorTexX, floorTexY;
floorTexX = int(currentFloorX * texWidth) % texWidth;
floorTexY = int(currentFloorY * texHeight) % texHeight;

int floorTexX, floorTexY;
floorTexX = int(currentFloorX * texWidth / 4) % texWidth;
floorTexY = int(currentFloorY * texHeight / 4) % texHeight;

//draw the floor from drawEnd to the bottom of the screen
for(int y = drawEnd + 1; y < h; y++)
{
currentDist = h / (2.0 * y  h); //you could make a small lookup table for this instead
double weight = (currentDist  distPlayer) / (distWall  distPlayer);
double currentFloorX = weight * floorXWall + (1.0  weight) * posX;
double currentFloorY = weight * floorYWall + (1.0  weight) * posY;
int floorTexX, floorTexY;
floorTexX = int(currentFloorX * texWidth) % texWidth;
floorTexY = int(currentFloorY * texHeight) % texHeight;
int checkerBoardPattern = (int(currentFloorX) + int(currentFloorY))) % 2;
int floorTexture;
if(checkerBoardPattern == 0) floorTexture = 3;
else floorTexture = 4;
//floor
buffer[y][x] = (texture[floorTexture][texWidth * floorTexY + floorTexX] >> 1) & 8355711;
//ceiling (symmetrical!)
buffer[h  y][x] = texture[6][texWidth * floorTexY + floorTexX];
}
}

The result looks the same (the floors are still horizontal), it's just rendered in a different way.
This technique works as follows: after you've drawn a vertical stripe from the wall,
you do the floor casting for every pixel below the bottom wall pixel until the bottom of the screen.
You need to know the exact coordinates of two points of the floor that are inside the current stripe,
two such points that can easily be found are: the position of the player, and, the point of the floor
right in front of the wall. Then, for every pixel, calculate the distance its projection on the floor
has to the player. With that distance, you can find the exact location of the floor that pixel
represents by using linear interpolation between the two points you found (the one at the wall and the
one at your position).
Once you've done all the floor calculations, out of the exact position you can easily find
the coordinates of the texel from the texture to get the color of the pixel you need to draw.
Because the floor and ceiling are symmetrical, you know the texel coordinates of the ceiling
texture are the same, you just draw it at the corresponding pixel in the upper half of the screen
instead and can use a different texture for the ceiling and the floor.
The distance the projection of the current pixel is to the floor can be calculated as follows:
for(int x = 0; x < w; x++)
{
//WALL CASTING
// [SNIP... the floor casting code goes in the same xforloop as the wall casting, wall casting code not duplicated here]
//FLOOR CASTING (vertical version, directly after drawing the vertical wall stripe for the current x)
double floorXWall, floorYWall; //x, y position of the floor texel at the bottom of the wall
//4 different wall directions possible
if(side == 0 && rayDirX > 0)
{
floorXWall = mapX;
floorYWall = mapY + wallX;
}
else if(side == 0 && rayDirX < 0)
{
floorXWall = mapX + 1.0;
floorYWall = mapY + wallX;
}
else if(side == 1 && rayDirY > 0)
{
floorXWall = mapX + wallX;
floorYWall = mapY;
}
else
{
floorXWall = mapX + wallX;
floorYWall = mapY + 1.0;
}
double distWall, distPlayer, currentDist;
distWall = perpWallDist;
distPlayer = 0.0;
if (drawEnd < 0) drawEnd = h; //becomes < 0 when the integer overflows
//draw the floor from drawEnd to the bottom of the screen
for(int y = drawEnd + 1; y < h; y++)
{
currentDist = h / (2.0 * y  h); //you could make a small lookup table for this instead
double weight = (currentDist  distPlayer) / (distWall  distPlayer);
double currentFloorX = weight * floorXWall + (1.0  weight) * posX;
double currentFloorY = weight * floorYWall + (1.0  weight) * posY;
int floorTexX, floorTexY;
floorTexX = int(currentFloorX * texWidth) % texWidth;
floorTexY = int(currentFloorY * texHeight) % texHeight;
//floor
buffer[y][x] = (texture[3][texWidth * floorTexY + floorTexX] >> 1) & 8355711;
//ceiling (symmetrical!)
buffer[h  y][x] = texture[6][texWidth * floorTexY + floorTexX];
}
}
