I'm currently struggling to make a 3D Sobel edge detector in C (which I am quite new to). It's not exactly working as expected (highlighting non-edges within a solid 3D object) and I was hoping someone might see where I've gone wrong. (and sorry for the poor spacing in this post)
First of all, im is the input image which has been copied into tm with a 1 pixel border on each side.
I loop through the image:
for (z = im.zlo; z <= im.zhi; z++) {
for (y = im.ylo; y <= im.yhi; y++) {
for (x = im.xlo; x <= im.xhi; x++) {
I make an array which will house the change in the x, y, and z directions, and loop through a 3x3x3 cube:
int dxdydz[3] = {0, 0, 0};
for (a = -1; a < 2; a++) {
for (b = -1; b < 2; b++) {
for (c = -1; c < 2; c++) {
Now here's the meat, where it gets a bit tricky. I'm weighting my Sobel operator such that if you imagine one 2D surface of the kernel, it would be {{1,2,1},{2,4,2},{1,2,1}}. In other words, the weight of a kernel pixel is related to its 4-connected nearness to the center pixel.
To accomplish this, I define e as 3 - (|a| + |b| + |c|), so that it is either 0, 1, or 2. The kernel will be weighted by 3^e at each pixel.
The sign of the kernel pixel will just be determined by the sign of a, b, or c.
int e = 3 - (abs(a) + abs(b) + abs(c));
Now I loop through a, b, and c by packaging them into an array and looping from 0-1-2. When a for example is 0, we don't want to add any values to x, so we exclude that with an if statement (8 levels deep!).
int abc[3] = {a, b, c};
for (i = 0; i < 3; i++) {
if (abc[i] != 0) {
The value to add should just be the image value at that pixel multiplied by the kernel value at that pixel. abc[i] is just -1 or 1, and (int)pow(3, e) is the nearness-to-center weight.
dxdydz[i] += abc[i]*(int)pow(3, e)*tm.u[z+a][y+b][x+c];
}
}
}
}
}
Lastly take the sqrt of the sum of the squared changes in x, y, and z.
int mag2 = 0;
for (i = 0; i < 3; i++) {
mag2 += (int)pow(dxdydz[i], 2);
}
im.u[z][y][x] = (int)sqrt(mag2);
}
}
}
Of course I could just loop through the image and multiply 3x3x3 cubes by the 3D kernels:
int kx[3][3][3] = {{{-1,-2,-1},{0,0,0},{1,2,1}},
{{-2,-4,-2},{0,0,0},{2,4,2}},
{{-1,-2,-1},{0,0,0},{1,2,1}}};
int ky[3][3][3] = {{{-1,-2,-1},{-2,-4,-2},{-1,-2,-1}},
{{0,0,0},{0,0,0},{0,0,0}},
{{1,2,1},{2,4,2},{1,2,1}}};
int kz[3][3][3] = {{{-1,0,1},{-2,0,2},{-1,0,1}},
{{-2,0,2},{-4,0,4},{-2,0,2}},
{{-1,0,1},{-1,0,1},{-1,0,1}}};
But I think the loop approach is a lot sexier.
Related
I'm making a 3D voxel game to learn OpenGL (think Minecraft). I know that rendering each face of each cube is slow, so I'm working on meshing. My meshing algorithm of choice is similar to greedy meshing, although it doesn't merge quads so that they all become one quad. Here's what some of my important code looks like:
void build_mesh(chunk *c) {
if (c->meshes != NULL) {
vector_free(c->meshes); // deleted old mesh list
}
c->meshes = vector_create(); // creates a new mesh list
for (int x = 0; x < CHUNK_SIZE; x++) {
for (int y = 0; y < CHUNK_HEIGHT; y++) {
for (int z = 0; z < CHUNK_SIZE; z++) {
if (c->data[x][y][z] == 1) {
mesh m;
m.pos.x = x;
m.pos.y = y;
m.pos.z = z;
if (x - 1 < 0 || c->data[x - 1][y][z] == 0) {
// if we're in here that means we have to render the quad
m.type = X_MIN;
vector_add(&c->meshes, m);
}
if (x + 1 >= CHUNK_SIZE || c->data[x + 1][y][z] == 0) {
m.type = X_POS;
vector_add(&c->meshes, m);
}
if (y - 1 < 0 || c->data[x][y - 1][z] == 0) {
m.type = Y_MIN;
vector_add(&c->meshes, m);
}
if (y + 1 >= CHUNK_HEIGHT || c->data[x][y + 1][z] == 0) {
m.type = Y_POS;
vector_add(&c->meshes, m);
}
if (z - 1 < 0 || c->data[x][y][z - 1] == 0) {
m.type = Z_MIN;
vector_add(&c->meshes, m);
}
if (z + 1 >= CHUNK_SIZE || c->data[x][y][z + 1] == 0) {
m.type = Z_POS;
vector_add(&c->meshes, m);
}
}
}
}
}
}
void render_chunk(chunk *c, vert *verts, unsigned int program, mat4 model, unsigned int modelLoc, bool greedy) {
// meshing code
if (greedy) {
for (int i = 0; i < vector_size(c->meshes); i++) {
glm_translate_make(model, (vec3){c->meshes[i].pos.x, c->meshes[i].pos.y, c->meshes[i].pos.z});
setMat4(modelLoc, model);
glBindVertexArray(verts[c->meshes[i].type].VAO);
glDrawArrays(GL_TRIANGLES, 0, 6);
}
return;
}
for (int x = 0; x < CHUNK_SIZE; x++) {
for (int y = 0; y < CHUNK_HEIGHT; y++) {
for (int z = 0; z < CHUNK_SIZE; z++) {
for (int i = 0; i < 6; i++) {
if (c->data[x][y][z] == 1) {
glm_translate_make(model, (vec3){x, y, z});
setMat4(modelLoc, model);
glBindVertexArray(verts[i].VAO);
glDrawArrays(GL_TRIANGLES, 0, 6);
}
}
}
}
}
}
build_mesh only gets called when the chunk gets updated and render_chunk gets called every frame. If greedy is true, greedy meshing is implemented. However, the problem is that greedy meshing is significantly slower than just rendering everything, which should not be happening. Does anyone have any ideas what's going on?
Edit: After timing the mesh rendering, it take ~30-40 ms per frame. However, it scales up really well and still take 30-40 ms regardless of how large the chunk is.
18432 calls to glDrawArrays is way too much as the call it self is a performance hit alone due the way how GL works.
You should group your meshes to much less VAO/VBOs ... for example 128 or less ... you can divide your voxel space into slices so if you got 128x32x32 cubes try to put 32x32 cubes into single VAO/VBOs and see if it makes any difference in speed ... also I would get rid of the translation of cubes and store the cube vertexes into VBO already translated.
My answer in the duplicate (sadly deleted) QA:
How to best write a voxel engine in C with performance in mind
did go one step further representing your voxel space in a 3D texture where each texel represents a voxel and ray tracing it in fragment shader using just single glDraw rendering single QUAD covering the screen. Using the same techniques as Wolfenstein like ray cast just ported to 3D.
The ray tracing (vertex shader casts the start rays) stuff was ported from this:
raytrace through 3D mesh
Here preview from the deleted QA:
IIRC it was 128x128x128 or 256x256x256 voxels rendered in 12.4ms (ignore the fps it was measuring something else). there where a lot of room to optimize more in the shaders as I wanted to keep them as simple and understandable as I could (so no more advanced optimizations)...
There are also other options like using point sprites, or geometry shader emitting the cubes etc ...
In case lowering the number of glDraws is not enough speed boost you might want to implement BVH structures to speed up rendering ... however for single 128x32x32 space I see no point in this as that should be handled with ease...
I need to make a spiral pattern made of stars '*' using nested for loops. I managed to make outter lines, now I don't know how to repeat smaller swirls in the same place.
What I should have:
*********
*
******* *
* * *
* *** * *
* * * *
* ***** *
* *
*********
Any help would be greatly appreciated.
After being thoroughly nerd-sniped, I came up with this:
#include <stdio.h>
void print_spiral(int size)
{
for (int y = 0; y < size; ++y)
{
for (int x = 0; x < size; ++x)
{
// reflect (x, y) to the top left quadrant as (a, b)
int a = x;
int b = y;
if (a >= size / 2) a = size - a - 1;
if (b >= size / 2) b = size - b - 1;
// calculate distance from center ring
int u = abs(a - size / 2);
int v = abs(b - size / 2);
int d = u > v ? u : v;
int L = size / 2;
if (size % 4 == 0) L--;
// fix the top-left-to-bottom-right diagonal
if (y == x + 1 && y <= L) d++;
printf((d + size / 2) % 2 == 0 ? "X" : " ");
}
printf("\n");
}
}
As others mentioned, it might be more intuitive to allocate an array representing the grid, and draw the spiral into the array (within which you can move freely), then print the array. But, this solution uses O(1) memory.
It could almost certainly be optimized and simplified a bit, but I'll "leave that as an exercise for the reader" as I've already spent too much time on this ;-)
Update
I'm not going to spend any more time on this, but I had an idea for a second attempt that might result in simpler code. If you check the output at increasingly large sizes, a pattern emerges:
Within each quadrant, the pattern is regular and can be easily coded. I think you would just have to carefully classify the (x, y) coordinates into one of the four quadrants and then apply the appropriate pattern.
The most sensible approach is to create a 2d array, then fill it with the * that you want.
Alternatively, you can try to come up with some "just in time" logic to avoid a buffer. This is more complicated.
I came up with an approach by thinking of the spiral as four different triangles that form a square. Here I have printed "a,b,c,d" for each of the four triangles to show what I mean:
aaaaaaaaaac
c
baaaaaac c
b c c
b baac c c
b b dd c c
b b c c
b dddddd c
b c
dddddddddd
There are two tricky parts to this. One is to align the diagonals correctly. Not so hard with with trial and error. The other tricky party is that not all squares divide into alternating lines the same way. You can see in the example above a square n=11, the left side is shifted by one. Perhaps there is a better solution, but this attempts to create alternating rows and columns.
n = 11;
for (int i = 0; i < n; i++)
{
for (int j = 0; j < n; j++)
{
// top
if (j > i - 2 && j < n - i && i % 2 == (n&1)) printf("a");
// left
else if (j < i - 1 && j < n - i && j % 2 == (n & 1)) printf("b");
// right
else if (j > n - i -1&& j > i && j % 2 == ((n+1) & 1)) printf("c");
// bottom
else if (j < i + 1 && j > n - i - 1 && i % 2 == ((n + 1) & 1)) printf("d");
else printf(" ");
}
printf("\n");
}
I would recommend taking a look at the NCurses library. It contains many methods for moving the cursor in the terminal window, such as mvaddch() and curs_set().
Here is a document that contains everything you'd need to know on how to use NCurses.
However, if you don't want to use external libraries, then you could define a 2D array of ints or bools and then print a * where an index is 1 or true, respectively.
Example of the latter:
#include <stdbool.h> //You need to include this header file if you want to use 'bool's
...
//Using a 10x10 array for this example
bool stars[10][10] = { /* initialize the 2D array here */ };
...
//Get the length of a row
int rowLength = (sizeof stars[0]) / (sizeof stars[0][0]);
//Get the amount of rows
int rowAmount = (sizeof stars) / (sizeof stars[0]));
//Print the spiral using the array "stars"
for(int r = 0; r < rowAmount; r++){
for(int c = 0; c < rowLength; c++){
if(stars[r][c])
printf("*");
else
printf(" ");
}
printf("\n");
}
...
I have a problem in some C code, I assume it belonged here over the Mathematics exchange.
I have an array of changes in x and y position generated by a user dragging a mouse, how could I determine if a straight line was drawn or not.
I am currently using linear regression, is there a better(more efficient) way to do this?
EDIT:
Hough transformation attempt:
#define abSIZE 100
#define ARRAYSIZE 10
int A[abSIZE][abSIZE]; //points in the a-b plane
int dX[10] = {0, 10, 13, 8, 20, 18, 19, 22, 12, 23};
int dY[10] = {0, 2, 3, 1, -1, -2, 0, 0, 3, 1};
int absX[10]; //absolute positions
int absY[10];
int error = 0;
int sumx = 0, sumy = 0, i;
//Convert deltas to absolute positions
for (i = 0; i<10; i++) {
absX[i] = sumx+=dX[i];
absY[i] = sumy+=dY[i];
}
//initialise array to zero
int a, b, x, y;
for(a = -abSIZE/2; a < abSIZE/2; a++) {
for(b = -abSIZE/2; b< abSIZE/2; b++) {
A[a+abSIZE/2][b+abSIZE/2] = 0;
}
}
//Hough transform
int aMax = 0;
int bMax = 0;
int highest = 0;
for(i=0; i<10; i++) {
x = absX[i];
y = absX[i];
for(a = -abSIZE/2; a < abSIZE/2; a++) {
for(b = -abSIZE/2; b< abSIZE/2; b++) {
if (a*x + b == y) {
A[a+abSIZE/2][b+abSIZE/2] += 1;
if (A[a+abSIZE/2][b+abSIZE/2] > highest) {
highest++; //highest = A[a+abSIZE/2][b+abSIZE/2]
aMax = a;
bMax = b;
}
}
}
}
}
printf("Line is Y = %d*X + %d\n",aMax,bMax);
//Calculate MSE
int e;
for (i = 0; i < ARRAYSIZE; i++) {
e = absY[i] - (aMax * absX[i] + bMax);
e = (int) pow((double)e, 2);
error += e;
}
printf("error is: %d\n", error);
Though linear regression sounds like a perfectly reasonable way to solve the task, here's another suggestion: Hough transform, which might be somewhat more robust against outliers. Here is a very rough sketch of how this can be applied:
initialize a large matrix A with zeros
transform your deltas to some absolute coordinates (x, y) in a x-y-plane (e.g. start with (0,0))
for each point
there are non-unique parameters a and b such that a*x + b = y. All such points (a,b) define a straight line in the a-b-plane
draw this "line" in the a-b-plane by adding ones to the corresponding cells in A, which represents the quantized plane
now you can find a maximum in the a-b-plane-matrix A, which will correspond to the parameters (a, b) of the straight line in the x-y-plane that has most support by the original points
finally, calculate MSE to the original points and decide with some threshold if the move was a straight line
More details e.g. here:
http://homepages.inf.ed.ac.uk/rbf/CVonline/LOCAL_COPIES/MARSHALL/node32.html
Edit: here's a quote from Wikipedia that explains why it's better to use a different parametrization to deal with vertical lines (where a would become infinite in ax+b=y):
However, vertical lines pose a problem. They are more naturally described as x = a and would give rise to unbounded values of the slope parameter m. Thus, for computational reasons, Duda and Hart proposed the use of a different pair of parameters, denoted r and theta, for the lines in the Hough transform. These two values, taken in conjunction, define a polar coordinate.
Thanks to Zaw Lin for pointing this out.
So we're reading a matrix and saving it in an array sequentially. We read the matrix from a starting [x,y] point which is provided. Here's an example of some code I wrote to get the values of [x-1,y] [x+1,y] [x,y-1] [x,y+1], which is a cross.
for(i = 0, n = -1, m = 0, array_pos = 0; i < 4; i++, n++, array_pos++) {
if(x+n < filter_matrix.src.columns && x+n >= 0 )
if(y+m < filter_matrix.src.lines && y+m >= 0){
for(k = 0; k < numpixels; k++) {
arrayToProcess[array_pos].rgb[h] = filter_matrix.src.points[x+n][y+m].rgb[h];
}
}
m = n;
m++;
}
(The if's are meant to avoid reading null positions, since it's an image we're reading the origin pixel can be located in a corner. Not relevant to the issue here.)
Now is there a similar generic algorithm which can read ALL the elements around as a square (not just a cross) based on a single parameter, which is the size of the square's side squared?
If it helps, the only values we're dealing with are 9, 25 and 49 (a 3x3 5x5 and 7x7 square).
Here is a generalized code for reading the square centered at (x,y) of size n
int startx = x-n/2;
int starty = y-n/2;
for(int u=0;u<n;u++) {
for(int v=0;v<n;v++) {
int i = startx + u;
int j = starty + v;
if(i>=0 && j>=0 && i<N && j<M) {
printf(Matrix[i][j]);
}
}
}
Explanation: Start from top left value which is (x - n/2, y-n/2) now consider that you are read a normal square matrix from where i and j are indices of Matrix[i][j]. So we just added startx & starty to shift the matrix at (0,0) to (x-n/2,y-n/2).
Given:
static inline int min(int x, int y) { return (x < y) ? x : y; }
static inline int max(int x, int y) { return (x > y) ? x : y; }
or equivalent macros, and given that:
the x-coordinates range from 0 to x_max (inclusive),
the y-coordinates range from 0 to y_max (inclusive),
the centre of the square (x,y) is within the bounds,
the square you are creating has sides of (2 * size + 1) (so size is 1, 2, or 3 for the 3x3, 5x5, and 7x7 cases; or if you prefer to have sq_side = one of 3, 5, 7, then size = sq_side / 2),
the integer types are all signed (so x - size can produce a negative value; if they're unsigned, you will get the wrong result using the expressions shown),
then you can ensure that you are within bounds by setting:
x_lo = max(x - size, 0);
x_hi = min(x + size, x_max);
y_lo = max(y - size, 0);
y_hi = min(y + size, y_max);
for (x_pos = x_lo; x_pos <= x_hi; x_pos++)
{
for (y_pos = y_lo; y_pos <= y_hi; y_pos++)
{
// Process the data at array[x_pos][y_pos]
}
}
Basically, the initial assignments determine the bounds of the the array from [x-size][y-size] to [x+size][y+size], but bounded by 0 on the low side and the maximum sizes on the high end. Then scan over the relevant rectangular (usually square) sub-section of the matrix. Note that this determines the valid ranges once, outside the loops, rather than repeatedly within the loops.
If the integer types are signed, you have ensure you never try to create a negative number during subtraction. The expressions could be rewritten as:
x_lo = x - min(x, size);
x_hi = min(x + size, x_max);
y_lo = y - min(y, size);
y_hi = min(y + size, y_max);
which isn't as symmetric but only uses the min function.
Given the coordinates (x,y), you first need to find the surrounding elements. You can do that with a double for loop, like this:
for (int i = x-1; i <= x+1; i++) {
for (int j = y-1; j <= y+1; j++) {
int elem = square[i][j];
}
}
Now you just need to do a bit of work to make sure that 0 <= i,j < n, where n is the length of a side;
I don't know whether the (X,Y) in your code is the center of the square. I assume it is.
If the side of the square is odd. generate the coordinates of the points on the square. I assume the center is (0,0). Then the points on the squares are
(-side/2, [-side/2,side/2 - 1]); ([-side/2 + 1,side/2], -side/2); (side/2,[side/2 - 1,-side/2]);([side/2 - 1, side/2],-side/2);
side is the length of the square
make use of this:
while(int i<=0 && int j<=0)
for (i = x-1; i <= x+1; i++) {
for (j = y-1; j <= y+1; j++) {
int elem = square[i][j];
}
}
}
Suppose one wanted to search for pairs of integers x and y a that satisfy some equation, such as (off the top of my head) 7 x^2 + x y - 3 y^2 = 5
(I know there are quite efficient methods for finding integer solutions to quadratics like that; but this is irrelevant for the purpose of the present question.)
The obvious approach is to use a simple double loop "for x = -max to max; for y = -max to max { blah}" But to allow the search to be stopped and resumed, a more convenient approach, picturing the possible integers of x and y as a square lattice of points in the plane, is to work round a "square spiral" outward from the origin, starting and stopping at (say) the top right corner.
So basically, I am asking for a simple and sound "pseudo-code" for the loops to start and stop this process at points (m, m) and (n, n) respectively.
For extra kudos, if the reader is inclined, I suggest also providing the loops if one of x can be assumed non-negative, or if both can be assumed non-negative. This is probably somewhat easier, especially the second.
I could whump this up myself without much difficulty, but am interested in seeing neat ideas of others.
This would make quite a good "constructive" interview challenge for those dreaded interviewers who like to torture candidates with white boards ;-)
def enumerateIntegerPairs(fromRadius, toRadius):
for radius in range(fromRadius, toRadius + 1):
if radius == 0: yield (0, 0)
for x in range(-radius, radius): yield (x, radius)
for y in range(-radius, radius): yield (radius, -y)
for x in range(-radius, radius): yield (-x, -radius)
for y in range(-radius, radius): yield (-radius, y)
Here is a straightforward implementation (also on ideone):
void turn(int *dr, int *dc) {
int tmp = *dc;
*dc = -*dr;
*dr = tmp;
}
int main(void) {
int N = 3;
int r = 0, c = 0;
int sz = 0;
int dr = 1, dc = 0, cnt = 0;
while (r != N+1 && c != N+1) {
printf("%d %d\n", r, c);
if (cnt == sz) {
turn(&dr, &dc);
cnt = 0;
if (dr == 0 && dc == -1) {
r++;
c++;
sz += 2;
}
}
cnt++;
r += dr;
c += dc;
}
return 0;
}
The key in the implementation is the turn function, that performs the right turn given a pair of {delta-Row, delta-Col}. The rest is straightforward arithmetic.