I am trying my attempt at Perlin Noise (3-dimensional) as outlined in this document: http://lodev.org/cgtutor/randomnoise.html
However, this is what I'm getting.
It looks like the smoothing isn't working. You can see blocks the size of the 'size' parameter. Can someone point out what I'm doing wrong?
Here's my code:
%ffp
ctl(1):standard,"Size",range=(1,256), pos=(300,20), size=(120,*),val=64,track, action=preview
onFilterStart:
{
allocArray(9,64,64,64,4); // Array for noise depth
for(int z = 0; z < 64; z++)
for(int y = 0; y < 64; y++)
for(int x = 0; x < 64; x++) {
fputArray(9,x,y,z,(float)(rand() % 32768) / 32768.0);
}
return false;
}
forEveryTile:
{
double fractX,fractY,fractZ,xx,yy,zz;
int x1,y1,z1,x2,y2,z2,col;
double value = 0.0, value2 = 0.0, size, isize=(float)ctl(1);
// int X=screen Width, int Y=screen Height
for(int y = 0; y < Y; y++) {
for(int x = 0; x < X; x++) {
//for(int z = 0; z < 64; z++) {
value2 = 0.0;
size = isize;
while (size >=1.0) {
xx=(float)x/size;
yy=(float)y/size;
zz=(float)clock()/size;
fractX = xx - (int)(xx);
fractY = yy - (int)(yy);
fractZ = zz - (int)(zz);
x1 = ((int)(xx) + 64) % 64;
y1 = ((int)(yy) + 64) % 64;
z1 = ((int)(zz) + 64) % 64;
x2 = (x1 + 64- 1) % 64;
y2 = (y1 + 64- 1) % 64;
z2 = (z1 + 64- 1) % 64;
value=0.0;
value += fractX * fractY * fractZ * fgetArray(9,z1,y1,x1);
value += fractX * (1 - fractY) * fractZ * fgetArray(9,z1,y2,x1);
value += (1 - fractX) * fractY * fractZ * fgetArray(9,z1,y1,x2);
value += (1 - fractX) * (1 - fractY) * fractZ * fgetArray(9,z1,y2,x2);
value += fractX * fractY * (1 - fractZ) * fgetArray(9,z2,y1,x1);
value += fractX * (1 - fractY) * (1 - fractZ) * fgetArray(9,z2,y2,x1);
value += (1 - fractX) * fractY * (1 - fractZ) * fgetArray(9,z2,y1,x2);
value += (1 - fractX) * (1 - fractY) * (1 - fractZ) * fgetArray(9,z2,y2,x2);
value2 += value*size;
size /= 2.0;
}
col=(int)((float)(128.0 * value2 / isize));
col=max(min(col,255),0);
psetp(x,y,RGB(col,col,col));
//} //z
} //x
} //y
return true;
}
Your code is kind of hard to read as written.
For Perlin noise start out with a integer noise function, that behaves like a hash.
float noise(int x, int y, int z) { return hash(x+y*5+z*7); }
or
float noise(int x, int y, int z) { return array[x%w+y%h*w+z%d*w*h]; }
Those are just examples. The important part is that noise(x,y,z) = noise(x,y,z). The noise function has to return the same value for the same parameters every time.
There is a problem though: The noise function only takes integer parameters! But we would like to sample it at float values.
float noisesample (float x, float y, float z) { ... }
The easiest way to to that is using linear filtering. Any positive float value is between (int)pos and ((int)pos)+1. At sub-position pos-(int)pos. This gets us:
float Lerp(float a, float b, float f) { return a+(b-a)*f; }
Where f is the sub-position in the [0..1] range and a,b are the values to the left and right. If f is 0, Lerp returns a, if it is 1, it returns b. In between it does linear interpolation.
So use this for a simple 1D noisesample function:
float noisesample(float x) { return Lerp(noise((int)x), noise((int)x+1), fract(x) }
with
float fract(float x) { return x-(int)x; }
I am using (int)x liberally here, it is the same as floor(x) if x is positive.
To go from a single parameter noisesample to x,y is easy: Do the Lerp twice for x at y and y+1, and Lerp between those:
float noisesample(float x, float y) {
float y0 = Lerp(noise((int)x,(int)y), noise((int)x+1,(int)y), fract(x) }
float y1 = Lerp(noise((int)x,(int)y+1), noise((int)x+1,(int)y+1), fract(x) }
return Lerp ( y0, y1, fract(y) );
}
First interpolate x, twice, then interpolate between the results in y. In total we sample noise() 4 times. I leave it as an exercise how to write noisesample ( float x, float y, float z). It will sample noise() eight times and call Lerp 7 times.
All that got us is that we can sample noise (somewhat smooth - there are smoother ways!) at float coordinates. And that is what we need to make perlin noise!
float perlin(float x, float y, float z, int oc=4) {
// maybe: x = x*2^oc, y, z...
float r = 0;
float s = 1;
for ( int i=0; i<oc; i++ ) {
r += noisesample(x,y,z) * s;
s/=2.0f; // to taste
x/=2.0f;
y/=2.0f;
z/=2.0f;
}
return r;
}
The key idea is to understand sampling. It's just a combination of sampling a simple integer noise function.
For a project I have been working on, the ability to draw lines with a gradient (I.E. they change color over the interval they are drawn) would be very useful. I have an algorithm for this, as I will paste below, but it turns out to be DREADFULLY slow. I'm using the Bresenham algorithm to find each point, but I fear that I have reached the limits of software rendering. I've been using SDL2 thus far, and my line drawing algorithm appears 200x slower than SDL_RenderDrawLine. This is an estimate, and gathered from comparing the two functions' times to draw 10,000 lines. My function would take near 500ms, and SDL_RenderDrawLine did it in 2-3ms on my machine. I even tested the functions with horizontal lines to ensure it wasn't just a botched Bresenham algorithm, and similar slowness hatched. Unfortunately, SDL doesn't have an API for drawing lines with a gradient (or if it does, I'm blind). I knew that any software rendering would be significantly slower than hardware, but the shear magnitude of slowness caught me by surprise. Is there a method that can be used to speed this up? Have I just botched the drawing system beyond reason? I've considered saving an array of the pixels I wish to draw and then shoving them to the screen all at once, but I don't know how to do this with SDL2 and I can't seem to find the API in the wiki or documentation that allows for this. Would that even be faster?
Thanks for the consideration!
void DRW_LineGradient(SDL_Renderer* rend, SDL_Color c1, int x1, int y1, SDL_Color c2, int x2, int y2){
Uint8 tmpr, tmpg, tmpb, tmpa;
SDL_GetRenderDrawColor(rend, &tmpr, &tmpg, &tmpb, &tmpa);
int dy = y2 - y1;
int dx = x2 - x1;
/* Use doubles for a simple gradient */
double d = (abs(x1 - x2) > abs(y1 - y2) ? abs(x1 - x2) : abs(y1 - y2));
double dr = (c2.r - c1.r) / d;
double dg = (c2.g - c1.g) / d;
double db = (c2.b - c1.b) / d;
double da = (c2.a - c1.a) / d;
double r = c1.r, g = c1.g, b = c1.b, a = c1.a;
/* The line is vertical */
if (dx == 0) {
int y;
if (y2 >= y1) {
for (y = y1; y <= y2; y++) {
SDL_SetRenderDrawColor(rend, r, g, b, a);
SDL_RenderDrawPoint(rend, x1, y);
r += dr;
g += dg;
b += db;
a += da;
}
return;
}
else{
for (y = y1; y >= y2; y--) {
SDL_SetRenderDrawColor(rend, r, g, b, a);
SDL_RenderDrawPoint(rend, x1, y);
r += dr;
g += dg;
b += db;
a += da;
}
return;
}
}
/* The line is horizontal */
if (dy == 0) {
int x;
if (x2 >= x1) {
for (x = x1; x <= x2; x++) {
SDL_SetRenderDrawColor(rend, r, g, b, a);
SDL_RenderDrawPoint(rend, x, y1);
r += dr;
g += dg;
b += db;
a += da;
}
return;
}
else{
for (x = x1; x >= x2; x--) {
SDL_SetRenderDrawColor(rend, r, g, b, a);
SDL_RenderDrawPoint(rend, x, y1);
r += dr;
g += dg;
b += db;
a += da;
}
return;
}
}
/* The line has a slope of 1 or -1 */
if (abs(dy) == abs(dx)) {
int xmult = 1, ymult = 1;
if (dx < 0) {
xmult = -1;
}
if (dy < 0) {
ymult = -1;
}
int x = x1, y = y1;
do {
SDL_SetRenderDrawColor(rend, r, g, b, a);
SDL_RenderDrawPoint(rend, x, y);
x += xmult;
y += ymult;
r += dr;
g += dg;
b += db;
a += da;
} while (x != x2);
return;
}
/* Use bresenham's algorithm to render the line */
int checky = dx >> 1;
int octant = findOctant((Line){x1, y1, x2, y2, dx, dy});
dy = abs(dy);
dx = abs(dx);
x2 = abs(x2 - x1) + x1;
y2 = abs(y2 - y1) + y1;
if (octant == 1 || octant == 2 || octant == 5 || octant == 6) {
int tmp = dy;
dy = dx;
dx = tmp;
}
int x, y = 0;
for (x = 0; x <= dx; x++) {
SDL_SetRenderDrawColor(rend, r, g, b, a);
switch (octant) {
case 0:
SDL_RenderDrawPoint(rend, x + x1, y + y1);
break;
case 1:
SDL_RenderDrawPoint(rend, y + x1, x + y1);
break;
case 2:
SDL_RenderDrawPoint(rend, -y + x1, x + y1);
break;
case 3:
SDL_RenderDrawPoint(rend, -x + x1, y + y1);
break;
case 4:
SDL_RenderDrawPoint(rend, -x + x1, -y + y1);
break;
case 5:
SDL_RenderDrawPoint(rend, -y + x1, -x + y1);
break;
case 6:
SDL_RenderDrawPoint(rend, y + x1, -x + y1);
break;
case 7:
SDL_RenderDrawPoint(rend, x + x1, -y + y1);
break;
default:
break;
}
checky += dy;
if (checky >= dx) {
checky -= dx;
y++;
}
r += dr;
g += dg;
b += db;
a += da;
}
SDL_SetRenderDrawColor(rend, tmpr, tmpg, tmpb, tmpa);
}
SIDE NOTE:
I am reluctant to just move on to using OpenGL 3.0+ (Which I hear SDL2 has support for) because I don't know how to use it. Most tutorials I have found have explained the process of setting up the contexts with SDL and then coloring the screen one solid color, but then stop before explaining how to draw shapes and such. If someone could offer a good place to start learning about this, that would also be extremely helpful.
A lot of the overhead of your function is in repeated calls to SDL_RenderDrawPoint. This is (most likely) a generic function which needs to do the following operations:
check if x and y are in range for your current surface;
calculate the position inside the surface by multiplying y with surface->pitch and x with surface->format->BytesPerPixel;
check the current color model of the surface using SDL_PixelFormat;
convert the provided color to the correct format for this color model.
All of the above must be done for each single pixel. In addition, calling a function in itself is overhead -- small as it may be, it still needs to be done for each separate pixel, even if it is not visible.
You can:
omit x and y range checking if you are sure the line start and end points are always visible;
omit the convert-to-address step by calculating it once for the start of the line, then updating it by adding BytesPerPixel and pitch for a horizontal or vertical movement;
omit the convert-to-color model step by calculating the correct RGB values once (well, for a single color line, at least -- it's a bit harder for a gradient);
omit the function call by inlining the code to set a single pixel inside the line routine.
Another -- smaller -- issue: you call your own routine "Bresenham's ... but it isn't. Bresenham's optimization is actually that it avoids double calculations entirely (and its strongest point is that it still gives the mathematically correct output; something I would not count on when using double variables...).
The following routine does not check for range, color model, color values, or (indeed) if the surface should be locked. All of these operations should be ideally done outside the tight drawing loop. As it is, it assumes a 24-bit RGB color screen, with the Red byte first. [*]
I wrote this code for my current SDL environs, which is still SDL-1.0, but it should work for newer versions as well.
It is possible to use Bresenham's calculations for the delta-Red, delta-Green, and delta-Blue values as well, but I deliberately omitted them here :) They would add a lot of extra variables -- at a guess, three per color channel --, extra checks, and, not least of all, not really a visibly better quality. The difference between two successive values for Red, say 127 and 128, are usually too small to notice in a single pixel wide line. Besides, this small step would only occur if your line is at least 256 pixels long and you cover the entire range of Red from 0 to 255 in the gradient.
[*] If you are 100% sure you are targeting a specific screen model with your own program, you can use this (adjusted for that particular screen model, of course). It's feasible to target a couple of different screen models as well; write a customized routine for each, and use a function pointer to call the correct one.
Most likely this is how SDL_RenderDrawLine is able to squeeze out every millisecond of performance. Well worth writing all that code for a library (which will be used on a wide variety of screen set-ups), but most likely not for a single program such as yours. Notice I commented out a single range check, which falls back to a plain line routine if necessary. You could do the same for unusual or unexpected screen set-ups, and in that case simply call your own, slower, drawing routine. (Your routine is more robust as it uses SDL's native routines.)
The original line routine below was copied from The Internet more than a single decade ago, as I have been using it for ages. I'd gladly attribute it to someone; if anybody recognizes the comments (they are mostly as appeared in the original code), do post a comment.
void gradient_line (int x1,int y1,int x2,int y2,
int r1,int g1, int b1,
int r2,int g2, int b2)
{
int d; /* Decision variable */
int dx,dy; /* Dx and Dy values for the line */
int Eincr,NEincr; /* Decision variable increments */
int t; /* Counters etc. */
unsigned char *ScrPos;
int LineIncr;
int rd,gd,bd;
if (x1 < 0 || y1 < 0 || x2 < 0 || y2 < 0 ||
x1 >= SCREEN_WIDE || x2 >= SCREEN_WIDE ||
y1 >= SCREEN_HIGH || y2 >= SCREEN_HIGH)
{
line (x1,y1, x2,y2, (r1<<16)+(g1<<8)+b1);
return;
}
rd = (r2-r1)<<8;
gd = (g2-g1)<<8;
bd = (b2-b1)<<8;
dx = x2 - x1;
if (dx < 0)
dx = -dx;
dy = y2 - y1;
if (dy < 0)
dy = -dy;
if (dy <= dx)
{
/* We have a line with a slope between -1 and 1
*
* Ensure that we are always scan converting the line from left to
* right to ensure that we produce the same line from P1 to P0 as the
* line from P0 to P1.
*/
if (x2 < x1)
{
t = x2; x2 = x1; x1 = t; /* Swap X coordinates */
t = y2; y2 = y1; y1 = t; /* Swap Y coordinates */
/* Swap colors */
r1 = r2;
g1 = g2;
b1 = b2;
rd = -rd;
gd = -gd;
bd = -bd;
}
r1 <<= 8;
g1 <<= 8;
b1 <<= 8;
if (y2 > y1)
{
LineIncr = screen->pitch;
} else
{
LineIncr = -screen->pitch;
}
d = 2*dy - dx; /* Initial decision variable value */
Eincr = 2*dy; /* Increment to move to E pixel */
NEincr = 2*(dy - dx); /* Increment to move to NE pixel */
ScrPos = (unsigned char *)(screen->pixels+screen->pitch*y1+x1*screen->format->BytesPerPixel);
rd /= dx;
gd /= dx;
bd /= dx;
/* Draw the first point at (x1,y1) */
ScrPos[0] = r1 >> 8;
ScrPos[1] = g1 >> 8;
ScrPos[2] = b1 >> 8;
r1 += rd;
g1 += gd;
b1 += bd;
/* Incrementally determine the positions of the remaining pixels */
for (x1++; x1 <= x2; x1++)
{
if (d < 0)
{
d += Eincr; /* Choose the Eastern Pixel */
} else
{
d += NEincr; /* Choose the North Eastern Pixel */
ScrPos += LineIncr;
}
ScrPos[0] = r1>>8;
ScrPos[1] = g1>>8;
ScrPos[2] = b1>>8;
ScrPos += screen->format->BytesPerPixel;
r1 += rd;
g1 += gd;
b1 += bd;
}
} else
{
/* We have a line with a slope between -1 and 1 (ie: includes
* vertical lines). We must swap our x and y coordinates for this.
*
* Ensure that we are always scan converting the line from left to
* right to ensure that we produce the same line from P1 to P0 as the
* line from P0 to P1.
*/
if (y2 < y1)
{
t = x2; x2 = x1; x1 = t; /* Swap X coordinates */
t = y2; y2 = y1; y1 = t; /* Swap Y coordinates */
/* Swap colors */
r1 = r2;
g1 = g2;
b1 = b2;
rd = -rd;
gd = -gd;
bd = -bd;
}
r1 <<= 8;
g1 <<= 8;
b1 <<= 8;
if (x2 > x1)
{
LineIncr = screen->format->BytesPerPixel;
} else
{
LineIncr = -screen->format->BytesPerPixel;
}
d = 2*dx - dy; /* Initial decision variable value */
Eincr = 2*dx; /* Increment to move to E pixel */
NEincr = 2*(dx - dy); /* Increment to move to NE pixel */
rd /= dy;
gd /= dy;
bd /= dy;
/* Draw the first point at (x1,y1) */
ScrPos = (unsigned char *)(screen->pixels+screen->pitch*y1+x1*screen->format->BytesPerPixel);
ScrPos[0] = r1 >> 8;
ScrPos[1] = g1 >> 8;
ScrPos[2] = b1 >> 8;
r1 += rd;
g1 += gd;
b1 += bd;
/* Incrementally determine the positions of the remaining pixels
*/
for (y1++; y1 <= y2; y1++)
{
ScrPos += screen->pitch;
if (d < 0)
{
d += Eincr; /* Choose the Eastern Pixel */
} else
{
d += NEincr; /* Choose the North Eastern Pixel */
ScrPos += LineIncr; /* (or SE pixel for dx/dy < 0!) */
}
ScrPos[0] = r1 >> 8;
ScrPos[1] = g1 >> 8;
ScrPos[2] = b1 >> 8;
r1 += rd;
g1 += gd;
b1 += bd;
}
}
}
.. and this is a section of a screenful of random lines with random colors, with on the right a close-up:
I did not time the difference between "native" SDL line drawing, your naive method, a pure solid color Bresenham's implementation and this one; then again, this ought not be very much slower than an SDL native line.
I am using Bresenham's circle algorithm for fast circle drawing. However, I also want to (at the request of the user) draw a filled circle.
Is there a fast and efficient way of doing this? Something along the same lines of Bresenham?
The language I am using is C.
Having read the Wikipedia page on Bresenham's (also 'Midpoint') circle algorithm, it would appear that the easiest thing to do would be to modify its actions, such that instead of
setPixel(x0 + x, y0 + y);
setPixel(x0 - x, y0 + y);
and similar, each time you instead do
lineFrom(x0 - x, y0 + y, x0 + x, y0 + y);
That is, for each pair of points (with the same y) that Bresenham would you have you plot, you instead connect with a line.
Just use brute force. This method iterates over a few too many pixels, but it only uses integer multiplications and additions. You completely avoid the complexity of Bresenham and the possible bottleneck of sqrt.
for(int y=-radius; y<=radius; y++)
for(int x=-radius; x<=radius; x++)
if(x*x+y*y <= radius*radius)
setpixel(origin.x+x, origin.y+y);
Here's a C# rough guide (shouldn't be that hard to get the right idea for C) - this is the "raw" form without using Bresenham to eliminate repeated square-roots.
Bitmap bmp = new Bitmap(200, 200);
int r = 50; // radius
int ox = 100, oy = 100; // origin
for (int x = -r; x < r ; x++)
{
int height = (int)Math.Sqrt(r * r - x * x);
for (int y = -height; y < height; y++)
bmp.SetPixel(x + ox, y + oy, Color.Red);
}
bmp.Save(#"c:\users\dearwicker\Desktop\circle.bmp");
You can use this:
void DrawFilledCircle(int x0, int y0, int radius)
{
int x = radius;
int y = 0;
int xChange = 1 - (radius << 1);
int yChange = 0;
int radiusError = 0;
while (x >= y)
{
for (int i = x0 - x; i <= x0 + x; i++)
{
SetPixel(i, y0 + y);
SetPixel(i, y0 - y);
}
for (int i = x0 - y; i <= x0 + y; i++)
{
SetPixel(i, y0 + x);
SetPixel(i, y0 - x);
}
y++;
radiusError += yChange;
yChange += 2;
if (((radiusError << 1) + xChange) > 0)
{
x--;
radiusError += xChange;
xChange += 2;
}
}
}
Great ideas here!
Since I'm at a project that requires many thousands of circles to be drawn, I have evaluated all suggestions here (and improved a few by precomputing the square of the radius):
http://quick-bench.com/mwTOodNOI81k1ddaTCGH_Cmn_Ag
The Rev variants just have x and y swapped because consecutive access along the y axis are faster with the way my grid/canvas structure works.
The clear winner is Daniel Earwicker's method ( DrawCircleBruteforcePrecalc ) that precomputes the Y value to avoid unnecessary radius checks. Somewhat surprisingly that negates the additional computation caused by the sqrt call.
Some comments suggest that kmillen's variant (DrawCircleSingleLoop) that works with a single loop should be very fast, but it's the slowest here. I assume that is because of all the divisions. But perhaps I have adapted it wrong to the global variables in that code. Would be great if someone takes a look.
EDIT: After looking for the first time since college years at some assembler code, I managed find that the final additions of the circle's origin are a culprit.
Precomputing those, I improved the fastest method by a factor of another 3.7-3.9 according to the bench!
http://quick-bench.com/7ZYitwJIUgF_OkDUgnyMJY4lGlA
Amazing.
This being my code:
for (int x = -radius; x < radius ; x++)
{
int hh = (int)std::sqrt(radius_sqr - x * x);
int rx = center_x + x;
int ph = center_y + hh;
for (int y = center_y-hh; y < ph; y++)
canvas[rx][y] = 1;
}
I like palm3D's answer. For being brute force, this is an amazingly fast solution. There are no square root or trigonometric functions to slow it down. Its one weakness is the nested loop.
Converting this to a single loop makes this function almost twice as fast.
int r2 = r * r;
int area = r2 << 2;
int rr = r << 1;
for (int i = 0; i < area; i++)
{
int tx = (i % rr) - r;
int ty = (i / rr) - r;
if (tx * tx + ty * ty <= r2)
SetPixel(x + tx, y + ty, c);
}
This single loop solution rivals the efficiency of a line drawing solution.
int r2 = r * r;
for (int cy = -r; cy <= r; cy++)
{
int cx = (int)(Math.Sqrt(r2 - cy * cy) + 0.5);
int cyy = cy + y;
lineDDA(x - cx, cyy, x + cx, cyy, c);
}
palm3D's brute-force algorithm I found to be a good starting point. This method uses the same premise, however it includes a couple of ways to skip checking most of the pixels.
First, here's the code:
int largestX = circle.radius;
for (int y = 0; y <= radius; ++y) {
for (int x = largestX; x >= 0; --x) {
if ((x * x) + (y * y) <= (circle.radius * circle.radius)) {
drawLine(circle.center.x - x, circle.center.x + x, circle.center.y + y);
drawLine(circle.center.x - x, circle.center.x + x, circle.center.y - y);
largestX = x;
break; // go to next y coordinate
}
}
}
Next, the explanation.
The first thing to note is that if you find the minimum x coordinate that is within the circle for a given horizontal line, you immediately know the maximum x coordinate.
This is due to the symmetry of the circle. If the minimum x coordinate is 10 pixels ahead of the left of the bounding box of the circle, then the maximum x is 10 pixels behind the right of the bounding box of the circle.
The reason to iterate from high x values to low x values, is that the minimum x value will be found with less iterations. This is because the minimum x value is closer to the left of the bounding box than the centre x coordinate of the circle for most lines, due to the circle being curved outwards, as seen on this image
The next thing to note is that since the circle is also symmetric vertically, each line you find gives you a free second line to draw, each time you find a line in the top half of the circle, you get one on the bottom half at the radius-y y coordinate. Therefore, when any line is found, two can be drawn and only the top half of the y values needs to be iterated over.
The last thing to note is that is that if you start from a y value that is at the centre of the circle and then move towards the top for y, then the minimum x value for each next line must be closer to the centre x coordinate of the circle than the last line. This is also due to the circle curving closer towards the centre x value as you go up the circle. Here is a visual on how that is the case.
In summary:
If you find the minimum x coordinate of a line, you get the maximum x coordinate for free.
Every line you find to draw on the top half of the circle gives you a line on the bottom half of the circle for free.
Every minimum x coordinate has to be closer to the centre of the circle than the previous x coordinate for each line when iterating from the centre y coordinate to the top.
You can also store the value of (radius * radius), and also (y * y) instead of calculating them
multiple times.
Here's how I'm doing it:
I'm using fixed point values with two bits precision (we have to manage half points and square values of half points)
As mentionned in a previous answer, I'm also using square values instead of square roots.
First, I'm detecting border limit of my circle in a 1/8th portion of the circle. I'm using symetric of these points to draw the 4 "borders" of the circle. Then I'm drawing the square inside the circle.
Unlike the midpoint circle algorith, this one will work with even diameters (and with real numbers diameters too, with some little changes).
Please forgive me if my explanations were not clear, I'm french ;)
void DrawFilledCircle(int circleDiameter, int circlePosX, int circlePosY)
{
const int FULL = (1 << 2);
const int HALF = (FULL >> 1);
int size = (circleDiameter << 2);// fixed point value for size
int ray = (size >> 1);
int dY2;
int ray2 = ray * ray;
int posmin,posmax;
int Y,X;
int x = ((circleDiameter&1)==1) ? ray : ray - HALF;
int y = HALF;
circlePosX -= (circleDiameter>>1);
circlePosY -= (circleDiameter>>1);
for (;; y+=FULL)
{
dY2 = (ray - y) * (ray - y);
for (;; x-=FULL)
{
if (dY2 + (ray - x) * (ray - x) <= ray2) continue;
if (x < y)
{
Y = (y >> 2);
posmin = Y;
posmax = circleDiameter - Y;
// Draw inside square and leave
while (Y < posmax)
{
for (X = posmin; X < posmax; X++)
setPixel(circlePosX+X, circlePosY+Y);
Y++;
}
// Just for a better understanding, the while loop does the same thing as:
// DrawSquare(circlePosX+Y, circlePosY+Y, circleDiameter - 2*Y);
return;
}
// Draw the 4 borders
X = (x >> 2) + 1;
Y = y >> 2;
posmax = circleDiameter - X;
int mirrorY = circleDiameter - Y - 1;
while (X < posmax)
{
setPixel(circlePosX+X, circlePosY+Y);
setPixel(circlePosX+X, circlePosY+mirrorY);
setPixel(circlePosX+Y, circlePosY+X);
setPixel(circlePosX+mirrorY, circlePosY+X);
X++;
}
// Just for a better understanding, the while loop does the same thing as:
// int lineSize = circleDiameter - X*2;
// Upper border:
// DrawHorizontalLine(circlePosX+X, circlePosY+Y, lineSize);
// Lower border:
// DrawHorizontalLine(circlePosX+X, circlePosY+mirrorY, lineSize);
// Left border:
// DrawVerticalLine(circlePosX+Y, circlePosY+X, lineSize);
// Right border:
// DrawVerticalLine(circlePosX+mirrorY, circlePosY+X, lineSize);
break;
}
}
}
void DrawSquare(int x, int y, int size)
{
for( int i=0 ; i<size ; i++ )
DrawHorizontalLine(x, y+i, size);
}
void DrawHorizontalLine(int x, int y, int width)
{
for(int i=0 ; i<width ; i++ )
SetPixel(x+i, y);
}
void DrawVerticalLine(int x, int y, int height)
{
for(int i=0 ; i<height ; i++ )
SetPixel(x, y+i);
}
To use non-integer diameter, you can increase precision of fixed point or use double values.
It should even be possible to make a sort of anti-alias depending on the difference between dY2 + (ray - x) * (ray - x) and ray2 (dx² + dy² and r²)
If you want a fast algorithm, consider drawing a polygon with N sides, the higher is N, the more precise will be the circle.
I would just generate a list of points and then use a polygon draw function for the rendering.
It may not be the algorithm yo are looking for and not the most performant one,
but I always do something like this:
void fillCircle(int x, int y, int radius){
// fill a circle
for(int rad = radius; rad >= 0; rad--){
// stroke a circle
for(double i = 0; i <= PI * 2; i+=0.01){
int pX = x + rad * cos(i);
int pY = y + rad * sin(i);
drawPoint(pX, pY);
}
}
}
The following two methods avoid the repeated square root calculation by drawing multiple parts of the circle at once and should therefore be quite fast:
void circleFill(const size_t centerX, const size_t centerY, const size_t radius, color fill) {
if (centerX < radius || centerY < radius || centerX + radius > width || centerY + radius > height)
return;
const size_t signedRadius = radius * radius;
for (size_t y = 0; y < radius; y++) {
const size_t up = (centerY - y) * width;
const size_t down = (centerY + y) * width;
const size_t halfWidth = roundf(sqrtf(signedRadius - y * y));
for (size_t x = 0; x < halfWidth; x++) {
const size_t left = centerX - x;
const size_t right = centerX + x;
pixels[left + up] = fill;
pixels[right + up] = fill;
pixels[left + down] = fill;
pixels[right + down] = fill;
}
}
}
void circleContour(const size_t centerX, const size_t centerY, const size_t radius, color stroke) {
if (centerX < radius || centerY < radius || centerX + radius > width || centerY + radius > height)
return;
const size_t signedRadius = radius * radius;
const size_t maxSlopePoint = ceilf(radius * 0.707106781f); //ceilf(radius * cosf(TWO_PI/8));
for (size_t i = 0; i < maxSlopePoint; i++) {
const size_t depth = roundf(sqrtf(signedRadius - i * i));
size_t left = centerX - depth;
size_t right = centerX + depth;
size_t up = (centerY - i) * width;
size_t down = (centerY + i) * width;
pixels[left + up] = stroke;
pixels[right + up] = stroke;
pixels[left + down] = stroke;
pixels[right + down] = stroke;
left = centerX - i;
right = centerX + i;
up = (centerY - depth) * width;
down = (centerY + depth) * width;
pixels[left + up] = stroke;
pixels[right + up] = stroke;
pixels[left + down] = stroke;
pixels[right + down] = stroke;
}
}
This was used in my new 3D printer Firmware, and it is proven the
fastest way for filled circle of a diameter from 1 to 43 pixel. If
larger is needed, the following memory block(or array) should be
extended following a structure I wont waste my time explaining...
If you have questions, or need larger diameter than 43, contact me, I
will help you drawing the fastest and perfect filled circles... or
Bresenham's circle drawing algorithm can be used above those
diameters, but having to fill the circle after, or incorporating the
fill into Bresenham's circle drawing algorithm, will only result in
slower fill circle than my code. I already benchmarked the different
codes, my solution is 4 to 5 times faster. As a test I have been
able to draw hundreds of filled circles of different size and colors
on a BigTreeTech tft24 1.1 running on a 1-core 72 Mhz cortex-m4
https://www.youtube.com/watch?v=7_Wp5yn3ADI
// this must be declared anywhere, as static or global
// as long as the function can access it !
uint8_t Rset[252]={
0,1,1,2,2,1,2,3,3,1,3,3,4,4,2,3,4,5,5,5,2,4,5,5,
6,6,6,2,4,5,6,6,7,7,7,2,4,5,6,7,7,8,8,8,2,5,6,7,
8,8,8,9,9,9,3,5,6,7,8,9,9,10,10,10,10,3,5,7,8,9,
9,10,10,11,11,11,11,3,5,7,8,9,10,10,11,11,12,12,
12,12,3,6,7,9,10,10,11,12,12,12,13,13,13,13,3,6,
8,9,10,11,12,12,13,13,13,14,14,14,14,3,6,8,9,10,
11,12,13,13,14,14,14,15,15,15,15,3,6,8,10,11,12,
13,13,14,14,15,15,15,16,16,16,16,4,7,8,10,11,12,
13,14,14,15,16,16,16,17,17,17,17,17,4,7,9,10,12,
13,14,14,15,16,16,17,17,17,18,18,18,18,18,4,7,9,
11,12,13,14,15,16,16,17,17,18,18,18,19,19,19,19,
19,7,9,11,12,13,15,15,16,17,18,18,19,19,20,20,20,
20,20,20,20,20,7,9,11,12,14,15,16,17,17,18,19,19
20,20,21,21,21,21,21,21,21,21};
// SOLUTION 1: (the fastest)
void FillCircle_v1(uint16_t x, uint16_t y, uint16_t r)
{
// all needed variables are created and set to their value...
uint16_t radius=(r<1) ? 1 : r ;
if (radius>21 ) {radius=21; }
uint16_t diam=(radius*2)+1;
uint16_t ymir=0, cur_y=0;
radius--; uint16_t target=(radius*radius+3*radius)/2; radius++;
// this part draws directly into the ILI94xx TFT buffer mem.
// using pointers..2 versions where you can draw
// pixels and lines with coordinates will follow
for (uint16_t yy=0; yy<diam; yy++)
{ ymir= (yy<=radius) ? yy+target : target+diam-(yy+1);
cur_y=y-radius+yy;
uint16_t *pixel=buffer_start_addr+x-Rset[ymir]+cur_y*buffer_width;
for (uint16_t xx= 0; xx<=(2*Rset[ymir]); xx++)
{ *pixel++ = CANVAS::draw_color; }}}
// SOLUTION 2: adaptable to any system that can
// add a pixel at a time: (drawpixel or add_pixel,etc_)
void FillCircle_v2(uint16_t x, uint16_t y, uint16_t r)
{
// all needed variables are created and set to their value...
uint16_t radius=(r<1) ? 1 : r ;
if (radius>21 ) {radius=21; }
uint16_t diam=(radius*2)+1;
uint16_t ymir=0, cur_y=0;
radius--; uint16_t target=(radius*radius+3*radius)/2; radius++;
for (uint16_t yy=0; yy<diam; yy++)
{ ymir= (yy<=radius) ? yy+target : target+diam-(yy+1);
cur_y=y-radius+yy;
uint16_t Pixel_x=x-Rset[ymir];
for (uint16_t xx= 0; xx<=(2*Rset[ymir]); xx++)
{ //use your add_pixel or draw_pixel here
// using those coordinates:
// X position will be... (Pixel_x+xx)
// Y position will be... (cur_y)
// and add those 3 brackets at the end
}}}
// SOLUTION 3: adaptable to any system that can draw fast
// horizontal lines
void FillCircle_v3(uint16_t x, uint16_t y, uint16_t r)
{
// all needed variables are created and set to their value...
uint16_t radius=(r<1) ? 1 : r ;
if (radius>21 ) {radius=21; }
uint16_t diam=(radius*2)+1;
uint16_t ymir=0, cur_y=0;
radius--; uint16_t target=(radius*radius+3*radius)/2; radius++;
for (uint16_t yy=0; yy<diam; yy++)
{ ymir= (yy<=radius) ? yy+target : target+diam-(yy+1);
cur_y=y-radius+yy;
uint16_t start_x=x-Rset[ymir];
uint16_t width_x=2*Rset[ymir];
// ... then use your best drawline function using those values:
// start_x: position X of the start of the line
// cur_y: position Y of the current line
// width_x: length of the line
// if you need a 2nd coordinate then :end_x=start_x+width_x
// and add those 2 brackets after !!!
}}
I did pretty much what AlegGeorge did but I changed three lines. I thought that this is faster but these are the results am I doing anything wrong? my function is called DrawBruteforcePrecalcV4. here's the code:
for (int x = 0; x < radius ; x++) // Instead of looping from -radius to radius I loop from 0 to radius
{
int hh = (int)std::sqrt(radius_sqr - x * x);
int rx = center_x + x;
int cmx = center_x - x;
int ph = center_y+hh;
for (int y = center_y-hh; y < ph; y++)
{
canvas[rx][y] = 1;
canvas[cmx][y] = 1;
}
}