integral based circle anti-aliasing test
parent
776dfe46d2
commit
3f9f643159
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@ -1,4 +1,5 @@
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#include <Windows.h>
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#include <math.h>
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////////////////////////////////
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//- Experiment Configuration
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@ -47,6 +48,8 @@ typedef double F64;
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#define PtrOffsetOf(T,m) (void*)(&Member(T,m))
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#define OffsetOf(T,m) U64FromPtr(&Member(T,m))
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#define Clamp(a,x,b) (((x)<(a))?(a):((b)<(x))?(b):(x))
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#define allocate_array(T,c) (T*)(malloc(sizeof(T)*(c)))
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@ -91,6 +94,248 @@ static void opengl_draw_texture_geometry(Vertex *v, U64 count, U32 texture);
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static void opengl_draw_rect_geometry(Vertex *v, U64 count);
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////////////////////////////////
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//- Circle Generator
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static F32
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integral_indef(F32 r, F32 x){
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Assert(fabs(x) <= fabs(r));
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F32 t = asinf(x/r);
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F32 result = r*r*0.5f*(t + 0.5f*sinf(2*t));
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return(result);
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}
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static F32
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integral_def(F32 r, F32 min_x, F32 max_x){
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F32 max_v = integral_indef(r, max_x);
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F32 min_v = integral_indef(r, min_x);
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F32 result = max_v - min_v;
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return(result);
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}
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static B32
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approx_equal(F32 a, F32 b){
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B32 result = (a - 0.0078125 <= b && b <= a + 0.0078125);
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return(result);
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}
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static void
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sanity_test_integrals(void){
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{
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F32 a = integral_def(1.f, -1.f, 1.f);
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Assert(approx_equal(a, 3.141593f*0.5f));
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}
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{
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F32 a = integral_def(2.f, -2.f, 2.f);
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Assert(approx_equal(a, 3.141593f*2.f));
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}
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{
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F32 a = integral_def(2.f, 0.f, 2.f);
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Assert(approx_equal(a, 3.141593f));
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}
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{
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F32 a0 = integral_def(3.f, 0.f, 1.f);
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F32 a1 = integral_def(3.f, 1.f, 2.f);
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F32 a2 = integral_def(3.f, 2.f, 3.f);
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Assert(approx_equal(a0 + a1 + a2, 3.141593f*9.f/4.f));
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}
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}
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static F32
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intersection_area(F32 cir_r, F32 unit_box_x0, F32 unit_box_y0){
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F32 rr = cir_r*cir_r;
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F32 rel_y0 = unit_box_y0;
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F32 rel_y1 = unit_box_y0 + 1.f;
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F32 rel_x0 = unit_box_x0;
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F32 rel_x1 = unit_box_x0 + 1.f;
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F32 y0y0 = rel_y0*rel_y0;
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F32 y1y1 = rel_y1*rel_y1;
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F32 x0x0 = rel_x0*rel_x0;
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F32 x1x1 = rel_x1*rel_x1;
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// check each corner for hitting the circle
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B32 corner_bl = ((y0y0 + x0x0) <= rr);
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B32 corner_tl = ((y1y1 + x0x0) <= rr);
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B32 corner_br = ((y0y0 + x1x1) <= rr);
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B32 corner_tr = ((y1y1 + x1x1) <= rr);
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// calculate area
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F32 a = 0.f;
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#define COMB(a,b,c,d) ((a)|((b)<<1)|((c)<<2)|((d)<<3))
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switch (COMB(corner_bl, corner_tl, corner_br, corner_tr)){
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// full miss
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case 0x0: a = 0.f; break;
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// full hit
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case 0xF: a = 1.f; break;
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// 1 corner hit
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case COMB(1,0,0,0): case COMB(0,1,0,0):
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case COMB(0,0,1,0): case COMB(0,0,0,1):
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{
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F32 intersection_y = 0.f;
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if (corner_bl || corner_br){
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intersection_y = rel_y0;
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}
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else{
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intersection_y = rel_y1;
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}
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F32 intersection_x = sqrtf(rr - intersection_y*intersection_y);
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if (intersection_x < rel_x0 || rel_x1 < intersection_x){
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intersection_x = -intersection_x;
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}
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F32 x_min = 0.f;
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F32 x_max = 0.f;
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if (corner_bl || corner_tl){
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x_min = rel_x0;
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x_max = intersection_x;
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}
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else{
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x_min = intersection_x;
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x_max = rel_x1;
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}
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F32 h = fabs(intersection_y);
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a = integral_def(cir_r, x_min, x_max) - h*(x_max - x_min);
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}break;
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// 2 corner hits (horizontal edge)
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case COMB(1,0,1,0): case COMB(0,1,0,1):
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{
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F32 h = 0.f;
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if (corner_bl){
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h = rel_y0;
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}
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else{
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h = -rel_y1;
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}
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a = integral_def(cir_r, rel_x0, rel_x1) - h;
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}break;
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// 2 corner hits (vertical edge)
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case COMB(1,1,0,0): case COMB(0,0,1,1):
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{
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F32 w = 0.f;
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if (corner_bl){
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w = rel_x0;
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}
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else{
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w = -rel_x1;
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}
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a = integral_def(cir_r, rel_y0, rel_y1) - w;
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}break;
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// 3 corner hits
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case COMB(0,1,1,1): case COMB(1,0,1,1):
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case COMB(1,1,0,1): case COMB(1,1,1,0):
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{
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F32 intersection_y = 0.f;
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if (!corner_bl || !corner_br){
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intersection_y = rel_y0;
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}
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else{
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intersection_y = rel_y1;
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}
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F32 intersection_x = sqrtf(rr - intersection_y*intersection_y);
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if (intersection_x < rel_x0 || rel_x1 < intersection_x){
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intersection_x = -intersection_x;
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}
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F32 w_extra = 0.f;
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F32 x_min = 0.f;
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F32 x_max = 0.f;
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if (!corner_bl || !corner_tl){
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x_min = rel_x0;
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x_max = intersection_x;
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w_extra = rel_x1 - intersection_x;
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}
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else{
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x_min = intersection_x;
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x_max = rel_x1;
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w_extra = intersection_x - rel_x0;
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}
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F32 h = fabs(intersection_y) - 1.f;
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a = integral_def(cir_r, x_min, x_max) - h*(x_max - x_min) + w_extra;
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}break;
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// these cases should be impossible
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default:
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{
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a = -1.f;
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}break;
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}
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#undef COMB
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return(a);
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}
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static void
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sanity_test_circle_area(void){
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{
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F32 cr = 5.f;
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F32 cx = 5.f;
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F32 cy = 5.f;
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F32 sum_area = 0.f;
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for (U32 y = 0; y < 10; y += 1){
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F32 box_y0 = (F32)y;
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for (U32 x = 0; x < 10; x += 1){
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F32 box_x0 = (F32)x;
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F32 a = intersection_area(cr, box_x0 - cx, box_y0 - cy);
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Assert(0.f <= a && a <= 1.f);
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sum_area += a;
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}
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}
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F32 formula_area = 3.141593f*cr*cr;
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Assert(approx_equal(sum_area, formula_area));
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}
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{
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F32 cr = 8.f;
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F32 cx = 8.1f;
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F32 cy = 8.7f;
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F32 sum_area = 0.f;
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for (U32 y = 0; y < 20; y += 1){
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F32 box_y0 = (F32)y;
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for (U32 x = 0; x < 20; x += 1){
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F32 box_x0 = (F32)x;
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F32 a = intersection_area(cr, box_x0 - cx, box_y0 - cy);
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Assert(0.f <= a && a <= 1.f);
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sum_area += a;
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}
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}
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F32 formula_area = 3.141593f*cr*cr;
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Assert(approx_equal(sum_area, formula_area));
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}
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}
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static void
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render_circle_in_buffer(F32 cir_r, F32 cir_x, F32 cir_y,
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U8 *buf, U32 buf_side_length){
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for (U32 y = 0; y < buf_side_length; y += 1){
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F32 box_y0 = (F32)y;
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for (U32 x = 0; x < buf_side_length; x += 1){
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F32 box_x0 = (F32)x;
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// calculate area of the intersection (circle & box)
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F32 a = intersection_area(cir_r, box_x0 - cir_x, box_y0 - cir_y);
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Assert(0.f <= a && a <= 1.f);
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U32 vraw = (U32)(256.f*a);
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U8 v = (vraw <= 255)?((U8)vraw):(U8)255;
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buf[x + buf_side_length*y] = v;
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}
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}
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}
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////////////////////////////////
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//- GL Definitions
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@ -434,6 +679,24 @@ static GLuint canvas_framebuffer = 0;
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static GLuint test3_texture = 0;
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#define CIRCLE5_RADIUS 5.f
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#define CIRCLE5_X 6.f
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#define CIRCLE5_Y 6.f
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#define CIRCLE5_SIDE 12
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static GLuint circle5_texture = 0;
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#define CIRCLE25_RADIUS 25.f
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#define CIRCLE25_X 30.f
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#define CIRCLE25_Y 30.f
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#define CIRCLE25_SIDE 60
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static GLuint circle25_texture = 0;
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#define CIRCLE125_RADIUS 125.f
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#define CIRCLE125_X 150.f
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#define CIRCLE125_Y 150.f
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#define CIRCLE125_SIDE 300
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static GLuint circle125_texture = 0;
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static void
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opengl_render_init(void){
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//- setup basic shader program
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@ -535,6 +798,81 @@ opengl_render_init(void){
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
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}
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//- circle5 texture
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{
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U8 buf[CIRCLE5_SIDE*CIRCLE5_SIDE] = {0};
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render_circle_in_buffer(CIRCLE5_RADIUS, CIRCLE5_X, CIRCLE5_Y,
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buf, CIRCLE5_SIDE);
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U8 img[CIRCLE5_SIDE*CIRCLE5_SIDE*3] = {0};
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for (U32 i = 0; i < CIRCLE5_SIDE*CIRCLE5_SIDE; i += 1){
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U8 c = buf[i];
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img[i*3 + 0] = c;
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img[i*3 + 1] = c;
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img[i*3 + 2] = c;
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}
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glGenTextures(1, &circle5_texture);
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glBindTexture(GL_TEXTURE_2D, circle5_texture);
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glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, CIRCLE5_SIDE, CIRCLE5_SIDE, 0,
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GL_RGB, GL_UNSIGNED_BYTE, img);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
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}
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//- circle25 texture
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{
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U8 buf[CIRCLE25_SIDE*CIRCLE25_SIDE] = {0};
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render_circle_in_buffer(CIRCLE25_RADIUS, CIRCLE25_X, CIRCLE25_Y,
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buf, CIRCLE25_SIDE);
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U8 img[CIRCLE25_SIDE*CIRCLE25_SIDE*3] = {0};
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for (U32 i = 0; i < CIRCLE25_SIDE*CIRCLE25_SIDE; i += 1){
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U8 c = buf[i];
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img[i*3 + 0] = c;
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img[i*3 + 1] = c;
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img[i*3 + 2] = c;
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}
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glGenTextures(1, &circle25_texture);
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glBindTexture(GL_TEXTURE_2D, circle25_texture);
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glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, CIRCLE25_SIDE, CIRCLE25_SIDE, 0,
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GL_RGB, GL_UNSIGNED_BYTE, img);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
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}
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//- circle125 texture
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{
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U8 buf[CIRCLE125_SIDE*CIRCLE125_SIDE] = {0};
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render_circle_in_buffer(CIRCLE125_RADIUS, CIRCLE125_X, CIRCLE125_Y,
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buf, CIRCLE125_SIDE);
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U8 img[CIRCLE125_SIDE*CIRCLE125_SIDE*3] = {0};
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for (U32 i = 0; i < CIRCLE125_SIDE*CIRCLE125_SIDE; i += 1){
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U8 c = buf[i];
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img[i*3 + 0] = c;
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img[i*3 + 1] = c;
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img[i*3 + 2] = c;
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}
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glGenTextures(1, &circle125_texture);
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glBindTexture(GL_TEXTURE_2D, circle125_texture);
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glTexImage2D(GL_TEXTURE_2D, 0, GL_RGB, CIRCLE125_SIDE, CIRCLE125_SIDE, 0,
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GL_RGB, GL_UNSIGNED_BYTE, img);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MIN_FILTER, GL_NEAREST);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_MAG_FILTER, GL_NEAREST);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_S, GL_CLAMP_TO_EDGE);
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glTexParameteri(GL_TEXTURE_2D, GL_TEXTURE_WRAP_T, GL_CLAMP_TO_EDGE);
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}
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//- check for setup errors
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if (glGetError() != 0){
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error_message("error in opengl renderer initialization");
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@ -638,6 +976,10 @@ WinMain(HINSTANCE hInstance,
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HINSTANCE hPrevInstance,
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LPSTR lpCmdLine,
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int nShowCmd){
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sanity_test_integrals();
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sanity_test_circle_area();
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// do graphics tests
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wgl_helper_make_graphics_window(hInstance);
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U64 frame_counter = 0;
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@ -675,6 +1017,7 @@ WinMain(HINSTANCE hInstance,
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F32 test4_y = graphics_h - 160.f;
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F32 test5_y = graphics_h - 340.f;
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F32 test6_y = graphics_h - 450.f;
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F32 test7_y = graphics_h - 480.f;
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// render to canvas frame buffer
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{
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@ -976,6 +1319,90 @@ WinMain(HINSTANCE hInstance,
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opengl_draw_rect_geometry(v, 6);
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}
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}
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// 7: circles rendered with analytical antialiasing via integration
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{
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F32 y = test7_y;
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F32 x = grad_x0;
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// circle5
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{
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F32 y1 = y;
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F32 y0 = y - CIRCLE5_SIDE;
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F32 x0 = x;
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F32 x1 = x + CIRCLE5_SIDE;
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x += CIRCLE5_SIDE + 10;
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Vertex v[6];
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v[0].px = x0; v[0].py = y0;
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v[0].uvx = 0.f; v[0].uvy = 0.f;
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v[1].px = x0; v[1].py = y1;
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v[1].uvx = 0.f; v[1].uvy = 1.f;
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v[2].px = x1; v[2].py = y0;
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v[2].uvx = 1.f; v[2].uvy = 0.f;
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v[3].px = x0; v[3].py = y1;
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v[3].uvx = 0.f; v[3].uvy = 1.f;
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v[4].px = x1; v[4].py = y0;
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v[4].uvx = 1.f; v[4].uvy = 0.f;
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v[5].px = x1; v[5].py = y1;
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v[5].uvx = 1.f; v[5].uvy = 1.f;
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opengl_draw_texture_geometry(v, 6, circle5_texture);
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}
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// circle25
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{
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F32 y1 = y;
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F32 y0 = y - CIRCLE25_SIDE;
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F32 x0 = x;
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F32 x1 = x + CIRCLE25_SIDE;
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x += CIRCLE25_SIDE + 10;
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Vertex v[6];
|
||||
v[0].px = x0; v[0].py = y0;
|
||||
v[0].uvx = 0.f; v[0].uvy = 0.f;
|
||||
v[1].px = x0; v[1].py = y1;
|
||||
v[1].uvx = 0.f; v[1].uvy = 1.f;
|
||||
v[2].px = x1; v[2].py = y0;
|
||||
v[2].uvx = 1.f; v[2].uvy = 0.f;
|
||||
v[3].px = x0; v[3].py = y1;
|
||||
v[3].uvx = 0.f; v[3].uvy = 1.f;
|
||||
v[4].px = x1; v[4].py = y0;
|
||||
v[4].uvx = 1.f; v[4].uvy = 0.f;
|
||||
v[5].px = x1; v[5].py = y1;
|
||||
v[5].uvx = 1.f; v[5].uvy = 1.f;
|
||||
|
||||
opengl_draw_texture_geometry(v, 6, circle25_texture);
|
||||
}
|
||||
|
||||
// circle125
|
||||
{
|
||||
F32 y1 = y;
|
||||
F32 y0 = y - CIRCLE125_SIDE;
|
||||
F32 x0 = x;
|
||||
F32 x1 = x + CIRCLE125_SIDE;
|
||||
|
||||
x += CIRCLE125_SIDE + 10;
|
||||
|
||||
Vertex v[6];
|
||||
v[0].px = x0; v[0].py = y0;
|
||||
v[0].uvx = 0.f; v[0].uvy = 0.f;
|
||||
v[1].px = x0; v[1].py = y1;
|
||||
v[1].uvx = 0.f; v[1].uvy = 1.f;
|
||||
v[2].px = x1; v[2].py = y0;
|
||||
v[2].uvx = 1.f; v[2].uvy = 0.f;
|
||||
v[3].px = x0; v[3].py = y1;
|
||||
v[3].uvx = 0.f; v[3].uvy = 1.f;
|
||||
v[4].px = x1; v[4].py = y0;
|
||||
v[4].uvx = 1.f; v[4].uvy = 0.f;
|
||||
v[5].px = x1; v[5].py = y1;
|
||||
v[5].uvx = 1.f; v[5].uvy = 1.f;
|
||||
|
||||
opengl_draw_texture_geometry(v, 6, circle125_texture);
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
}
|
||||
|
|
|
|||
Loading…
Reference in New Issue