Over the weekend I thought it might be fun to implement a very basic 3d wireframe renderer. I basically copied all the math from the OpenGL docs and used sgorsten's vector math library.
This is what I got so far:
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 | /* watch -n.1 "clang++ --std=c++11 -g main.cpp -shared -o _target.so && mv _target.so target.so" # clang++ --std=c++11 -g main.cpp -o target && ./target */ #include <assert.h> #include <stdio.h> #include "linalg.h" #include <math.h> #include <time.h> #define FOR_RANGE(index, count) for ((index) = 0; (index) < (count); (index)++) using namespace linalg::aliases; using namespace linalg; struct GC { unsigned char * render_buffer; int width; int height; float near; float far; }; void draw_line(float2 p1, float2 p2, GC *gc) { if (p1[0] == INFINITY || p1[0] == -INFINITY || isnan(p1[0]) || p1[1] == INFINITY || p1[1] == -INFINITY || isnan(p1[1]) || p2[0] == INFINITY || p2[0] == -INFINITY || isnan(p2[0]) || p2[1] == INFINITY || p2[1] == -INFINITY || isnan(p2[1])) return; float2 d = normalize(p2 - p1); float2 last_p = p1; float minx = p1[0]; if (p2[0] < p1[0]) minx = p2[0]; float miny = p1[1]; if (p2[1] < p1[1]) miny = p2[1]; float maxx = p1[0]; if (p2[0] > p1[0]) maxx = p2[0]; float maxy = p1[1]; if (p2[1] > p1[1]) maxy = p2[1]; for(;;) { int x = last_p[0]; int y = last_p[1]; if (x >= 0 && y>=0 && x <gc->width && y < gc->height) { *(gc->render_buffer + 4 * (x + gc->width * y) + 0) = 0x00; *(gc->render_buffer + 4 * (x + gc->width * y) + 1) = 0x00; *(gc->render_buffer + 4 * (x + gc->width * y) + 2) = 0x00; *(gc->render_buffer + 4 * (x + gc->width * y) + 3) = 0xFF; } // else { printf("clip!\n");}; last_p += d; if ( (d[0]==0 && d[1]==0) || d[0] == INFINITY || d[0] == -INFINITY || isnan(d[0]) || d[1] == INFINITY || d[1] == -INFINITY || isnan(d[1]) || last_p[0] < minx || last_p[1] < miny || last_p[0] > maxx || last_p[1] > maxy ) break; } } float4x4 look_at() { // gluLookAt float la_ey_x = 0.0f; float la_ey_y = 0.0f; float la_ey_z = 5.0f; float la_cn_x = 0.0f; float la_cn_y = 0.0f; float la_cn_z = 0.0f; float la_up_x = 0.0f; float la_up_y = 1.0f; float la_up_z = 0.0f; float3 la_F = {la_cn_x - la_ey_x, la_cn_y - la_ey_y, la_cn_z - la_ey_z}; float3 la_UP = {la_up_x, la_up_y, la_up_z}; float3 la_f = normalize(la_F); float3 la_UP_norm = normalize(la_UP); // float3 la_s = la_f * la_UP_norm; // float3 la_u = normalize(la_s) * la_f; float3 la_s = cross(la_f, la_UP_norm); float3 la_u = cross(normalize(la_s), la_f); return {{ la_s[0], la_s[1], la_s[2], 0}, { la_u[0], la_u[1], la_u[2], 0}, { -la_f[0], -la_f[1], -la_f[2], 0}, { 0, 0, 0, 1}}; } float4x4 translate(float3 trans_p) { return {{ 1, 0, 0, trans_p[0]}, { 0, 1, 0, trans_p[1]}, { 0, 0, 1, trans_p[2]}, { 0, 0, 0, 1}}; } float4x4 rotate(float3 r_p, float r_angle) { r_p = normalize(r_p); float r_c = cos(r_angle * M_PI / 180); float r_s = sin(r_angle * M_PI / 180); return {{ powf(r_p.x, 2) * (1 - r_c) + r_c, r_p.x * r_p.y * (1 - r_c) - r_p.z * r_s, r_p.x * r_p.z * (1-r_c) + r_p.y * r_s, 0 }, { r_p.y * r_p.x * (1 - r_c) + r_p.z * r_s, powf(r_p.y, 2) * (1 - r_c) + r_c, r_p.y * r_p.z * (1-r_c) - r_p.x * r_s, 0 }, { r_p.x * r_p.z * (1 - r_c) - r_p.y * r_s, r_p.y * r_p.z * (1 - r_c) + r_p.x * r_s, powf(r_p.z, 2) * (1 - r_c) + r_c, 0 }, { 0, 0, 0, 1 }}; } float4x4 ortho() { float o_left = -2.0f; float o_right = 2.0f; float o_bottom = -2.0f; float o_top = 2.0f; float o_near = -2.0f; float o_far = 2.0f; float o_tx = (o_right + o_left) / (o_right - o_left); float o_ty = (o_top + o_bottom) / (o_top - o_bottom); float o_tz = (o_far + o_near) / (o_far - o_near); return {{ 2.0f / (o_right - o_left), 0, 0, o_tx}, { 0, 2.0f / (o_top - o_bottom), 0, o_ty}, { 0, 0, 2.0f / (o_far - o_near), o_tz}, { 0, 0, -1, 1}}; } float4x4 perspective() { // gluPerspective float field_of_view = 40.0f; float aspect_ratio = 1.0f; float z_near = 8.60f; float z_far = 10.0f; // float f = cotangent(field_of_view / 2.0f); float f = 1.0f / tan(field_of_view / (float)(M_PI) / 180.0f / 2.0f); float4x4 projection = {{ f/aspect_ratio, 0, 0, 0}, { 0, f, 0, 0}, { 0, 0, (z_far + z_near) / (z_near - z_far), (2.0f * z_far * z_near) / (z_near - z_far)}, { 0, 0, -1, 0}}; return {{ f/aspect_ratio, 1, 0, 0}, { 0, f, 0, 0}, { 0, 0, (z_far + z_near) / (z_near - z_far), (2.0f * z_far * z_near) / (z_near - z_far)}, { 0, 0, -1, 0}}; } float3 nd_cord(GC* gc, float4 clip_cord) { return { clip_cord.x / clip_cord.w, clip_cord.y / clip_cord.w, clip_cord.z / clip_cord.w}; } float3 window_cord(GC* gc, float3 nd_cord) { float vp_x = 0; // glViewport float vp_y = 0; // glViewport float vp_w = gc->width; // glViewport float vp_h = gc->height; // glViewport float dr_n = gc->near; //glDepthRange float dr_f = gc->far; //glDepthRange return { (vp_w / 2.0f) * nd_cord.x + (vp_x + vp_w/2.0f), (vp_h / 2.0f) * nd_cord.y + (vp_y + vp_h/2.0f), ((dr_f - dr_n)/2.0f) * nd_cord.z + (dr_f + dr_n)/2.0f }; } extern "C" void target(float current_time, void * _render_buffer, int width, int height) { GC gc = {(unsigned char *)_render_buffer, width, height, 1, 10}; unsigned char * render_buffer = (unsigned char *)_render_buffer; // printf("\033[1A"); // printf("\033[1A"); // printf("\033[1A"); // printf("\033[1A"); // printf("\033[1A"); // printf("\033[1A"); // Clear white memset(render_buffer, 0xFF, width * height * 4); float4x4 identity = {{ 1, 0, 0 , 0}, { 0, 1, 0, 0}, { 0, 0, 1, 0}, { 0, 0, 0, 1}}; // Object cords float4 oc_p0 = { 1, 1, 1, 1}; float4 oc_p1 = { 1, 1, -1, 1}; float4 oc_p2 = { 1, -1, -1, 1}; float4 oc_p3 = { 1, -1, 1, 1}; float4 oc_p4 = {-1, 1, 1, 1}; float4 oc_p5 = {-1, 1, -1, 1}; float4 oc_p6 = {-1, -1, -1, 1}; float4 oc_p7 = {-1, -1, 1, 1}; // Cube with lines: p0, p1, p1,p2 p2,p3 p3,p0 p4,p5 p5,p6 p6,p7 p7,p4 p0,p4 p1,p5 p2,p6 p3,p7 float4x4 model_view = identity; // model_view = mul(model_view, look_at()); // model_view = mul(model_view, translate({0.0, 0.0, -1.0})); model_view = mul(model_view, rotate({1.0, 0.0, 0.0}, 20.0f)); model_view = mul(model_view, rotate({0.0, 0.0, 1.0}, -10.0f)); model_view = mul(model_view, rotate({0.0, 1.0, 0.0}, -10.0f)); // eye cords float4 ec_p0 = mul(model_view, oc_p0); float4 ec_p1 = mul(model_view, oc_p1); float4 ec_p2 = mul(model_view, oc_p2); float4 ec_p3 = mul(model_view, oc_p3); float4 ec_p4 = mul(model_view, oc_p4); float4 ec_p5 = mul(model_view, oc_p5); float4 ec_p6 = mul(model_view, oc_p6); float4 ec_p7 = mul(model_view, oc_p7); float4x4 projection = identity; projection = mul(projection, ortho()); //projection = mul(projection, perspective()); // clip cords float4 cc_p0 = mul(projection, ec_p0); float4 cc_p1 = mul(projection, ec_p1); float4 cc_p2 = mul(projection, ec_p2); float4 cc_p3 = mul(projection, ec_p3); float4 cc_p4 = mul(projection, ec_p4); float4 cc_p5 = mul(projection, ec_p5); float4 cc_p6 = mul(projection, ec_p6); float4 cc_p7 = mul(projection, ec_p7); // Normalized device coordinates float3 ndc_p0 = nd_cord(&gc, cc_p0); float3 ndc_p1 = nd_cord(&gc, cc_p1); float3 ndc_p2 = nd_cord(&gc, cc_p2); float3 ndc_p3 = nd_cord(&gc, cc_p3); float3 ndc_p4 = nd_cord(&gc, cc_p4); float3 ndc_p5 = nd_cord(&gc, cc_p5); float3 ndc_p6 = nd_cord(&gc, cc_p6); float3 ndc_p7 = nd_cord(&gc, cc_p7); // Window Cords float3 wc_p0 = window_cord(&gc, ndc_p0); float3 wc_p1 = window_cord(&gc, ndc_p1); float3 wc_p2 = window_cord(&gc, ndc_p2); float3 wc_p3 = window_cord(&gc, ndc_p3); float3 wc_p4 = window_cord(&gc, ndc_p4); float3 wc_p5 = window_cord(&gc, ndc_p5); float3 wc_p6 = window_cord(&gc, ndc_p6); float3 wc_p7 = window_cord(&gc, ndc_p7); #if 0 time_t timer; char buffer[26]; struct tm* tm_info; time(&timer); tm_info = localtime(&timer); strftime(buffer, 26, "%Y:%m:%d %H:%M:%S", tm_info); printf("%s Points 0:%f,%f 1:%f,%f 2:%f,%f 3:%f,%f 4:%f,%f 5:%f,%f 6:%f,%f 7:%f,%f \n", buffer, wc_p0[0], wc_p0[1], wc_p1[0], wc_p1[1], wc_p2[0], wc_p2[1], wc_p3[0], wc_p3[1], wc_p4[0], wc_p4[1], wc_p5[0], wc_p5[1], wc_p6[0], wc_p6[1], wc_p7[0], wc_p7[1] ); printf("%s Pointz 0:%f 1:%f 2:%f 3:%f 4:%f 5:%f 6:%f 7:%f \n", buffer, wc_p0[2], wc_p1[2], wc_p2[2], wc_p3[2], wc_p4[2], wc_p5[2], wc_p6[2], wc_p7[2] ); #endif // lines: p0, p1, p1,p2 p2,p3 p3,p0 p4,p5 p5,p6 p6,p7 p7,p4 p0,p4 p1,p5 p2,p6 p3,p7 draw_line({wc_p0[0], wc_p0[1]}, {wc_p1[0], wc_p1[1]}, &gc); draw_line({wc_p1[0], wc_p1[1]}, {wc_p2[0], wc_p2[1]}, &gc); draw_line({wc_p2[0], wc_p2[1]}, {wc_p3[0], wc_p3[1]}, &gc); draw_line({wc_p3[0], wc_p3[1]}, {wc_p0[0], wc_p0[1]}, &gc); draw_line({wc_p4[0], wc_p4[1]}, {wc_p5[0], wc_p5[1]}, &gc); draw_line({wc_p5[0], wc_p5[1]}, {wc_p6[0], wc_p6[1]}, &gc); draw_line({wc_p6[0], wc_p6[1]}, {wc_p7[0], wc_p7[1]}, &gc); draw_line({wc_p7[0], wc_p7[1]}, {wc_p4[0], wc_p4[1]}, &gc); draw_line({wc_p0[0], wc_p0[1]}, {wc_p4[0], wc_p4[1]}, &gc); draw_line({wc_p1[0], wc_p1[1]}, {wc_p5[0], wc_p5[1]}, &gc); draw_line({wc_p2[0], wc_p2[1]}, {wc_p6[0], wc_p6[1]}, &gc); draw_line({wc_p3[0], wc_p3[1]}, {wc_p7[0], wc_p7[1]}, &gc); } |
See also: Gist, along with hot-loader (For OS X, but should run on anywhere, along as you have SDL)
If I just use orthographic projection I get something that I expect:
However, if I get try to use a perspective matrix, or even apply a translation matrix, I get really odd results:
I'm kinda at a loss at this point, I checked the math a few times, but I probably still have a mistake somewhere...
Anyway, here is what I based the code off of:
"OpenGL Transformation" Basicall...ertices translate to window cords
glTranslate
gluPerspective