├── .gitattributes
├── .gitignore
├── README.md
├── hypercube.sln
└── hypercube
├── hypercube.vcxproj
├── hypercube.vcxproj.filters
└── main.c
/.gitattributes:
--------------------------------------------------------------------------------
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--------------------------------------------------------------------------------
/README.md:
--------------------------------------------------------------------------------
1 | # Hypercube
2 |
3 | This project generates an ASCII projection of a rotating 4D hypercube in the Windows console. It is based on the paper [Four-Space Visualization of 4D Objects](https://hollasch.github.io/ray4/Four-Space_Visualization_of_4D_Objects.html#chapter4).
4 |
5 | There is a [Linux port](https://github.com/dominicmkennedy/hypercube) by [dominicmkennedy](https://github.com/dominicmkennedy/).
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 |
--------------------------------------------------------------------------------
/hypercube.sln:
--------------------------------------------------------------------------------
1 |
2 | Microsoft Visual Studio Solution File, Format Version 12.00
3 | # Visual Studio Version 16
4 | VisualStudioVersion = 16.0.31729.503
5 | MinimumVisualStudioVersion = 10.0.40219.1
6 | Project("{8BC9CEB8-8B4A-11D0-8D11-00A0C91BC942}") = "hypercube", "hypercube\hypercube.vcxproj", "{0781FA37-E169-46B4-B4F8-017057958492}"
7 | EndProject
8 | Global
9 | GlobalSection(SolutionConfigurationPlatforms) = preSolution
10 | Debug|x64 = Debug|x64
11 | Debug|x86 = Debug|x86
12 | Release|x64 = Release|x64
13 | Release|x86 = Release|x86
14 | EndGlobalSection
15 | GlobalSection(ProjectConfigurationPlatforms) = postSolution
16 | {0781FA37-E169-46B4-B4F8-017057958492}.Debug|x64.ActiveCfg = Debug|x64
17 | {0781FA37-E169-46B4-B4F8-017057958492}.Debug|x64.Build.0 = Debug|x64
18 | {0781FA37-E169-46B4-B4F8-017057958492}.Debug|x86.ActiveCfg = Debug|Win32
19 | {0781FA37-E169-46B4-B4F8-017057958492}.Debug|x86.Build.0 = Debug|Win32
20 | {0781FA37-E169-46B4-B4F8-017057958492}.Release|x64.ActiveCfg = Release|x64
21 | {0781FA37-E169-46B4-B4F8-017057958492}.Release|x64.Build.0 = Release|x64
22 | {0781FA37-E169-46B4-B4F8-017057958492}.Release|x86.ActiveCfg = Release|Win32
23 | {0781FA37-E169-46B4-B4F8-017057958492}.Release|x86.Build.0 = Release|Win32
24 | EndGlobalSection
25 | GlobalSection(SolutionProperties) = preSolution
26 | HideSolutionNode = FALSE
27 | EndGlobalSection
28 | GlobalSection(ExtensibilityGlobals) = postSolution
29 | SolutionGuid = {36D6D34D-B3E6-47F6-B44B-E3CC36656EAA}
30 | EndGlobalSection
31 | EndGlobal
32 |
--------------------------------------------------------------------------------
/hypercube/hypercube.vcxproj:
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1 |
2 |
3 |
4 |
5 | Debug
6 | Win32
7 |
8 |
9 | Release
10 | Win32
11 |
12 |
13 | Debug
14 | x64
15 |
16 |
17 | Release
18 | x64
19 |
20 |
21 |
22 | 16.0
23 | Win32Proj
24 | {0781fa37-e169-46b4-b4f8-017057958492}
25 | hypercube
26 | 10.0
27 |
28 |
29 |
30 | Application
31 | true
32 | v142
33 | Unicode
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35 |
36 | Application
37 | false
38 | v142
39 | true
40 | Unicode
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42 |
43 | Application
44 | true
45 | v142
46 | Unicode
47 |
48 |
49 | Application
50 | false
51 | v142
52 | true
53 | Unicode
54 |
55 |
56 |
57 |
58 |
59 |
60 |
61 |
62 |
63 |
64 |
65 |
66 |
67 |
68 |
69 |
70 |
71 |
72 |
73 |
74 | true
75 |
76 |
77 | false
78 |
79 |
80 | true
81 |
82 |
83 | false
84 |
85 |
86 |
87 | Level3
88 | true
89 | WIN32;_DEBUG;_CONSOLE;%(PreprocessorDefinitions)
90 | true
91 |
92 |
93 | Console
94 | true
95 |
96 |
97 |
98 |
99 | Level3
100 | true
101 | true
102 | true
103 | WIN32;NDEBUG;_CONSOLE;%(PreprocessorDefinitions)
104 | true
105 |
106 |
107 | Console
108 | true
109 | true
110 | true
111 |
112 |
113 |
114 |
115 | Level3
116 | true
117 | _DEBUG;_CONSOLE;%(PreprocessorDefinitions)
118 | true
119 |
120 |
121 | Console
122 | true
123 |
124 |
125 |
126 |
127 | Level3
128 | true
129 | true
130 | true
131 | NDEBUG;_CONSOLE;%(PreprocessorDefinitions)
132 | true
133 |
134 |
135 | Console
136 | true
137 | true
138 | true
139 |
140 |
141 |
142 |
143 |
144 |
145 |
146 |
147 |
--------------------------------------------------------------------------------
/hypercube/hypercube.vcxproj.filters:
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1 |
2 |
3 |
4 |
5 | {4FC737F1-C7A5-4376-A066-2A32D752A2FF}
6 | cpp;c;cc;cxx;c++;cppm;ixx;def;odl;idl;hpj;bat;asm;asmx
7 |
8 |
9 | {93995380-89BD-4b04-88EB-625FBE52EBFB}
10 | h;hh;hpp;hxx;h++;hm;inl;inc;ipp;xsd
11 |
12 |
13 | {67DA6AB6-F800-4c08-8B7A-83BB121AAD01}
14 | rc;ico;cur;bmp;dlg;rc2;rct;bin;rgs;gif;jpg;jpeg;jpe;resx;tiff;tif;png;wav;mfcribbon-ms
15 |
16 |
17 |
18 |
19 | Source Files
20 |
21 |
22 |
--------------------------------------------------------------------------------
/hypercube/main.c:
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1 | #include
2 | #define _USE_MATH_DEFINES
3 | #include
4 | #include
5 |
6 | // width and height of screen
7 | #define ww 100
8 | #define wh 50
9 |
10 | void clr(CHAR_INFO* d)
11 | {
12 | for (int i = 0; i < ww * wh; ++i)
13 | {
14 | d[i].Attributes = FOREGROUND_GREEN;
15 | d[i].Char.UnicodeChar = ' ';
16 | }
17 | }
18 |
19 | void set(CHAR_INFO* d, COORD pt, char c)
20 | {
21 | d[pt.Y * ww + pt.X].Char.UnicodeChar = c;
22 | }
23 |
24 | char getp(CHAR_INFO* d, COORD* pts, double err)
25 | {
26 | if (abs(pts[0].Y - pts[2].Y) < 2)
27 | {
28 | if (err > 0.5)
29 | {
30 | return '-';
31 | }
32 | return '_';
33 | }
34 |
35 | if (abs(pts[0].X - pts[2].X) < 2 &&
36 | (pts[0].X >= pts[2].X || pts[1].X != pts[2].X) &&
37 | (pts[0].X <= pts[2].X || pts[1].X != pts[0].X))
38 | {
39 | return '|';
40 | }
41 |
42 | int mX = pts[0].Y < pts[2].Y ? pts[0].X : pts[2].X;
43 | return mX < pts[1].X ? '\\' : '/';\
44 | }
45 |
46 | void ln(CHAR_INFO* d, COORD a, COORD b)
47 | {
48 | set(d, a, '@');
49 | set(d, b, '@');
50 |
51 | int dx = abs(b.X - a.X), sx = a.X < b.X ? 1 : -1;
52 | int dy = abs(b.Y - a.Y), sy = a.Y < b.Y ? 1 : -1;
53 | int err = (dx > dy ? dx : -dy) / 2, e2;
54 |
55 | COORD pts[3];
56 | double ers[3];
57 |
58 | for (int i = 0; i < 3; ++i)
59 | {
60 | pts[i] = a;
61 | ers[i] = ((double)err - dx) / ((double)dy - dx);
62 | ers[i] = sy == 1 ? 1.0f - ers[i] : ers[i];
63 |
64 | if (a.X == b.X && a.Y == b.Y) {
65 | return;
66 | }
67 |
68 | e2 = err;
69 | if (e2 > -dx) { err -= dy; a.X += sx; }
70 | if (e2 < dy) { err += dx; a.Y += sy; }
71 | }
72 |
73 | for (;;)
74 | {
75 | set(d, pts[1], getp(d, pts, ers[1]));
76 |
77 | pts[0] = pts[1];
78 | pts[1] = pts[2];
79 | pts[2] = a;
80 |
81 | ers[0] = ers[1];
82 | ers[1] = ers[2];
83 | ers[2] = ((double)err - dx) / ((double)dy - dx);
84 | ers[2] = sy == 1 ? 1.0f - ers[2] : ers[2];
85 |
86 | if (a.X == b.X && a.Y == b.Y) {
87 | break;
88 | }
89 |
90 | e2 = err;
91 | if (e2 > -dx) { err -= dy; a.X += sx; }
92 | if (e2 < dy) { err += dx; a.Y += sy; }
93 | }
94 |
95 | // add the final point
96 | set(d, pts[1], getp(d, pts, ers[1]));
97 | }
98 |
99 | // hypercube vertices in 4D
100 | double V4[16][4] =
101 | {
102 | {-1, -1, -1, -1},
103 | { 1, -1, -1, -1},
104 | {-1, 1, -1, -1},
105 | { 1, 1, -1, -1},
106 | {-1, -1, 1, -1},
107 | { 1, -1, 1, -1},
108 | {-1, 1, 1, -1},
109 | { 1, 1, 1, -1},
110 | {-1, -1, -1, 1},
111 | { 1, -1, -1, 1},
112 | {-1, 1, -1, 1},
113 | { 1, 1, -1, 1},
114 | {-1, -1, 1, 1},
115 | { 1, -1, 1, 1},
116 | {-1, 1, 1, 1},
117 | { 1, 1, 1, 1},
118 | };
119 |
120 | // store the vertices once they have been projected to 3D
121 | double V3[16][3];
122 |
123 | // final 2D projection
124 | double V2[16][2];
125 |
126 | // the indices for each line
127 | int indices[32][2] =
128 | {
129 | // cube #1
130 | {0, 1},
131 | {0, 2},
132 | {0, 4},
133 | {1, 3},
134 | {1, 5},
135 | {2, 3},
136 | {2, 6},
137 | {3, 7},
138 | {4, 5},
139 | {4, 6},
140 | {5, 7},
141 | {6, 7},
142 |
143 | // in-between lines
144 | {0, 8},
145 | {1, 9},
146 | {2, 10},
147 | {3, 11},
148 | {4, 12},
149 | {5, 13},
150 | {6, 14},
151 | {7, 15},
152 |
153 | // cube #2
154 | {8, 9},
155 | {8, 10},
156 | {8, 12},
157 | {9, 11},
158 | {9, 13},
159 | {10, 11},
160 | {10, 14},
161 | {11, 15},
162 | {12, 13},
163 | {12, 14},
164 | {13, 15},
165 | {14, 15},
166 | };
167 |
168 | double dot4(const double* V, const double* U)
169 | {
170 | return (V[0] * U[0]) + (V[1] * U[1]) + (V[2] * U[2]) + (V[3] * U[3]);
171 | }
172 |
173 | double norm4(const double* V)
174 | {
175 | return sqrt(dot4(V, V));
176 | }
177 |
178 | // cross4 computes the four-dimensional cross product of the three vectors
179 | // U, V and W, in that order.
180 | // returns the resulting four-vector.
181 | void cross4(double* result, const double* U, const double* V, const double* W)
182 | {
183 | // intermediate values
184 | double A, B, C, D, E, F;
185 |
186 | // calculate intermediate values
187 | A = (V[0] * W[1]) - (V[1] * W[0]);
188 | B = (V[0] * W[2]) - (V[2] * W[0]);
189 | C = (V[0] * W[3]) - (V[3] * W[0]);
190 | D = (V[1] * W[2]) - (V[2] * W[1]);
191 | E = (V[1] * W[3]) - (V[3] * W[1]);
192 | F = (V[2] * W[3]) - (V[3] * W[2]);
193 |
194 | // calculate the result-vector components
195 | result[0] = (U[1] * F) - (U[2] * E) + (U[3] * D);
196 | result[1] = -(U[0] * F) + (U[2] * C) - (U[3] * B);
197 | result[2] = (U[0] * E) - (U[1] * C) + (U[3] * A);
198 | result[3] = -(U[0] * D) + (U[1] * B) - (U[2] * A);
199 | }
200 |
201 | void vecSub4(double* result, const double* a, const double* b)
202 | {
203 | result[0] = a[0] - b[0];
204 | result[1] = a[1] - b[1];
205 | result[2] = a[2] - b[2];
206 | result[3] = a[3] - b[3];
207 | }
208 |
209 | void vecScale4(double* vec, double m)
210 | {
211 | vec[0] *= m;
212 | vec[1] *= m;
213 | vec[2] *= m;
214 | vec[3] *= m;
215 | }
216 |
217 | void matVecMul4(double* result, const double* mat, const double* vec)
218 | {
219 | for (int row = 0; row < 4; ++row)
220 | {
221 | result[row] = 0;
222 | for (int col = 0; col < 4; ++col)
223 | {
224 | result[row] += mat[col * 4 + row] * vec[col];
225 | }
226 | }
227 | }
228 |
229 | // creates a rotation matrix for the XW plane
230 | // T is the angle in radians
231 | void rotXW4(double* result, double T)
232 | {
233 | // column vectors
234 | double* Wa = result + 4 * 0;
235 | double* Wb = result + 4 * 1;
236 | double* Wc = result + 4 * 2;
237 | double* Wd = result + 4 * 3;
238 |
239 | Wa[0] = cos(T);
240 | Wa[1] = 0;
241 | Wa[2] = 0;
242 | Wa[3] = -sin(T);
243 |
244 | Wb[0] = 0;
245 | Wb[1] = 1;
246 | Wb[2] = 0;
247 | Wb[3] = 0;
248 |
249 | Wc[0] = 0;
250 | Wc[1] = 0;
251 | Wc[2] = 1;
252 | Wc[3] = 0;
253 |
254 | Wd[0] = sin(T);
255 | Wd[1] = 0;
256 | Wd[2] = 0;
257 | Wd[3] = cos(T);
258 | }
259 |
260 | double from4[4] = { 5, 0, 0, 0 };
261 | double to4[4] = { 0, 0, 0, 0 };
262 | double up4[4] = { 0, 1, 0, 0 };
263 | double over4[4] = { 0, 0, 1, 0 };
264 |
265 | // generate a 4D view matrix
266 | void view4(double* result)
267 | {
268 | // column vectors
269 | double* Wa = result + 4 * 0;
270 | double* Wb = result + 4 * 1;
271 | double* Wc = result + 4 * 2;
272 | double* Wd = result + 4 * 3;
273 |
274 | // vector norm
275 | double norm;
276 |
277 | // get the normalized Wd column-vector.
278 | vecSub4(Wd, to4, from4);
279 | norm = norm4(Wd);
280 | vecScale4(Wd, 1 / norm);
281 |
282 | // calculate the normalized Wa column-vector.
283 | cross4(Wa, up4, over4, Wd);
284 | norm = norm4(Wa);
285 | vecScale4(Wa, 1 / norm);
286 |
287 | // calculate the normalized Wb column-vector.
288 | cross4(Wb, over4, Wd, Wa);
289 | norm = norm4(Wb);
290 | vecScale4(Wb, 1 / norm);
291 |
292 | // calculate the Wc column-vector.
293 | cross4(Wc, Wd, Wa, Wb);
294 | }
295 |
296 | void projectTo3D(double vAngle, const double* matView, const double* matRotation)
297 | {
298 | // column vectors
299 | const double* Wa = matView + 4 * 0;
300 | const double* Wb = matView + 4 * 1;
301 | const double* Wc = matView + 4 * 2;
302 | const double* Wd = matView + 4 * 3;
303 |
304 | // divisor Values
305 | double S, T;
306 |
307 | T = 1 / tan(vAngle / 2);
308 |
309 | for (int i = 0; i < 16; ++i)
310 | {
311 | double V[4];
312 | matVecMul4(V, matRotation, V4[i]);
313 |
314 | double Vf[4];
315 | vecSub4(Vf, V, from4);
316 |
317 | S = T / dot4(Vf, Wd);
318 |
319 | V3[i][0] = S * dot4(Vf, Wa);
320 | V3[i][1] = S * dot4(Vf, Wb);
321 | V3[i][2] = S * dot4(Vf, Wc);
322 | }
323 | }
324 |
325 | double dot3(const double* V, const double* U)
326 | {
327 | return (V[0] * U[0]) + (V[1] * U[1]) + (V[2] * U[2]);
328 | }
329 |
330 | double norm3(const double* V)
331 | {
332 | return sqrt(dot3(V, V));
333 | }
334 |
335 | void cross3(double* result, const double* U, const double* V)
336 | {
337 | result[0] = (U[1] * V[2]) - (U[2] * V[1]);
338 | result[1] = (U[2] * V[0]) - (U[0] * V[2]);
339 | result[2] = (U[0] * V[1]) - (U[1] * V[0]);
340 | }
341 | void vecSub3(double* result, const double* a, const double* b)
342 | {
343 | result[0] = a[0] - b[0];
344 | result[1] = a[1] - b[1];
345 | result[2] = a[2] - b[2];
346 | }
347 |
348 | void vecScale3(double* vec, double m)
349 | {
350 | vec[0] *= m;
351 | vec[1] *= m;
352 | vec[2] *= m;
353 | }
354 |
355 | void matVecMul3(double* result, const double* mat, const double* vec)
356 | {
357 | for (int row = 0; row < 3; ++row)
358 | {
359 | result[row] = 0;
360 | for (int col = 0; col < 3; ++col)
361 | {
362 | result[row] += mat[col * 3 + row] * vec[col];
363 | }
364 | }
365 | }
366 |
367 | void rotXZ3(double* result, double T)
368 | {
369 | // column vectors
370 | double* Va = result + 3 * 0;
371 | double* Vb = result + 3 * 1;
372 | double* Vc = result + 3 * 2;
373 |
374 | Va[0] = cos(T);
375 | Va[1] = 0;
376 | Va[2] = -sin(T);
377 |
378 | Vb[0] = 0;
379 | Vb[1] = 1;
380 | Vb[2] = 0;
381 |
382 | Vc[0] = sin(T);
383 | Vc[1] = 0;
384 | Vc[2] = cos(T);
385 | }
386 |
387 | double from3[3] = { 3.00f, 0.99f, 1.82f };
388 | double to3[3] = { 0, 0, 0 };
389 | double up3[3] = { 0, -1, 0 };
390 |
391 | // generate a 3D view matrix
392 | void view3(double* result)
393 | {
394 | double* Va = result + 3 * 0;
395 | double* Vb = result + 3 * 1;
396 | double* Vc = result + 3 * 2;
397 |
398 | double norm;
399 |
400 | // Get the normalized Vc column-vector.
401 | vecSub3(Vc, to3, from3);
402 | norm = norm3(Vc);
403 | vecScale3(Vc, 1 / norm);
404 |
405 | // Calculate the normalized Va column-vector.
406 | cross3(Va, Vc, up3);
407 | norm = norm3(Va);
408 | vecScale3(Va, 1 / norm);
409 |
410 | // Calculate the Vb column-vector.
411 | cross3(Vb, Va, Vc);
412 | }
413 |
414 | void projectTo2D(double vAngle, const double* matView, const double* matRotation)
415 | {
416 | // column vectors
417 | const double* Va = matView + 3 * 0;
418 | const double* Vb = matView + 3 * 1;
419 | const double* Vc = matView + 3 * 2;
420 |
421 | // divisor values
422 | double S, T;
423 |
424 | T = 1 / tan(vAngle / 2);
425 |
426 | for (int i = 0; i < 16; ++i)
427 | {
428 | double V[3];
429 | matVecMul3(V, matRotation, V3[i]);
430 |
431 | double Vf[3];
432 | vecSub3(Vf, V, from3);
433 |
434 | S = T / dot3(Vf, Vc);
435 |
436 | V2[i][0] = (ww / 2) + (ww * S * dot3(Vf, Va));
437 | V2[i][1] = (wh / 2) + (wh * S * dot3(Vf, Vb));
438 | }
439 | }
440 |
441 | int main(int argc, const char* argv[])
442 | {
443 | // get the console handle
444 | HANDLE h = GetStdHandle(STD_OUTPUT_HANDLE);
445 |
446 | // set console dimensions
447 | COORD s = { ww, wh };
448 | SMALL_RECT r = { 0, 0, ww, wh };
449 | COORD z = { 0, 0 };
450 | SetConsoleScreenBufferSize(h, s);
451 | SetConsoleWindowInfo(h, TRUE, &r);
452 |
453 | CHAR_INFO d[wh * ww];
454 |
455 | double viewMat4[4 * 4];
456 | view4(viewMat4);
457 | double rot4[4 * 4];
458 |
459 | double viewMat3[3 * 3];
460 | view3(viewMat3);
461 | double rot3[3 * 3];
462 |
463 | double rotation = 0;
464 |
465 | for (;;)
466 | {
467 | rotation += 0.01f;
468 |
469 | rotXW4(rot4, rotation);
470 | projectTo3D(M_PI / 3, viewMat4, rot4);
471 |
472 | rotXZ3(rot3, rotation * 0.3);
473 | projectTo2D(M_PI / 4, viewMat3, rot3);
474 |
475 | clr(d);
476 |
477 | for (int i = 0; i < 32; ++i)
478 | {
479 | int a = indices[i][0];
480 | int b = indices[i][1];
481 | COORD c1 = { (SHORT)V2[a][0], (SHORT)V2[a][1] };
482 | COORD c2 = { (SHORT)V2[b][0], (SHORT)V2[b][1] };
483 | ln(d, c1, c2);
484 | }
485 |
486 | WriteConsoleOutput(h, d, s, z, &r);
487 |
488 | Sleep(1);
489 | }
490 | }
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