ardour
CurveTest.cpp
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1 #include "CurveTest.hpp"
2 #include "evoral/ControlList.hpp"
3 #include "evoral/Curve.hpp"
4 #include <stdlib.h>
5 
6 CPPUNIT_TEST_SUITE_REGISTRATION (CurveTest);
7 
8 using namespace Evoral;
9 
10 // linear y = Y0 + YS * x ; with x = i * (X1 - X0) + X0; and i = [0..1023]
11 #define VEC1024LINCMP(X0, X1, Y0, YS) \
12  cl->curve ().get_vector ((X0), (X1), vec, 1024); \
13  for (int i = 0; i < 1024; ++i) { \
14  char msg[64]; \
15  snprintf (msg, 64, "at i=%d (x0=%.1f, x1=%.1f, y0=%.1f, ys=%.3f)", \
16  i, X0, X1, Y0, YS); \
17  CPPUNIT_ASSERT_DOUBLES_EQUAL_MESSAGE ( \
18  msg, \
19  (Y0) + i * (YS), vec[i], \
20  1e-24 \
21  ); \
22  }
23 
24 void
25 CurveTest::twoPointLinear ()
26 {
27  float vec[1024];
28 
29  boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
30 
31  cl->create_curve ();
32  cl->set_interpolation (ControlList::Linear);
33 
34  // add two points to curve
35  cl->fast_simple_add ( 0.0 , 2048.0);
36  cl->fast_simple_add (8192.0 , 4096.0);
37 
38  cl->curve ().get_vector (1024.0, 2047.0, vec, 1024);
39 
40  VEC1024LINCMP (1024.0, 2047.0, 2304.f, .25f);
41  VEC1024LINCMP (2048.0, 2559.5, 2560.f, .125f);
42  VEC1024LINCMP ( 0.0, 4092.0, 2048.f, 1.f);
43 
44  // greetings to tartina
45  cl->curve ().get_vector (2048.0, 2048.0, vec, 1);
46  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048..2048", 2560.f, vec[0]);
47 
48  /* XXX WHAT DO WE EXPECT WITH veclen=1 AND x1 > x0 ? */
49 #if 0
50  /* .. interpolated value at (x1+x0)/2 */
51  cl->curve ().get_vector (2048.0, 2049.0, vec, 1);
52  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048-2049", 2560.125f, vec[0]);
53 
54  cl->curve ().get_vector (2048.0, 2056.0, vec, 1);
55  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048-2049", 2561.f, vec[0]);
56 #else
57  /* .. value at x0 */
58  cl->curve ().get_vector (2048.0, 2049.0, vec, 1);
59  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 , 2048..2049", 2560.f, vec[0]);
60 
61  cl->curve ().get_vector (2048.0, 2056.0, vec, 1);
62  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 , 2048..2049", 2560.f, vec[0]);
63 #endif
64 
65  cl->curve ().get_vector (2048.0, 2048.0, vec, 2);
66  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2048 @ 0", 2560.f, vec[0]);
67  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2048 @ 1", 2560.f, vec[1]);
68 
69  cl->curve ().get_vector (2048.0, 2056.0, vec, 2);
70  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2056 @ 0", 2560.f, vec[0]);
71  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2056 @ 0", 2562.f, vec[1]);
72 
73  cl->curve ().get_vector (2048.0, 2056.0, vec, 3);
74  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 0", 2560.f, vec[0]);
75  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 1", 2561.f, vec[1]);
76  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 2", 2562.f, vec[2]);
77 
78  /* check out-of range..
79  * we expect the first and last value - no interpolation
80  */
81  cl->curve ().get_vector (-1, -1, vec, 1);
82  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ -1", 2048.f, vec[0]);
83 
84  cl->curve ().get_vector (9999.0, 9999.0, vec, 1);
85  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 9999", 4096.f, vec[0]);
86 
87  cl->curve ().get_vector (-999.0, 0, vec, 13);
88  for (int i = 0; i < 13; ++i) {
89  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=13 @ -999..0", 2048.f, vec[i]);
90  }
91 
92  cl->curve ().get_vector (9998.0, 9999.0, vec, 8);
93  for (int i = 0; i < 8; ++i) {
94  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=8 @ 9998..9999", 4096.f, vec[i]);
95  }
96 }
97 
98 void
99 CurveTest::threePointLinear ()
100 {
101  float vec[4];
102 
103  boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
104 
105  cl->create_curve ();
106  cl->set_interpolation (ControlList::Linear);
107 
108  // add 3 points to curve
109  cl->fast_simple_add ( 0.0 , 2.0);
110  cl->fast_simple_add ( 100.0 , 4.0);
111  cl->fast_simple_add ( 200.0 , 0.0);
112 
113  cl->curve ().get_vector (50.0, 60.0, vec, 1);
114  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 50", 3.f, vec[0]);
115 
116  cl->curve ().get_vector (100.0, 100.0, vec, 1);
117  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 100", 4.f, vec[0]);
118 
119  cl->curve ().get_vector (150.0, 150.0, vec, 1);
120  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 150", 2.f, vec[0]);
121 
122  cl->curve ().get_vector (130.0, 150.0, vec, 3);
123  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 0", 2.8f, vec[0]);
124  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 2", 2.4f, vec[1]);
125  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 3", 2.0f, vec[2]);
126 
127  cl->curve ().get_vector (80.0, 160.0, vec, 3);
128  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 0", 3.6f, vec[0]);
129  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 2", 3.2f, vec[1]);
130  CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 3", 1.6f, vec[2]);
131 }
132 
133 void
134 CurveTest::threePointDiscete ()
135 {
136  boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
137  cl->set_interpolation (ControlList::Discrete);
138 
139  // add 3 points to curve
140  cl->fast_simple_add ( 0.0 , 2.0);
141  cl->fast_simple_add ( 100.0 , 4.0);
142  cl->fast_simple_add ( 200.0 , 0.0);
143 
144  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
145  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
146  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
147 
148  cl->set_interpolation (ControlList::Linear);
149 
150  CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
151  CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
152  CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
153 }
154 
155 void
156 CurveTest::ctrlListEval ()
157 {
158  boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
159 
160  cl->fast_simple_add ( 0.0 , 2.0);
161 
162  cl->set_interpolation (ControlList::Discrete);
163  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
164  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(120.));
165  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(160.));
166 
167  cl->set_interpolation (ControlList::Linear);
168  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
169  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(120.));
170  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(160.));
171 
172  cl->fast_simple_add ( 100.0 , 4.0);
173 
174  cl->set_interpolation (ControlList::Discrete);
175  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
176  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
177  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
178 
179  cl->set_interpolation (ControlList::Linear);
180  CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
181  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
182  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
183 
184  cl->fast_simple_add ( 200.0 , 0.0);
185 
186  cl->set_interpolation (ControlList::Discrete);
187  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
188  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
189  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
190 
191  cl->set_interpolation (ControlList::Linear);
192  CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
193  CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
194  CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
195 
196  cl->fast_simple_add ( 300.0 , 8.0);
197 
198  cl->set_interpolation (ControlList::Discrete);
199  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
200  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
201  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
202  CPPUNIT_ASSERT_EQUAL(0.0, cl->unlocked_eval(250.));
203  CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(999.));
204 
205  cl->set_interpolation (ControlList::Linear);
206  CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
207  CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
208  CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
209  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(250.));
210  CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(999.));
211 
212  cl->fast_simple_add ( 400.0 , 9.0);
213 
214  cl->set_interpolation (ControlList::Discrete);
215  CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
216  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
217  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
218  CPPUNIT_ASSERT_EQUAL(0.0, cl->unlocked_eval(250.));
219  CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(350.));
220  CPPUNIT_ASSERT_EQUAL(9.0, cl->unlocked_eval(999.));
221 
222  cl->set_interpolation (ControlList::Linear);
223  CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
224  CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
225  CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
226  CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(250.));
227  CPPUNIT_ASSERT_EQUAL(8.5, cl->unlocked_eval(350.));
228  CPPUNIT_ASSERT_EQUAL(9.0, cl->unlocked_eval(999.));
229 }
230 
231 void
232 CurveTest::constrainedCubic ()
233 {
234 
235  struct point {
236  int x, y;
237  };
238 
239  static const struct point data[] = {
240  /* values from worked example in www.korf.co.uk/spline.pdf */
241  { 0, 30 },
242  { 10, 130 },
243  { 30, 150 },
244  { 50, 150 },
245  { 70, 170 },
246  { 90, 220 },
247  { 100, 320 },
248  };
249 
250  int32_t type = 0;
251  Evoral::Parameter p(type);
252  Evoral::ParameterDescriptor pd;
253  Evoral::ControlList l(p,pd);
254 
255  size_t i;
256  l.set_interpolation(Evoral::ControlList::Curved);
257 
258  for (i=0; i<sizeof(data)/sizeof(data[0]); i++) {
259  l.add (data[i].x, data[i].y);
260  }
261 
262  Evoral::Curve curve(l);
263 
264  float f[121];
265  curve.get_vector(-10, 110, f, 121);
266 
267  const float *g = &f[10]; /* so g starts at x==0 */
268 
269  /* given points - should be exactly equal */
270  CPPUNIT_ASSERT_EQUAL( 30.0f, g[-10]);
271  CPPUNIT_ASSERT_EQUAL( 30.0f, g[ 0]);
272  CPPUNIT_ASSERT_EQUAL(130.0f, g[ 10]);
273  CPPUNIT_ASSERT_EQUAL(150.0f, g[ 30]);
274  CPPUNIT_ASSERT_EQUAL(150.0f, g[ 40]);
275  CPPUNIT_ASSERT_EQUAL(150.0f, g[ 50]);
276  CPPUNIT_ASSERT_EQUAL(320.0f, g[100]);
277  CPPUNIT_ASSERT_EQUAL(320.0f, g[110]);
278 
279  /*
280  First segment, i=1, for 0 <= x <= 10
281  f'1(x1) = 2/((x2 – x1)/(y2 – y1) + (x1 – x0)/(y1 – y0))
282  = 2/((30 – 10)/(150 – 130) + (10 – 0)/(130 – 30))
283  = 1.8181
284  f'1(x0) = 3/2*(y1 – y0)/(x1 – x0) - f'1(x1)/2
285  = 3/2*(130 – 30)/(10 – 0) – 1.818/2
286  = 14.0909
287  f"1(x0) = -2*(f'1(x1) + 2* f'1(x0))/(x1 – x0) + 6*(y1 – y0)/ (x1 – x0)^2
288  = -2*(1.8181 + 2*14.0909)/(10 – 0) + 6*(130 – 30)/(10 – 0)^2
289  = 0
290  f"1(x1) = 2*(2*f'1(x1) + f'1(x0))/(x1 – x0) - 6*(y1 – y0)/ (x1 – x0)^2
291  = 2*(2*1.818 + 14.0909)/(10 – 0) – 6*(130 – 30)/(10 – 0)^2
292  = -2.4545
293  d1 = 1/6 * (f"1(x1) - f"1(x0))/(x1 – x0)
294  = 1/6 * (-2.4545 – 0)/(10 – 0)
295  = -0.0409
296  c1 = 1/2 * (x1*f"1(x0) – x0*f"1(x1))/(x1 – x0)
297  = 1/2 * (10*0 – 0*1.8181)/(10 – 0)
298  = 0
299  b1 = ((y1 – y0) – c1*(x21 – x20) – d1*( x31 – x30))/(x1 – x0)
300  = ((130 – 30) – 0*(102 – 02) + 0.0409*(103 – 03))/(10 – 0)
301  = 14.09
302  a1 = y0 – b1*x0 – c1*x20 – d1*x30
303  = 30
304  y1 = 30 + 14.09x - 0.0409x3 for 0 <= x <= 10
305  */
306  /*
307  Second segment, i=2, for 10 <= x <= 30
308  f'2(x2) = 2/((x3 – x2)/(y3 – y2) + (x2 – x1)/(y2 – y1))
309  = 2/((50 – 30)/(150 – 150) + (30 – 10)/(150 – 130))
310  = 0
311  f'2(x1) = 2/((x2 – x1)/(y2 – y1) + (x1 – x0)/(y1 – y0))
312  = 1.8181
313 
314  f"2(x1) = -2*(f'2(x2) + 2* f'2(x1))/(x2 – x1) + 6*(y2 – y1)/ (x2 – x1)^2
315  = -2*(0 + 2*1.8181)/(30 – 10) + 6*(150 – 130)/(30 – 10)2
316  = -0.063636
317  f"2(x2) = 2*(2*f'2(x2) + f'2(x1))/(x2 – x1) - 6*(y2 – y1)/ (x2 – x1)^2
318  = 2*(2*0 + 1.8181)/(30 – 10) – 6*(150 – 130)/(30 – 10)^2
319  = -0.11818
320 
321  d2 = 1/6 * (f"2(x2) - f"2(x1))/(x2 – x1)
322  = 1/6 * (-0.11818 + 0.063636)/(30 – 10)
323  = -0.0004545
324  c2 = 1/2 * (x2*f"2(x1) – x1*f"2(x2))/(x2 – x1)
325  = 1/2 * (-30*0.063636 + 10*0.11818)/(30 – 10)
326  = -0.01818
327  b2 = ((y2 – y1) – c2*(x2^2 – x1^2) – d2*( x2^3 – x1^3))/(x2 – x1)
328  = ((150 – 130) + 0.01818*(302 – 102) + 0.0004545*(303 – 103))/(30 – 10)
329  = 2.31818
330  a2 = y1 – b2*x1 – c2*x1^2 – d2*x1^3
331  = 130 – 2.31818*10 + 0.01818*102 + 0.0004545*103
332  = 109.09
333  y2 = 109.09 + 2.31818x - 0.01818x^2 - 0.0004545x^3 for 10 <= x <= 30
334  */
335 
336 
337  int x;
338  long double a1, b1, c1, d1, a2, b2, c2, d2, fdx0, fddx0, fdx1, fdx2, fddx1, fddx2;
339  double x0 = data[0].x;
340  double y0 = data[0].y;
341  double x1 = data[1].x;
342  double y1 = data[1].y;
343  double x2 = data[2].x;
344  double y2 = data[2].y;
345  double x3 = data[3].x;
346  double y3 = data[3].y;
347 
348  double dx0 = x1 - x0;
349  double dy0 = y1 - y0;
350  double dx1 = x2 - x1;
351  double dy1 = y2 - y1;
352  double dx2 = x3 - x2;
353  double dy2 = y3 - y2;
354 
355  // First (leftmost) segment
356  fdx1 = 2.0 / ( dx1 / dy1 + dx0 / dy0 );
357  fdx0 = 3.0 / 2.0 * dy0 / dx0 - fdx1 / 2.0;
358 
359  fddx0 = -2.0 * (fdx1 + 2.0 * fdx0) / dx0 + 6.0 * dy0 / (dx0*dx0);
360  fddx1 = 2.0 * (2.0 * fdx1 + fdx0) / dx0 - 6.0 * dy0 / (dx0*dx0);
361  d1 = 1.0 / 6.0 * (fddx1 - fddx0) / dx0;
362  c1 = 1.0 / 2.0 * (x1 * fddx0 - x0 * fddx1) / dx0;
363  b1 = (dy0 - c1 * (x1* x1 - x0*x0) - d1 * (x1*x1*x1 - x0*x0*x0)) / dx0;
364  a1 = y0 - b1*x0 - c1*x0*x0 - d1*x0*x0*x0;
365 
366  // printf("dx0=%f, dy0=%f, dx1=%f, dy1=%f\n", dx0, dy0, dx1, dy1);
367  // printf("fdx0=%Lf, fdx1=%Lf, fddx0=%Lf, fddx1=%Lf\n", fdx0, fdx1, fddx0, fddx1);
368  // printf("a1=%Lf, b1=%Lf, c1=%Lf, d1=%Lf\n", a1, b1, c1, d1);
369 
370  // values from worked example: deltas rather arbitrary, I'm afraid
371  CPPUNIT_ASSERT_DOUBLES_EQUAL(30.0, a1, 0);
372  CPPUNIT_ASSERT_DOUBLES_EQUAL(14.09, b1, 0.001);
373  CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, c1, 0);
374  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.0409, d1, 0.00001);
375 
376  for (x = 0; x <= 10; x++) {
377  double v = a1 + b1*x + c1*x*x + d1*x*x*x;
378  char msg[64];
379  snprintf(msg, 64, "interpolating %d: v=%f, x=%f...\n", x, v, g[x]);
380  CPPUNIT_ASSERT_DOUBLES_EQUAL(v, g[x], 0.000004);
381  }
382 
383  // Second segment
384  fdx2 = 2.0 / ( dx2 / dy2 + dx1 / dy1 );
385 
386  fddx1 = -2.0 * (fdx2 + 2.0 * fdx1) / dx1 + 6.0 * dy1 / (dx1*dx1);
387  fddx2 = 2.0 * (2.0 * fdx2 + fdx1) / dx1 - 6.0 * dy1 / (dx1*dx1);
388  d2 = 1.0 / 6.0 * (fddx2 - fddx1) / dx1;
389  c2 = 1.0 / 2.0 * (x2 * fddx1 - x1 * fddx2) / dx1;
390  b2 = (dy1 - c2 * (x2*x2 - x1*x1) - d2 * (x2*x2*x2 - x1*x1*x1)) / dx1;
391  a2 = y1 - b2*x1 - c2*x1*x1 - d2*x1*x1*x1;
392 
393  // printf("dx0=%f, dy0=%f, dx1=%f, dy1=%f dx2=%f, dy2=%f\n", dx0, dy0, dx1, dy1, dx2, dy2);
394  // printf("fdx1=%Lf, fdx2=%Lf, fddx1=%Lf, fddx2=%Lf\n", fdx1, fdx2, fddx1, fddx2);
395  // printf("a2=%Lf, b2=%Lf, c2=%Lf, d2=%Lf\n", a2, b2, c2, d2);
396 
397  // values from worked example: deltas rather arbitrary, I'm afraid
398  CPPUNIT_ASSERT_DOUBLES_EQUAL(109.09, a2, 0.001);
399  CPPUNIT_ASSERT_DOUBLES_EQUAL(2.31818, b2, 0.00001);
400  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.01818, c2, 0.00001);
401  CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.0004545, d2, 0.0000001);
402 
403  for (x = 10; x <= 30; x++) {
404  double v = a2 + b2*x + c2*x*x + d2*x*x*x;
405  char msg[64];
406  snprintf(msg, 64, "interpolating %d: v=%f, x=%f...\n", x, v, g[x]);
407  CPPUNIT_ASSERT_DOUBLES_EQUAL(v, g[x], 0.000008);
408  }
409 }
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