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livetrax/libs/evoral/test/CurveTest.cpp

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minimalistic Evoral::Curve Unit Test.
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#include "CurveTest.hpp"
#include "evoral/ControlList.hpp"
#include "evoral/Curve.hpp"
#include <stdlib.h>
CPPUNIT_TEST_SUITE_REGISTRATION (CurveTest);
using namespace Evoral;
2-point Curve Linear Interpolation Test
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// linear y = Y0 + YS * x ; with x = i * (X1 - X0) + X0; and i = [0..1023]
#define VEC1024LINCMP(X0, X1, Y0, YS) \
cl->curve ().get_vector ((X0), (X1), vec, 1024); \
for (int i = 0; i < 1024; ++i) { \
char msg[64]; \
snprintf (msg, 64, "at i=%d (x0=%.1f, x1=%.1f, y0=%.1f, ys=%.3f)", \
i, X0, X1, Y0, YS); \
CPPUNIT_ASSERT_DOUBLES_EQUAL_MESSAGE ( \
msg, \
(Y0) + i * (YS), vec[i], \
1e-24 \
); \
}
minimalistic Evoral::Curve Unit Test.
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void
2-point Curve Linear Interpolation Test
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CurveTest::twoPointLinear ()
minimalistic Evoral::Curve Unit Test.
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{
float vec[1024];
2-point Curve Linear Interpolation Test
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boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
cl->create_curve ();
cl->set_interpolation (ControlList::Linear);
// add two points to curve
cl->fast_simple_add ( 0.0 , 2048.0);
cl->fast_simple_add (8192.0 , 4096.0);
cl->curve ().get_vector (1024.0, 2047.0, vec, 1024);
VEC1024LINCMP (1024.0, 2047.0, 2304.f, .25f);
VEC1024LINCMP (2048.0, 2559.5, 2560.f, .125f);
VEC1024LINCMP ( 0.0, 4092.0, 2048.f, 1.f);
// greetings to tartina
cl->curve ().get_vector (2048.0, 2048.0, vec, 1);
few more basic ControList/Curve Tests
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048..2048", 2560.f, vec[0]);
2-point Curve Linear Interpolation Test
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/* XXX WHAT DO WE EXPECT WITH veclen=1 AND x1 > x0 ? */
#if 0
/* .. interpolated value at (x1+x0)/2 */
cl->curve ().get_vector (2048.0, 2049.0, vec, 1);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048-2049", 2560.125f, vec[0]);
minimalistic Evoral::Curve Unit Test.
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2-point Curve Linear Interpolation Test
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cl->curve ().get_vector (2048.0, 2056.0, vec, 1);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048-2049", 2561.f, vec[0]);
#else
/* .. value at x0 */
cl->curve ().get_vector (2048.0, 2049.0, vec, 1);
few more basic ControList/Curve Tests
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 , 2048..2049", 2560.f, vec[0]);
minimalistic Evoral::Curve Unit Test.
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2-point Curve Linear Interpolation Test
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cl->curve ().get_vector (2048.0, 2056.0, vec, 1);
few more basic ControList/Curve Tests
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 , 2048..2049", 2560.f, vec[0]);
2-point Curve Linear Interpolation Test
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#endif
minimalistic Evoral::Curve Unit Test.
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2-point Curve Linear Interpolation Test
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cl->curve ().get_vector (2048.0, 2048.0, vec, 2);
few more basic ControList/Curve Tests
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2048 @ 0", 2560.f, vec[0]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2048 @ 1", 2560.f, vec[1]);
minimalistic Evoral::Curve Unit Test.
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2-point Curve Linear Interpolation Test
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cl->curve ().get_vector (2048.0, 2056.0, vec, 2);
few more basic ControList/Curve Tests
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2056 @ 0", 2560.f, vec[0]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2056 @ 0", 2562.f, vec[1]);
minimalistic Evoral::Curve Unit Test.
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2-point Curve Linear Interpolation Test
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cl->curve ().get_vector (2048.0, 2056.0, vec, 3);
few more basic ControList/Curve Tests
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 0", 2560.f, vec[0]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 1", 2561.f, vec[1]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 2", 2562.f, vec[2]);
/* check out-of range..
* we expect the first and last value - no interpolation
*/
cl->curve ().get_vector (-1, -1, vec, 1);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ -1", 2048.f, vec[0]);
cl->curve ().get_vector (9999.0, 9999.0, vec, 1);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 9999", 4096.f, vec[0]);
cl->curve ().get_vector (-999.0, 0, vec, 13);
for (int i = 0; i < 13; ++i) {
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=13 @ -999..0", 2048.f, vec[i]);
}
cl->curve ().get_vector (9998.0, 9999.0, vec, 8);
for (int i = 0; i < 8; ++i) {
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=8 @ 9998..9999", 4096.f, vec[i]);
}
}
void
CurveTest::threePointLinear ()
{
float vec[4];
boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
cl->create_curve ();
cl->set_interpolation (ControlList::Linear);
// add 3 points to curve
cl->fast_simple_add ( 0.0 , 2.0);
cl->fast_simple_add ( 100.0 , 4.0);
cl->fast_simple_add ( 200.0 , 0.0);
cl->curve ().get_vector (50.0, 60.0, vec, 1);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 50", 3.f, vec[0]);
cl->curve ().get_vector (100.0, 100.0, vec, 1);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 100", 4.f, vec[0]);
cl->curve ().get_vector (150.0, 150.0, vec, 1);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 150", 2.f, vec[0]);
cl->curve ().get_vector (130.0, 150.0, vec, 3);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 0", 2.8f, vec[0]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 2", 2.4f, vec[1]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 3", 2.0f, vec[2]);
cl->curve ().get_vector (80.0, 160.0, vec, 3);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 0", 3.6f, vec[0]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 2", 3.2f, vec[1]);
CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 3", 1.6f, vec[2]);
}
void
CurveTest::threePointDiscete ()
{
boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
cl->set_interpolation (ControlList::Discrete);
// add 3 points to curve
cl->fast_simple_add ( 0.0 , 2.0);
cl->fast_simple_add ( 100.0 , 4.0);
cl->fast_simple_add ( 200.0 , 0.0);
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
cl->set_interpolation (ControlList::Linear);
CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
}
void
CurveTest::ctrlListEval ()
{
boost::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
cl->fast_simple_add ( 0.0 , 2.0);
cl->set_interpolation (ControlList::Discrete);
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(160.));
cl->set_interpolation (ControlList::Linear);
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(160.));
cl->fast_simple_add ( 100.0 , 4.0);
cl->set_interpolation (ControlList::Discrete);
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
cl->set_interpolation (ControlList::Linear);
CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
cl->fast_simple_add ( 200.0 , 0.0);
cl->set_interpolation (ControlList::Discrete);
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
cl->set_interpolation (ControlList::Linear);
CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
cl->fast_simple_add ( 300.0 , 8.0);
cl->set_interpolation (ControlList::Discrete);
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
CPPUNIT_ASSERT_EQUAL(0.0, cl->unlocked_eval(250.));
CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(999.));
cl->set_interpolation (ControlList::Linear);
CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(250.));
CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(999.));
cl->fast_simple_add ( 400.0 , 9.0);
cl->set_interpolation (ControlList::Discrete);
CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(160.));
CPPUNIT_ASSERT_EQUAL(0.0, cl->unlocked_eval(250.));
CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(350.));
CPPUNIT_ASSERT_EQUAL(9.0, cl->unlocked_eval(999.));
cl->set_interpolation (ControlList::Linear);
CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(80.));
CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(120.));
CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(160.));
CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(250.));
CPPUNIT_ASSERT_EQUAL(8.5, cl->unlocked_eval(350.));
CPPUNIT_ASSERT_EQUAL(9.0, cl->unlocked_eval(999.));
minimalistic Evoral::Curve Unit Test.
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}
Add a test for the constrained cubic interpolation of Evoral::Curve Add a test, based on the worked example in www.korf.co.uk/spline.pdf, for the constrained cubic spline interpolation. The delta values for the float comparisons are rather arbitrary, I'm sorry to say: they're basically chosen so that everything passes.
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void
CurveTest::constrainedCubic ()
{
struct point {
int x, y;
};
static const struct point data[] = {
/* values from worked example in www.korf.co.uk/spline.pdf */
{ 0, 30 },
{ 10, 130 },
{ 30, 150 },
{ 50, 150 },
{ 70, 170 },
{ 90, 220 },
{ 100, 320 },
};
int32_t type = 0;
Evoral::Parameter p(type);
Evoral::ParameterDescriptor pd;
Evoral::ControlList l(p,pd);
size_t i;
l.set_interpolation(Evoral::ControlList::Curved);
for (i=0; i<sizeof(data)/sizeof(data[0]); i++) {
l.add (data[i].x, data[i].y);
}
Evoral::Curve curve(l);
float f[121];
curve.get_vector(-10, 110, f, 121);
const float *g = &f[10]; /* so g starts at x==0 */
/* given points - should be exactly equal */
CPPUNIT_ASSERT_EQUAL( 30.0f, g[-10]);
CPPUNIT_ASSERT_EQUAL( 30.0f, g[ 0]);
CPPUNIT_ASSERT_EQUAL(130.0f, g[ 10]);
CPPUNIT_ASSERT_EQUAL(150.0f, g[ 30]);
CPPUNIT_ASSERT_EQUAL(150.0f, g[ 40]);
CPPUNIT_ASSERT_EQUAL(150.0f, g[ 50]);
CPPUNIT_ASSERT_EQUAL(320.0f, g[100]);
CPPUNIT_ASSERT_EQUAL(320.0f, g[110]);
/*
First segment, i=1, for 0 <= x <= 10
f'1(x1) = 2/((x2 – x1)/(y2 – y1) + (x1 – x0)/(y1 – y0))
= 2/((30 – 10)/(150 – 130) + (10 – 0)/(130 – 30))
= 1.8181
f'1(x0) = 3/2*(y1 – y0)/(x1 – x0) - f'1(x1)/2
= 3/2*(130 – 30)/(10 – 0) – 1.818/2
= 14.0909
f"1(x0) = -2*(f'1(x1) + 2* f'1(x0))/(x1 – x0) + 6*(y1 – y0)/ (x1 – x0)^2
= -2*(1.8181 + 2*14.0909)/(10 – 0) + 6*(130 – 30)/(10 – 0)^2
= 0
f"1(x1) = 2*(2*f'1(x1) + f'1(x0))/(x1 – x0) - 6*(y1 – y0)/ (x1 – x0)^2
= 2*(2*1.818 + 14.0909)/(10 – 0) – 6*(130 – 30)/(10 – 0)^2
= -2.4545
d1 = 1/6 * (f"1(x1) - f"1(x0))/(x1 – x0)
= 1/6 * (-2.4545 – 0)/(10 – 0)
= -0.0409
c1 = 1/2 * (x1*f"1(x0) – x0*f"1(x1))/(x1 – x0)
= 1/2 * (10*0 – 0*1.8181)/(10 – 0)
= 0
b1 = ((y1 – y0) – c1*(x21 – x20) – d1*( x31 – x30))/(x1 – x0)
= ((130 – 30) – 0*(102 – 02) + 0.0409*(103 – 03))/(10 – 0)
= 14.09
a1 = y0 – b1*x0 – c1*x20 – d1*x30
= 30
y1 = 30 + 14.09x - 0.0409x3 for 0 <= x <= 10
*/
/*
Second segment, i=2, for 10 <= x <= 30
f'2(x2) = 2/((x3 – x2)/(y3 – y2) + (x2 – x1)/(y2 – y1))
= 2/((50 – 30)/(150 – 150) + (30 – 10)/(150 – 130))
= 0
f'2(x1) = 2/((x2 – x1)/(y2 – y1) + (x1 – x0)/(y1 – y0))
= 1.8181
f"2(x1) = -2*(f'2(x2) + 2* f'2(x1))/(x2 – x1) + 6*(y2 – y1)/ (x2 – x1)^2
= -2*(0 + 2*1.8181)/(30 – 10) + 6*(150 – 130)/(30 – 10)2
= -0.063636
f"2(x2) = 2*(2*f'2(x2) + f'2(x1))/(x2 – x1) - 6*(y2 – y1)/ (x2 – x1)^2
= 2*(2*0 + 1.8181)/(30 – 10) – 6*(150 – 130)/(30 – 10)^2
= -0.11818
d2 = 1/6 * (f"2(x2) - f"2(x1))/(x2 – x1)
= 1/6 * (-0.11818 + 0.063636)/(30 – 10)
= -0.0004545
c2 = 1/2 * (x2*f"2(x1) – x1*f"2(x2))/(x2 – x1)
= 1/2 * (-30*0.063636 + 10*0.11818)/(30 – 10)
= -0.01818
b2 = ((y2 – y1) – c2*(x2^2 – x1^2) – d2*( x2^3 – x1^3))/(x2 – x1)
= ((150 – 130) + 0.01818*(302 – 102) + 0.0004545*(303 – 103))/(30 – 10)
= 2.31818
a2 = y1 – b2*x1 – c2*x1^2 – d2*x1^3
= 130 – 2.31818*10 + 0.01818*102 + 0.0004545*103
= 109.09
y2 = 109.09 + 2.31818x - 0.01818x^2 - 0.0004545x^3 for 10 <= x <= 30
*/
int x;
long double a1, b1, c1, d1, a2, b2, c2, d2, fdx0, fddx0, fdx1, fdx2, fddx1, fddx2;
double x0 = data[0].x;
double y0 = data[0].y;
double x1 = data[1].x;
double y1 = data[1].y;
double x2 = data[2].x;
double y2 = data[2].y;
double x3 = data[3].x;
double y3 = data[3].y;
double dx0 = x1 - x0;
double dy0 = y1 - y0;
double dx1 = x2 - x1;
double dy1 = y2 - y1;
double dx2 = x3 - x2;
double dy2 = y3 - y2;
// First (leftmost) segment
fdx1 = 2.0 / ( dx1 / dy1 + dx0 / dy0 );
fdx0 = 3.0 / 2.0 * dy0 / dx0 - fdx1 / 2.0;
fddx0 = -2.0 * (fdx1 + 2.0 * fdx0) / dx0 + 6.0 * dy0 / (dx0*dx0);
fddx1 = 2.0 * (2.0 * fdx1 + fdx0) / dx0 - 6.0 * dy0 / (dx0*dx0);
d1 = 1.0 / 6.0 * (fddx1 - fddx0) / dx0;
c1 = 1.0 / 2.0 * (x1 * fddx0 - x0 * fddx1) / dx0;
b1 = (dy0 - c1 * (x1* x1 - x0*x0) - d1 * (x1*x1*x1 - x0*x0*x0)) / dx0;
a1 = y0 - b1*x0 - c1*x0*x0 - d1*x0*x0*x0;
// printf("dx0=%f, dy0=%f, dx1=%f, dy1=%f\n", dx0, dy0, dx1, dy1);
// printf("fdx0=%Lf, fdx1=%Lf, fddx0=%Lf, fddx1=%Lf\n", fdx0, fdx1, fddx0, fddx1);
// printf("a1=%Lf, b1=%Lf, c1=%Lf, d1=%Lf\n", a1, b1, c1, d1);
// values from worked example: deltas rather arbitrary, I'm afraid
CPPUNIT_ASSERT_DOUBLES_EQUAL(30.0, a1, 0);
CPPUNIT_ASSERT_DOUBLES_EQUAL(14.09, b1, 0.001);
CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, c1, 0);
CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.0409, d1, 0.00001);
for (x = 0; x <= 10; x++) {
double v = a1 + b1*x + c1*x*x + d1*x*x*x;
char msg[64];
snprintf(msg, 64, "interpolating %d: v=%f, x=%f...\n", x, v, g[x]);
CPPUNIT_ASSERT_DOUBLES_EQUAL(v, g[x], 0.000004);
}
// Second segment
fdx2 = 2.0 / ( dx2 / dy2 + dx1 / dy1 );
fddx1 = -2.0 * (fdx2 + 2.0 * fdx1) / dx1 + 6.0 * dy1 / (dx1*dx1);
fddx2 = 2.0 * (2.0 * fdx2 + fdx1) / dx1 - 6.0 * dy1 / (dx1*dx1);
d2 = 1.0 / 6.0 * (fddx2 - fddx1) / dx1;
c2 = 1.0 / 2.0 * (x2 * fddx1 - x1 * fddx2) / dx1;
b2 = (dy1 - c2 * (x2*x2 - x1*x1) - d2 * (x2*x2*x2 - x1*x1*x1)) / dx1;
a2 = y1 - b2*x1 - c2*x1*x1 - d2*x1*x1*x1;
// printf("dx0=%f, dy0=%f, dx1=%f, dy1=%f dx2=%f, dy2=%f\n", dx0, dy0, dx1, dy1, dx2, dy2);
// printf("fdx1=%Lf, fdx2=%Lf, fddx1=%Lf, fddx2=%Lf\n", fdx1, fdx2, fddx1, fddx2);
// printf("a2=%Lf, b2=%Lf, c2=%Lf, d2=%Lf\n", a2, b2, c2, d2);
// values from worked example: deltas rather arbitrary, I'm afraid
CPPUNIT_ASSERT_DOUBLES_EQUAL(109.09, a2, 0.001);
CPPUNIT_ASSERT_DOUBLES_EQUAL(2.31818, b2, 0.00001);
CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.01818, c2, 0.00001);
CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.0004545, d2, 0.0000001);
for (x = 10; x <= 30; x++) {
double v = a2 + b2*x + c2*x*x + d2*x*x*x;
char msg[64];
snprintf(msg, 64, "interpolating %d: v=%f, x=%f...\n", x, v, g[x]);
CPPUNIT_ASSERT_DOUBLES_EQUAL(v, g[x], 0.000008);
}
}
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