526 lines
17 KiB
C++
526 lines
17 KiB
C++
#include "CurveTest.h"
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#include "evoral/ControlList.h"
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#include "evoral/Curve.h"
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#include <stdlib.h>
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CPPUNIT_TEST_SUITE_REGISTRATION (CurveTest);
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#if defined(PLATFORM_WINDOWS) && defined(COMPILER_MINGW)
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/* cppunit-1.13.2 uses assertion_traits<double>
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* sprintf( , "%.*g", precision, x)
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* to format a double. The actual comparison is performed on a string.
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* This is problematic with mingw/windows|wine, "%.*g" formatting fails.
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*
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* This quick hack compares float, however float compatisons are at most Y.MMMM+eXX,
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* the max precision needs to be limited. to the last mantissa digit.
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*
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* Anyway, actual maths is verified with Linux and OSX unit-tests,
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* and this needs to go to https://sourceforge.net/p/cppunit/bugs/
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*/
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#define MAXPREC(P) ((P) < .0005 ? .0005 : (P))
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#define CPPUNIT_ASSERT_DOUBLES_EQUAL_MESSAGE(M,A,B,P) CPPUNIT_ASSERT_EQUAL_MESSAGE(M, (float)rint ((A) / MAXPREC(P)),(float)rint ((B) / MAXPREC(P)))
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#define CPPUNIT_ASSERT_DOUBLES_EQUAL(A,B,P) CPPUNIT_ASSERT_EQUAL((float)rint ((A) / MAXPREC(P)),(float)rint ((B) / MAXPREC(P)))
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#endif
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using namespace Evoral;
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using namespace Temporal;
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// linear y = Y0 + YS * x ; with x = i * (X1 - X0) + X0; and i = [0..1023]
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#define VEC1024LINCMP(X0, X1, Y0, YS) \
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cl->curve ().get_vector ((X0), (X1), vec, 1024); \
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for (int i = 0; i < 1024; ++i) { \
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char msg[64]; \
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snprintf (msg, 64, "at i=%d (x0=%s, x1=%s, y0=%.1f, ys=%.3f)", \
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i, (X0).str().c_str(), (X1).str().c_str(), Y0, YS); \
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CPPUNIT_ASSERT_DOUBLES_EQUAL_MESSAGE ( \
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msg, \
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(Y0) + i * (YS), vec[i], \
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1e-24 \
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); \
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}
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void
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CurveTest::trivial ()
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{
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float vec[1024];
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std::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
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cl->create_curve ();
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timepos_t t1024 (1024.0);
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timepos_t t2047 (2047.0);
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// Empty curve
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cl->curve().get_vector (t1024, t2047, vec, 1024);
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for (int i = 0; i < 1024; ++i) {
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CPPUNIT_ASSERT_EQUAL (0.0f, vec[i]);
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}
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// Single point curve
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cl->fast_simple_add(timepos_t (0), 42.0);
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cl->curve().get_vector (t1024, t2047, vec, 1024);
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for (int i = 0; i < 1024; ++i) {
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CPPUNIT_ASSERT_EQUAL (42.0f, vec[i]);
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}
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}
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void
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CurveTest::rtGet ()
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{
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float vec[1024];
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timepos_t t1024 (1024.0);
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timepos_t t2047 (2047.0);
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// Create simple control list
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std::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
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cl->create_curve ();
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cl->fast_simple_add(timepos_t(0), 42.0);
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{
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// Write-lock list
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Glib::Threads::RWLock::WriterLock lm(cl->lock());
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// Attempt to get vector in RT (expect failure)
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CPPUNIT_ASSERT (!cl->curve().rt_safe_get_vector (t1024, t2047, vec, 1024));
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}
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// Attempt to get vector in RT (expect success)
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CPPUNIT_ASSERT (cl->curve().rt_safe_get_vector (t1024, t2047, vec, 1024));
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for (int i = 0; i < 1024; ++i) {
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CPPUNIT_ASSERT_EQUAL (42.0f, vec[i]);
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}
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}
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void
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CurveTest::twoPointLinear ()
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{
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float vec[1024];
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std::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
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cl->create_curve ();
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cl->set_interpolation (ControlList::Linear);
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timepos_t t0 (0);
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timepos_t t1024 (1024);
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timepos_t t2048 (2048);
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timepos_t t2047 (2047);
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timepos_t t2049 (2049);
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timepos_t t2056 (2056);
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timepos_t t4092 (4092);
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timepos_t t8192 (8192);
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// add two points to curve
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cl->fast_simple_add (t0 , 2048.0);
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cl->fast_simple_add (t8192, 4096.0);
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cl->curve ().get_vector (t1024, t2047, vec, 1024);
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VEC1024LINCMP (t1024, t2047, 2304.f, .25f);
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//VEC1024LINCMP (t2048, timepos_t (2559.5), 2560.f, .125f);
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VEC1024LINCMP (t0, t4092, 2048.f, 1.f);
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// greetings to tartina
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cl->curve ().get_vector (t2048, t2048, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048..2048", 2560.f, vec[0]);
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/* XXX WHAT DO WE EXPECT WITH veclen=1 AND x1 > x0 ? */
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#if 0
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/* .. interpolated value at (x1+x0)/2 */
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cl->curve ().get_vector (2048.0, t2049, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048-2049", 2560.125f, vec[0]);
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cl->curve ().get_vector (2048.0, 2056.0, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 2048-2049", 2561.f, vec[0]);
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#else
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/* .. value at x0 */
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cl->curve ().get_vector (t2048, t2049, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 , 2048..2049", 2560.f, vec[0]);
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cl->curve ().get_vector (t2048, t2056, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 , 2048..2049", 2560.f, vec[0]);
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#endif
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cl->curve ().get_vector (t2048, t2048, vec, 2);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2048 @ 0", 2560.f, vec[0]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2048 @ 1", 2560.f, vec[1]);
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cl->curve ().get_vector (t2048, t2056, vec, 2);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2056 @ 0", 2560.f, vec[0]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=2 , 2048..2056 @ 0", 2562.f, vec[1]);
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cl->curve ().get_vector (t2048, t2056, vec, 3);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 0", 2560.f, vec[0]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 1", 2561.f, vec[1]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 , 2048..2056 @ 2", 2562.f, vec[2]);
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/* check out-of range..
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* we expect the first and last value - no interpolation
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*/
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timepos_t tm1 (-1);
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timepos_t tm999 (-999);
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timepos_t t9998 (9998);
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timepos_t t9999 (9999);
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cl->curve ().get_vector (tm1, tm1, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ -1", 2048.f, vec[0]);
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cl->curve ().get_vector (t9999, t9999, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 9999", 4096.f, vec[0]);
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cl->curve ().get_vector (tm999, t0, vec, 13);
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for (int i = 0; i < 13; ++i) {
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=13 @ -999..0", 2048.f, vec[i]);
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}
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cl->curve ().get_vector (t9998, t9999, vec, 8);
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for (int i = 0; i < 8; ++i) {
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=8 @ 9998..9999", 4096.f, vec[i]);
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}
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}
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void
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CurveTest::threePointLinear ()
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{
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float vec[4];
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std::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
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cl->create_curve ();
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cl->set_interpolation (ControlList::Linear);
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timepos_t t0 (0);
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timepos_t t50 (50);
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timepos_t t60 (60);
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timepos_t t80 (80);
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timepos_t t100 (100);
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timepos_t t130 (130);
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timepos_t t150 (150);
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timepos_t t160 (160);
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timepos_t t200 (200);
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// add 3 points to curve
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cl->fast_simple_add ( t0 , 2.0);
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cl->fast_simple_add (t100 , 4.0);
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cl->fast_simple_add (t200 , 0.0);
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cl->curve ().get_vector (t50, t60, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 50", 3.f, vec[0]);
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cl->curve ().get_vector (t100, t100, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 100", 4.f, vec[0]);
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cl->curve ().get_vector (t150, t150, vec, 1);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=1 @ 150", 2.f, vec[0]);
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cl->curve ().get_vector (t130, t150, vec, 3);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 0", 2.8f, vec[0]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 2", 2.4f, vec[1]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 130..150 @ 3", 2.0f, vec[2]);
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cl->curve ().get_vector (t80, t160, vec, 3);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 0", 3.6f, vec[0]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 2", 3.2f, vec[1]);
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CPPUNIT_ASSERT_EQUAL_MESSAGE ("veclen=3 80..160 @ 3", 1.6f, vec[2]);
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}
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void
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CurveTest::threePointDiscete ()
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{
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std::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
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cl->set_interpolation (ControlList::Discrete);
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timepos_t t0 (0);
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timepos_t t80 (80);
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timepos_t t100 (100);
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timepos_t t120 (120);
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timepos_t t160 (160);
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timepos_t t200 (200);
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// add 3 points to curve
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cl->fast_simple_add ( t0 , 2.0);
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cl->fast_simple_add (t100 , 4.0);
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cl->fast_simple_add (t200 , 0.0);
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t160));
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cl->set_interpolation (ControlList::Linear);
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CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(t160));
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}
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void
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CurveTest::ctrlListEval ()
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{
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std::shared_ptr<Evoral::ControlList> cl = TestCtrlList();
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timepos_t t0 (0);
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timepos_t t80 (80);
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timepos_t t100 (100);
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timepos_t t120 (120);
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timepos_t t160 (160);
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timepos_t t200 (200);
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timepos_t t250 (250);
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timepos_t t300 (300);
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timepos_t t350 (350);
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timepos_t t400 (400);
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timepos_t t999 (999);
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cl->fast_simple_add (t0 , 2.0);
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cl->set_interpolation (ControlList::Discrete);
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t160));
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cl->set_interpolation (ControlList::Linear);
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t160));
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cl->fast_simple_add (t100 , 4.0);
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cl->set_interpolation (ControlList::Discrete);
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t160));
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cl->set_interpolation (ControlList::Linear);
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CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t160));
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cl->fast_simple_add (t200 , 0.0);
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cl->set_interpolation (ControlList::Discrete);
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t160));
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cl->set_interpolation (ControlList::Linear);
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CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(t160));
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cl->fast_simple_add (t300 , 8.0);
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cl->set_interpolation (ControlList::Discrete);
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t160));
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CPPUNIT_ASSERT_EQUAL(0.0, cl->unlocked_eval(t250));
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CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(t999));
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cl->set_interpolation (ControlList::Linear);
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CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(t160));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t250));
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CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(t999));
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cl->fast_simple_add (t400 , 9.0);
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cl->set_interpolation (ControlList::Discrete);
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CPPUNIT_ASSERT_EQUAL(2.0, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t160));
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CPPUNIT_ASSERT_EQUAL(0.0, cl->unlocked_eval(t250));
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CPPUNIT_ASSERT_EQUAL(8.0, cl->unlocked_eval(t350));
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CPPUNIT_ASSERT_EQUAL(9.0, cl->unlocked_eval(t999));
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cl->set_interpolation (ControlList::Linear);
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CPPUNIT_ASSERT_EQUAL(3.6, cl->unlocked_eval(t80));
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CPPUNIT_ASSERT_EQUAL(3.2, cl->unlocked_eval(t120));
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CPPUNIT_ASSERT_EQUAL(1.6, cl->unlocked_eval(t160));
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CPPUNIT_ASSERT_EQUAL(4.0, cl->unlocked_eval(t250));
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CPPUNIT_ASSERT_EQUAL(8.5, cl->unlocked_eval(t350));
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CPPUNIT_ASSERT_EQUAL(9.0, cl->unlocked_eval(t999));
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}
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void
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CurveTest::constrainedCubic ()
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{
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struct point {
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int x, y;
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};
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static const struct point data[] = {
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/* values from worked example in www.korf.co.uk/spline.pdf */
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{ 0, 30 },
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{ 10, 130 },
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{ 30, 150 },
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{ 50, 150 },
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{ 70, 170 },
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{ 90, 220 },
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{ 100, 320 },
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};
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int32_t type = 0;
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Evoral::Parameter p(type);
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Evoral::ParameterDescriptor pd;
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pd.lower = 5;
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pd.upper = 325;
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Evoral::ControlList l(p, pd, Temporal::TimeDomainProvider (AudioTime));
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size_t i;
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l.set_interpolation(Evoral::ControlList::Curved);
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for (i=0; i<sizeof(data)/sizeof(data[0]); i++) {
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l.add (timepos_t (data[i].x), data[i].y);
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}
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Evoral::Curve curve(l);
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float f[121];
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curve.get_vector(timepos_t (-10), timepos_t (110), f, 121);
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const float *g = &f[10]; /* so g starts at x==0 */
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/* given points - should be exactly equal */
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CPPUNIT_ASSERT_EQUAL( 30.0f, g[-10]);
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CPPUNIT_ASSERT_EQUAL( 30.0f, g[ 0]);
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CPPUNIT_ASSERT_EQUAL(130.0f, g[ 10]);
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CPPUNIT_ASSERT_EQUAL(150.0f, g[ 30]);
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CPPUNIT_ASSERT_EQUAL(150.0f, g[ 40]);
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CPPUNIT_ASSERT_EQUAL(150.0f, g[ 50]);
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CPPUNIT_ASSERT_EQUAL(320.0f, g[100]);
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CPPUNIT_ASSERT_EQUAL(320.0f, g[110]);
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/*
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First segment, i=1, for 0 <= x <= 10
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f'1(x1) = 2/((x2 – x1)/(y2 – y1) + (x1 – x0)/(y1 – y0))
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= 2/((30 – 10)/(150 – 130) + (10 – 0)/(130 – 30))
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= 1.8181
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f'1(x0) = 3/2*(y1 – y0)/(x1 – x0) - f'1(x1)/2
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= 3/2*(130 – 30)/(10 – 0) – 1.818/2
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= 14.0909
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f"1(x0) = -2*(f'1(x1) + 2* f'1(x0))/(x1 – x0) + 6*(y1 – y0)/ (x1 – x0)^2
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= -2*(1.8181 + 2*14.0909)/(10 – 0) + 6*(130 – 30)/(10 – 0)^2
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= 0
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f"1(x1) = 2*(2*f'1(x1) + f'1(x0))/(x1 – x0) - 6*(y1 – y0)/ (x1 – x0)^2
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= 2*(2*1.818 + 14.0909)/(10 – 0) – 6*(130 – 30)/(10 – 0)^2
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= -2.4545
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d1 = 1/6 * (f"1(x1) - f"1(x0))/(x1 – x0)
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= 1/6 * (-2.4545 – 0)/(10 – 0)
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= -0.0409
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c1 = 1/2 * (x1*f"1(x0) – x0*f"1(x1))/(x1 – x0)
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= 1/2 * (10*0 – 0*1.8181)/(10 – 0)
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= 0
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b1 = ((y1 – y0) – c1*(x21 – x20) – d1*( x31 – x30))/(x1 – x0)
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= ((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, 0.1);
|
||
CPPUNIT_ASSERT_DOUBLES_EQUAL(14.09, b1, 0.01);
|
||
CPPUNIT_ASSERT_DOUBLES_EQUAL(0.0, c1, 0.1);
|
||
CPPUNIT_ASSERT_DOUBLES_EQUAL(-0.0409, d1, 0.0001);
|
||
|
||
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, 0.01);
|
||
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);
|
||
}
|
||
}
|