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#include "testing.h"
#include <iostream>
#include <2geom/bezier.h>
#include <2geom/sbasis.h>
#include <2geom/sbasis-to-bezier.h>
#include <vector>
#include <iterator>
#include <glib.h>
using namespace std;
using namespace Geom;
bool are_equal(SBasis const &A, SBasis const &B) {
int maxSize = max(A.size(), B.size());
double t = 0., dt = 1./maxSize;
for(int i = 0; i <= maxSize; i++) {
EXPECT_FLOAT_EQ(A.valueAt(t), B.valueAt(t));// return false;
t += dt;
}
return true;
}
class SBasisTest : public ::testing::Test {
protected:
friend class Geom::SBasis;
SBasisTest()
: zero(fragments[0])
, unit(fragments[1])
, hump(fragments[2])
, wiggle(fragments[3])
{
zero = SBasis(Bezier(0.0).toSBasis());
unit = SBasis(Bezier(0.0,1.0).toSBasis());
hump = SBasis(Bezier(0,1,0).toSBasis());
wiggle = SBasis(Bezier(0,1,-2,3).toSBasis());
}
SBasis fragments[4];
SBasis &zero, &unit, &hump, &wiggle;
};
TEST_F(SBasisTest, UnitTests) {
EXPECT_TRUE(Bezier(0,0,0,0).toSBasis().isZero());
EXPECT_TRUE(Bezier(0,1,2,3).toSBasis().isFinite());
// note: "size" of sbasis equals half the number of coefficients
EXPECT_EQ(2u, Bezier(0,2,4,5).toSBasis().size());
EXPECT_EQ(2u, hump.size());
}
TEST_F(SBasisTest, ValueAt) {
EXPECT_EQ(0.0, wiggle.at0());
EXPECT_EQ(3.0, wiggle.at1());
EXPECT_EQ(0.0, wiggle.valueAt(0.5));
EXPECT_EQ(0.0, wiggle(0.5));
}
TEST_F(SBasisTest, MultiDerivative) {
vector<double> vnd = wiggle.valueAndDerivatives(0.5, 5);
expect_array((const double[]){0,0,12,72,0,0}, vnd);
}
/*
TEST_F(SBasisTest, DegreeElevation) {
EXPECT_TRUE(are_equal(wiggle, wiggle));
SBasis Q = wiggle;
SBasis P = Q.elevate_degree();
EXPECT_EQ(P.size(), Q.size()+1);
//EXPECT_EQ(0, P.forward_difference(1)[0]);
EXPECT_TRUE(are_equal(Q, P));
Q = wiggle;
P = Q.elevate_to_degree(10);
EXPECT_EQ(10, P.order());
EXPECT_TRUE(are_equal(Q, P));
//EXPECT_EQ(0, P.forward_difference(10)[0]);
}*/
//std::pair<SBasis, SBasis > subdivide(Coord t);
SBasis linear_root(double t) {
return SBasis(Linear(0-t, 1-t));
}
SBasis array_roots(vector<double> x) {
SBasis b(1);
for(double i : x) {
b = multiply(b, linear_root(i));
}
return b;
}
/*TEST_F(SBasisTest, Deflate) {
SBasis b = array_roots(vector_from_array((const double[]){0,0.25,0.5}));
EXPECT_FLOAT_EQ(0, b.at0());
b = b.deflate();
EXPECT_FLOAT_EQ(0, b.valueAt(0.25));
b = b.subdivide(0.25).second;
EXPECT_FLOAT_EQ(0, b.at0());
b = b.deflate();
const double rootposition = (0.5-0.25) / (1-0.25);
EXPECT_FLOAT_EQ(0, b.valueAt(rootposition));
b = b.subdivide(rootposition).second;
EXPECT_FLOAT_EQ(0, b.at0());
}*/
TEST_F(SBasisTest, Roots) {
expect_array((const double[]){0, 0.5, 0.5}, roots(wiggle));
// The results of our rootfinding are at the moment fairly inaccurate.
double eps = 5e-4;
vector<vector<double> > tests;
tests.push_back(vector_from_array((const double[]){0}));
tests.push_back(vector_from_array((const double[]){0.5}));
tests.push_back(vector_from_array((const double[]){0.25,0.75}));
tests.push_back(vector_from_array((const double[]){0.5,0.5}));
tests.push_back(vector_from_array((const double[]){0, 0.2, 0.6,0.6, 1}));
tests.push_back(vector_from_array((const double[]){.1,.2,.3,.4,.5,.6}));
tests.push_back(vector_from_array((const double[]){0.25,0.25,0.25,0.75,0.75,0.75}));
for(auto & test : tests) {
SBasis b = array_roots(test);
std::cout << test << ": " << b << std::endl;
std::cout << roots(b) << std::endl;
EXPECT_vector_near(test, roots(b), eps);
}
vector<Linear> broken;
broken.emplace_back(0, 42350.1);
broken.emplace_back(-71082.3, -67071.5);
broken.emplace_back(1783.41, 796047);
SBasis b(broken);
Bezier bz;
sbasis_to_bezier(bz, b);
cout << "roots(SBasis(broken))\n";
for(int i = 0; i < 10; i++) {
double t = i*0.01 + 0.1;
cout << b(t) << "," << bz(t) << endl;
}
cout << roots(b) << endl;
EXPECT_EQ(0, bz[0]);
//bz = bz.deflate();
cout << bz << endl;
cout << bz.roots() << endl;
}
TEST_F(SBasisTest, Subdivide) {
std::vector<std::pair<SBasis, double> > errors;
for (unsigned i = 0; i < 10000; ++i) {
double t = g_random_double_range(0, 1e-6);
for (auto & input : fragments) {
std::pair<SBasis, SBasis> result;
result.first = portion(input, 0, t);
result.second = portion(input, t, 1);
// the endpoints must correspond exactly
EXPECT_EQ(result.first.at0(), input.at0());
EXPECT_EQ(result.first.at1(), result.second.at0());
EXPECT_EQ(result.second.at1(), input.at1());
// ditto for valueAt
EXPECT_EQ(result.first.valueAt(0), input.valueAt(0));
EXPECT_EQ(result.first.valueAt(1), result.second.valueAt(0));
EXPECT_EQ(result.second.valueAt(1), input.valueAt(1));
if (result.first.at1() != result.second.at0()) {
errors.emplace_back(input, t);
}
}
}
if (!errors.empty()) {
std::cout << "Found " << errors.size() << " subdivision errors" << std::endl;
for (unsigned i = 0; i < errors.size(); ++i) {
std::cout << "Error #" << i << ":\n"
<< "SBasis: " << errors[i].first << "\n"
<< "t: " << format_coord_nice(errors[i].second) << std::endl;
}
}
}
TEST_F(SBasisTest, Reverse) {
SBasis reverse_wiggle = reverse(wiggle);
EXPECT_EQ(reverse_wiggle.at0(), wiggle.at1());
EXPECT_EQ(reverse_wiggle.at1(), wiggle.at0());
EXPECT_EQ(reverse_wiggle.valueAt(0.5), wiggle.valueAt(0.5));
EXPECT_EQ(reverse_wiggle.valueAt(0.25), wiggle.valueAt(0.75));
EXPECT_TRUE(are_equal(reverse(reverse_wiggle), wiggle));
}
TEST_F(SBasisTest,Operators) {
//cout << "scalar operators\n";
//cout << hump + 3 << endl;
//cout << hump - 3 << endl;
//cout << hump*3 << endl;
//cout << hump/3 << endl;
//cout << "SBasis derivative(const SBasis & a);\n";
//std::cout << derivative(hump) <<std::endl;
//std::cout << integral(hump) <<std::endl;
EXPECT_TRUE(are_equal(derivative(integral(wiggle)), wiggle));
//std::cout << derivative(integral(hump)) << std::endl;
expect_array((const double []){0.5}, roots(derivative(hump)));
EXPECT_TRUE(bounds_fast(hump)->contains(Interval(0,hump.valueAt(0.5))));
EXPECT_EQ(Interval(0,hump.valueAt(0.5)), *bounds_exact(hump));
Interval tight_local_bounds(min(hump.valueAt(0.3),hump.valueAt(0.6)),
hump.valueAt(0.5));
EXPECT_TRUE(bounds_local(hump, Interval(0.3, 0.6))->contains(tight_local_bounds));
SBasis Bs[] = {unit, hump, wiggle};
for(auto B : Bs) {
SBasis product = multiply(B, B);
for(int i = 0; i <= 16; i++) {
double t = i/16.0;
double b = B.valueAt(t);
EXPECT_FLOAT_EQ(b*b, product.valueAt(t));
}
}
}
TEST_F(SBasisTest, ToCubicBezier)
{
vector<double> params = { 0, 1, -2, 3 };
D2<SBasis> sb(wiggle, wiggle);
vector<Point> bz;
sbasis_to_cubic_bezier(bz, sb);
for (int i = 0; i < params.size(); i++) {
EXPECT_FLOAT_EQ(bz[i][0], params[i]);
EXPECT_FLOAT_EQ(bz[i][1], params[i]);
}
}
/*
Local Variables:
mode:c++
c-file-style:"stroustrup"
c-file-offsets:((innamespace . 0)(inline-open . 0)(case-label . +))
indent-tabs-mode:nil
fill-column:99
End:
*/
// vim: filetype=cpp:expandtab:shiftwidth=4:tabstop=8:softtabstop=4:fileencoding=utf-8:textwidth=99 :
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