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#include <gtest/gtest.h>
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#include "autoopt/quadric.hpp"
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#include <iostream>
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using namespace autoopt;
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TEST(QuadricTest, ParabolaRotation) {
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quadric<double> q(1.0, 0.0, 0.0, 0.0, -1.0, 0.0); // y = x^2
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EXPECT_DOUBLE_EQ(q.at(-1.0), 1.0); // At x=1, y=1
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EXPECT_DOUBLE_EQ(q.at(0.0), 0.0); // At x=0, y=0
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EXPECT_DOUBLE_EQ(q.at(1.0), 1.0); // At x=1, y=1
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double angle = M_PI / 4; // 45 degrees
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quadric<double> q_rotated = q.rotated_by(angle);
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EXPECT_NEAR(q_rotated.at(-1.0), -0.11729096183611623, 1e-9);
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EXPECT_NEAR(q_rotated.at(0.0), 0.0, 1e-9);
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EXPECT_TRUE(std::isnan(q_rotated.at(1.0))); // Expect NaN due to no real solution
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}
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