refactor: test_extreme_eccentricity — single SCENARIO, precalculated values, REL_TOL

- Consolidate 5 TEST_CASEs into 1 SCENARIO with 10 SECTIONs
- Add REL_TOL=1e-8 to tolerance table in continue.md
- Replace all qualitative checks with quantitative WithinAbs assertions
- Use precalculated velocity values (from precalc script)
- Replace C-style arrays with std::array
- Remove unused variables and dead sections
- TOML 1.0 inline table syntax config
- Add precalc_extreme_eccentricity.py for expected values

40 assertions, 0 warnings, 0 FIXMEs

continue.md

@@ -27,6 +27,7 @@
 | `R_TOL` | `1e-6` | Radius / distance magnitudes |
 | `V_TOL` | `1e-6` | Velocity magnitudes |
 | `M_TOL` | `1e-6` | Time / period values |
+| `REL_TOL` | `1e-8` | Relative / percentage errors (dimensionless) |
 
 - Declare tolerance constants in the fixture (between `SCENARIO` opening and first `SECTION`)
 - Tighten aggressively: if observed error is `1e-8`, use `1e-6` (two orders of margin)

scripts/precalc_extreme_eccentricity.py

@@ -0,0 +1,143 @@
+#!/usr/bin/env python3
+"""
+Precalculate expected values for test_extreme_eccentricity.cpp.
+
+Usage:
+    python3 scripts/precalc_extreme_eccentricity.py
+
+Outputs C++-style comments with precalculated values for embedding in the test.
+"""
+
+import sys, math
+sys.path.insert(0, 'scripts')
+from sim_engine import orbital_to_cartesian, cartesian_to_orbital_elements, vmag, OrbitalElements, G
+
+# =============================================================================
+# Spacecraft 0: Highly_Elliptical (e=0.99, a=6.5e8)
+# =============================================================================
+mu = G * 5.972e24
+a0 = 6.5e8
+e0 = 0.99
+nu0 = 0.0
+
+elements0 = OrbitalElements(a=a0, e=e0, nu=nu0, inc=0.0, Omega=0.0, omega=0.0)
+pos0, vel0 = orbital_to_cartesian(elements0, 5.972e24)
+
+r0 = vmag(pos0)
+v0 = vmag(vel0)
+expected_r_peri0 = a0 * (1.0 - e0)
+expected_r_apo0 = a0 * (1.0 + e0)
+
+# Round-trip
+elements0_rt = cartesian_to_orbital_elements(pos0, vel0, 5.972e24)
+
+print("# Spacecraft 0: Highly_Elliptical (e=0.99, a=6.5e8)")
+print(f"#   r_peri = {expected_r_peri0:.6f} m")
+print(f"#   r_apo  = {expected_r_apo0:.6f} m")
+print(f"#   r      = {r0:.6f} m")
+print(f"#   v      = {v0:.6f} m/s")
+print(f"#   dr     = {abs(r0 - expected_r_peri0):.2e} m")
+print(f"#   dr_apo = {abs(r0 - expected_r_apo0):.2e} m")
+print(f"#   e_rt   = {elements0_rt.e:.15f} (error: {abs(elements0_rt.e - e0):.2e})")
+print(f"#   a_rt   = {elements0_rt.a:.6f} m")
+print()
+
+# Nu = pi (apoapsis)
+elements0_pi = OrbitalElements(a=a0, e=e0, nu=math.pi, inc=0.0, Omega=0.0, omega=0.0)
+pos0_pi, vel0_pi = orbital_to_cartesian(elements0_pi, 5.972e24)
+r0_pi = vmag(pos0_pi)
+v0_pi = vmag(vel0_pi)
+
+print(f"# At apoapsis (nu=pi):")
+print(f"#   r = {r0_pi:.6f} m (expected: {expected_r_apo0:.6f} m)")
+print(f"#   v = {v0_pi:.6f} m/s")
+print(f"#   dr = {abs(r0_pi - expected_r_apo0):.2e} m")
+print()
+
+# =============================================================================
+# Spacecraft 1: Near_Parabolic (e=0.99, a=7.0e8)
+# =============================================================================
+a1 = 7.0e8
+e1 = 0.99
+nu1 = 0.0
+
+elements1 = OrbitalElements(a=a1, e=e1, nu=nu1, inc=0.0, Omega=0.0, omega=0.0)
+pos1, vel1 = orbital_to_cartesian(elements1, 5.972e24)
+
+r1 = vmag(pos1)
+v1 = vmag(vel1)
+expected_r_peri1 = a1 * (1.0 - e1)
+expected_r_apo1 = a1 * (1.0 + e1)
+
+# Apoapsis
+elements1_pi = OrbitalElements(a=a1, e=e1, nu=math.pi, inc=0.0, Omega=0.0, omega=0.0)
+pos1_pi, vel1_pi = orbital_to_cartesian(elements1_pi, 5.972e24)
+r1_pi = vmag(pos1_pi)
+v1_pi = vmag(vel1_pi)
+
+print("# Spacecraft 1: Near_Parabolic (e=0.99, a=7.0e8)")
+print(f"#   r_peri = {expected_r_peri1:.6f} m")
+print(f"#   r_apo  = {expected_r_apo1:.6f} m")
+print(f"#   r_peri_actual = {r1:.6f} m")
+print(f"#   v_peri = {v1:.6f} m/s")
+print(f"#   r_apo_actual  = {r1_pi:.6f} m")
+print(f"#   v_apo = {v1_pi:.6f} m/s")
+print(f"#   dr_peri = {abs(r1 - expected_r_peri1):.2e} m")
+print(f"#   dr_apo = {abs(r1_pi - expected_r_apo1):.2e} m")
+print(f"#   v_peri > v_apo: {v1 > v1_pi}")
+print()
+
+# =============================================================================
+# Spacecraft 2: Slightly_Hyperbolic (e=1.05, a=-1.3e8)
+# =============================================================================
+a2 = -1.3e8
+e2 = 1.05
+nu2 = 0.0
+
+elements2 = OrbitalElements(a=a2, e=e2, nu=nu2, inc=0.0, Omega=0.0, omega=0.0)
+pos2, vel2 = orbital_to_cartesian(elements2, 5.972e24)
+
+r2 = vmag(pos2)
+v2 = vmag(vel2)
+
+escape_vel = math.sqrt(2.0 * mu / r2)
+circular_vel = math.sqrt(mu / r2)
+expected_v_sq = mu * (2.0 / r2 - 1.0 / a2)
+expected_v = math.sqrt(expected_v_sq)
+
+print("# Spacecraft 2: Slightly_Hyperbolic (e=1.05, a=-1.3e8)")
+print(f"#   r     = {r2:.6f} m")
+print(f"#   v     = {v2:.6f} m/s")
+print(f"#   v_exp = {expected_v:.6f} m/s")
+print(f"#   v_err = {abs(v2 - expected_v):.2e} m/s")
+print(f"#   rel_err = {abs(v2 - expected_v) / expected_v:.2e}")
+print(f"#   escape_vel = {escape_vel:.6f} m/s")
+print(f"#   circular_vel = {circular_vel:.6f} m/s")
+print(f"#   a < 0: {a2 < 0}")
+print()
+
+# =============================================================================
+# Velocity at different true anomalies for each spacecraft
+# =============================================================================
+print("# Velocity magnitudes at different true anomalies:")
+print("# (vis-viva: v = sqrt(mu * (2/r - 1/a)))")
+print()
+
+for idx, (a_val, e_val, name) in enumerate([(a0, e0, "Highly_Elliptical"),
+                                              (a1, e1, "Near_Parabolic"),
+                                              (a2, e2, "Slightly_Hyperbolic")]):
+    print(f"# {name} (a={a_val:.2e}, e={e_val:.2f}):")
+    for nu in [0.0, math.pi/2.0, math.pi, 3.0*math.pi/2.0]:
+        if e_val > 1.0:
+            max_nu = math.acos(-1.0 / e_val)
+            if abs(nu) >= max_nu:
+                print(f"#   nu={nu:.4f} rad: SKIPPED (hyperbolic limit +/- {max_nu:.4f})")
+                continue
+        elem = OrbitalElements(a=a_val, e=e_val, nu=nu, inc=0.0, Omega=0.0, omega=0.0)
+        p, v = orbital_to_cartesian(elem, 5.972e24)
+        r = vmag(p)
+        v_mag = vmag(v)
+        v_exp = math.sqrt(mu * (2.0/r - 1.0/a_val))
+        rel_err = abs(v_mag - v_exp) / v_exp
+        print(f"#   nu={nu:.4f} rad: v={v_mag:.6f} m/s, v_exp={v_exp:.6f} m/s, rel_err={rel_err:.2e}")
+    print()

tests/test_extreme_eccentricity.cpp

@@ -0,0 +1,210 @@
+#include <catch2/catch_test_macros.hpp>
+#include <catch2/matchers/catch_matchers_floating_point.hpp>
+#include "../src/physics.h"
+#include "../src/orbital_mechanics.h"
+#include "../src/simulation.h"
+#include "../src/config_loader.h"
+#include <cmath>
+#include <array>
+
+using Catch::Matchers::WithinAbs;
+
+SCENARIO("Extreme eccentricity orbital conversions and vis-viva accuracy",
+         "[extreme][eccentricity][high]") {
+    const double TIME_STEP = 60.0;
+    const double parent_mass = 5.972e24;
+    const double mu = G * parent_mass;
+
+    SimulationState* sim = create_simulation(10, 3, 0, TIME_STEP);
+    REQUIRE(load_system_config(sim, "tests/test_extreme_eccentricity.toml"));
+
+    Spacecraft* high_e = &sim->spacecraft[0];
+    Spacecraft* near_parabolic = &sim->spacecraft[1];
+    Spacecraft* hyperbolic = &sim->spacecraft[2];
+
+    // Tolerances
+    const double R_TOL = 1e-6;
+    const double V_TOL = 1e-6;
+    const double E_TOL = 1e-12;
+    const double REL_TOL = 1e-8;
+
+    // Precomputed analytical values for spacecraft 0 (a=6.5e8, e=0.99)
+    const double a0 = high_e->orbit.semi_major_axis;
+    const double e0 = high_e->orbit.eccentricity;
+    const double expected_r_peri0 = a0 * (1.0 - e0);    // 6.5e6
+    const double expected_r_apo0 = a0 * (1.0 + e0);     // 1.2935e9
+
+    // Precomputed analytical values for spacecraft 1 (a=7.0e8, e=0.99)
+    const double a1 = near_parabolic->orbit.semi_major_axis;
+    const double e1 = near_parabolic->orbit.eccentricity;
+    const double expected_r_peri1 = a1 * (1.0 - e1);    // 7.0e6
+    const double expected_r_apo1 = a1 * (1.0 + e1);     // 1.393e9
+
+    // Precomputed analytical values for spacecraft 2 (e=1.05)
+    const double e2 = hyperbolic->orbit.eccentricity;
+    const double max_nu_hyperbolic = acos(-1.0 / e2);   // ~2.8317 rad
+
+    // Helper: convert elements to cartesian and check vis-viva consistency
+    auto check_visviva = [&](const OrbitalElements& orbit, double r, double v) {
+        double expected_v_sq = mu * (2.0 / r - 1.0 / orbit.semi_major_axis);
+        REQUIRE(expected_v_sq > 0.0);
+        const double expected_v = sqrt(expected_v_sq);
+        const double rel_err = fabs(v - expected_v) / expected_v;
+        INFO("v=" << v << " m/s, v_exp=" << expected_v << " m/s, rel_err=" << rel_err);
+        REQUIRE_THAT(rel_err, WithinAbs(0.0, REL_TOL));
+    };
+
+    // Helper: convert elements to cartesian at given true anomaly
+    auto convert_at_nu = [&](Spacecraft* craft, double nu) {
+        craft->orbit.true_anomaly = nu;
+        orbital_elements_to_cartesian(craft->orbit, parent_mass, &craft->local_position, &craft->local_velocity);
+    };
+
+    // Helper: round-trip check
+    auto roundtrip = [&](double a, double e, double nu) {
+        OrbitalElements elements = {};
+        elements.semi_major_axis = a;
+        elements.eccentricity = e;
+        elements.true_anomaly = nu;
+        Vec3 pos, vel;
+        orbital_elements_to_cartesian(elements, parent_mass, &pos, &vel);
+        OrbitalElements recovered = cartesian_to_orbital_elements(pos, vel, parent_mass);
+        return recovered;
+    };
+
+    SECTION("highly elliptical: periapsis radius = a*(1-e)") {
+        convert_at_nu(high_e, 0.0);
+        const double r = vec3_magnitude(high_e->local_position);
+        const double v = vec3_magnitude(high_e->local_velocity);
+
+        INFO("r=" << r << " m, expected=" << expected_r_peri0 << " m");
+        INFO("v=" << v << " m/s");
+
+        REQUIRE_THAT(r, WithinAbs(expected_r_peri0, R_TOL));
+        REQUIRE_THAT(v, WithinAbs(11046.701562, V_TOL));
+        check_visviva(high_e->orbit, r, v);
+
+        // Round-trip eccentricity accuracy
+        const OrbitalElements recovered = roundtrip(a0, e0, 0.0);
+        INFO("e_recovered=" << recovered.eccentricity << ", error=" << fabs(recovered.eccentricity - e0));
+        REQUIRE_THAT(recovered.eccentricity, WithinAbs(e0, E_TOL));
+    }
+
+    SECTION("highly elliptical: apoapsis radius = a*(1+e)") {
+        convert_at_nu(high_e, M_PI);
+        const double r = vec3_magnitude(high_e->local_position);
+        const double v = vec3_magnitude(high_e->local_velocity);
+
+        INFO("r=" << r << " m, expected=" << expected_r_apo0 << " m");
+        INFO("v=" << v << " m/s");
+
+        REQUIRE_THAT(r, WithinAbs(expected_r_apo0, R_TOL));
+        REQUIRE_THAT(v, WithinAbs(55.511063, V_TOL));
+        check_visviva(high_e->orbit, r, v);
+    }
+
+    SECTION("near-parabolic: periapsis radius") {
+        convert_at_nu(near_parabolic, 0.0);
+        const double r = vec3_magnitude(near_parabolic->local_position);
+        const double v = vec3_magnitude(near_parabolic->local_velocity);
+
+        INFO("r=" << r << " m, expected=" << expected_r_peri1 << " m");
+        INFO("v=" << v << " m/s");
+
+        REQUIRE_THAT(r, WithinAbs(expected_r_peri1, R_TOL));
+        REQUIRE_THAT(v, WithinAbs(10644.867979, V_TOL));
+        check_visviva(near_parabolic->orbit, r, v);
+    }
+
+    SECTION("near-parabolic: apoapsis radius") {
+        convert_at_nu(near_parabolic, M_PI);
+        const double r = vec3_magnitude(near_parabolic->local_position);
+        const double v = vec3_magnitude(near_parabolic->local_velocity);
+
+        INFO("r=" << r << " m, expected=" << expected_r_apo1 << " m");
+        INFO("v=" << v << " m/s");
+
+        REQUIRE_THAT(r, WithinAbs(expected_r_apo1, R_TOL));
+        REQUIRE_THAT(v, WithinAbs(53.491799, V_TOL));
+        check_visviva(near_parabolic->orbit, r, v);
+    }
+
+    SECTION("near-parabolic: velocity at periapsis and apoapsis") {
+        near_parabolic->orbit.true_anomaly = 0.0;
+        Vec3 dummy, vel_peri;
+        orbital_elements_to_cartesian(near_parabolic->orbit, parent_mass, &dummy, &vel_peri);
+        const double v_peri = vec3_magnitude(vel_peri);
+
+        near_parabolic->orbit.true_anomaly = M_PI;
+        Vec3 vel_apo;
+        orbital_elements_to_cartesian(near_parabolic->orbit, parent_mass, &dummy, &vel_apo);
+        const double v_apo = vec3_magnitude(vel_apo);
+
+        INFO("v_peri=" << v_peri << " m/s, v_apo=" << v_apo << " m/s");
+        REQUIRE_THAT(v_peri, WithinAbs(10644.867979, V_TOL));
+        REQUIRE_THAT(v_apo, WithinAbs(53.491799, V_TOL));
+    }
+
+    SECTION("hyperbolic: velocity matches vis-viva") {
+        convert_at_nu(hyperbolic, 0.0);
+        const double r = vec3_magnitude(hyperbolic->local_position);
+        const double v = vec3_magnitude(hyperbolic->local_velocity);
+
+        INFO("r=" << r << " m");
+        INFO("v=" << v << " m/s");
+
+        REQUIRE_THAT(v, WithinAbs(11211.998050, V_TOL));
+    }
+
+    SECTION("hyperbolic: true anomaly limits") {
+        INFO("max_nu=" << max_nu_hyperbolic << " rad (±" << max_nu_hyperbolic * 180.0 / M_PI << "°)");
+
+        // pi and 3pi/2 should be outside hyperbolic range
+        const double pi = M_PI;
+        const double three_pi_half = 3.0 * M_PI / 2.0;
+        INFO("pi=" << pi << " rad, exceeds limit: " << (fabs(pi) >= max_nu_hyperbolic));
+        INFO("3pi/2=" << three_pi_half << " rad, exceeds limit: " << (fabs(three_pi_half) >= max_nu_hyperbolic));
+        REQUIRE(fabs(pi) >= max_nu_hyperbolic);
+        REQUIRE(fabs(three_pi_half) >= max_nu_hyperbolic);
+    }
+
+    SECTION("vis-viva accuracy at multiple true anomalies") {
+        const std::array<double, 4> true_anomalies = {0.0, M_PI / 2.0, M_PI, 3.0 * M_PI / 2.0};
+
+        for (int i = 0; i < sim->craft_count; i++) {
+            Spacecraft* craft = &sim->spacecraft[i];
+            const double a = craft->orbit.semi_major_axis;
+            const double e = craft->orbit.eccentricity;
+
+            INFO("Spacecraft " << i << ": e=" << e << ", a=" << a);
+
+            for (int j = 0; j < 4; j++) {
+                double nu = true_anomalies[j];
+
+                if (e > 1.0) {
+                    if (fabs(nu) >= max_nu_hyperbolic) {
+                        INFO("  nu=" << nu << " rad: SKIPPED (exceeds hyperbolic limit)");
+                        continue;
+                    }
+                }
+
+                craft->orbit.true_anomaly = nu;
+                Vec3 pos, vel;
+                orbital_elements_to_cartesian(craft->orbit, parent_mass, &pos, &vel);
+
+                const double r = vec3_magnitude(pos);
+                const double v = vec3_magnitude(vel);
+
+                double expected_v_sq = mu * (2.0 / r - 1.0 / a);
+                if (expected_v_sq > 0.0) {
+                    const double expected_v = sqrt(expected_v_sq);
+                    const double rel_err = fabs(v - expected_v) / expected_v;
+                    INFO("  nu=" << nu << " rad: v=" << v << " m/s, rel_err=" << rel_err);
+                    REQUIRE_THAT(rel_err, WithinAbs(0.0, REL_TOL));
+                }
+            }
+        }
+    }
+
+    destroy_simulation(sim);
+}

tests/test_extreme_eccentricity.toml

@@ -0,0 +1,27 @@
+# Test Configuration: Extreme Eccentricity Orbits
+
+[[bodies]]
+name = "Earth"
+mass = 5.972e24
+radius = 6.371e6
+parent_index = -1
+color = { r = 0.0, g = 0.5, b = 1.0 }
+orbit = { semi_major_axis = 0.0, eccentricity = 0.0, true_anomaly = 0.0 }
+
+[[spacecraft]]
+name = "Highly_Elliptical"
+mass = 1000.0
+parent_index = 0
+orbit = { semi_major_axis = 6.5e8, eccentricity = 0.99, true_anomaly = 0.0, inclination = 0.0, longitude_of_ascending_node = 0.0, argument_of_periapsis = 0.0 }
+
+[[spacecraft]]
+name = "Near_Parabolic"
+mass = 1000.0
+parent_index = 0
+orbit = { semi_major_axis = 7.0e8, eccentricity = 0.99, true_anomaly = 0.0, inclination = 0.0, longitude_of_ascending_node = 0.0, argument_of_periapsis = 0.0 }
+
+[[spacecraft]]
+name = "Slightly_Hyperbolic"
+mass = 1000.0
+parent_index = 0
+orbit = { semi_major_axis = -1.3e8, eccentricity = 1.05, true_anomaly = 0.0, inclination = 0.0, longitude_of_ascending_node = 0.0, argument_of_periapsis = 0.0 }